Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This paper focuses on the design of a chattering free mathematical error-based tuning sliding mode controller (MTSMC) for highly nonlinear dynamic robot manipulator, in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller is selected. Pure sliding mode controller can be used to control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure sliding mode controller is used in many applications; it has an important drawback namely; chattering phenomenon which it can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers. In order to reduce the chattering this research is used the switching function in presence of mathematical error-based method instead of switching function method in pure sliding mode controller. The results demonstrate that the sliding mode controller with switching function is a model-based controllers which works well in certain and partly uncertain system. Pure sliding mode controller has difficulty in handling unstructured model uncertainties. To solve this problem applied mathematical model-free tuning method to sliding mode controller for adjusting the sliding surface gain (ë ). Since the sliding surface gain (ë) is adjusted by mathematical model free-based tuning method, it is nonlinear and continuous. In this research new ë is obtained by the previous ë multiple sliding surface slopes updating factor (á). Chattering free mathematical error-based tuning sliding mode controller is stable controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in mathematical error-based tuning sliding mode controller with switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).
Evaluation Performance of 2nd Order Nonlinear System: Baseline Control Tunabl...Waqas Tariq
Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., internal combustion engine) is one of the most important challenging works. This paper focuses on the comparative study between two important nonlinear controllers namely; computed torque controller (CTC) and sliding mode controller (SMC) and applied to internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure SMC and CTC can be used to control of partly known nonlinear dynamic parameters of IC engine. Pure sliding mode controller and computed torque controller have difficulty in handling unstructured model uncertainties. To solve this problem applied linear error-based tuning method to sliding mode controller and computed torque controller for adjusting the sliding surface gain (ë ) and linear inner loop gain (K). Since the sliding surface gain (ë) and linear inner loop gain (K) are adjusted by linear error-based tuning method. In this research new ë and new K are obtained by the previous ë and K multiple gains updating factor(á). The results demonstrate that the error-based linear SMC and CTC are model-based controllers which works well in certain and uncertain system. These controllers have acceptable performance in presence of uncertainty.
Design Auto Adjust Sliding Surface Slope: Applied to Robot ManipulatorWaqas Tariq
The main target in this paper is to present the nonlinear methods in order to control the robot manipulators and also the related results. Also the important role of sliding surface slope in sliding mode fuzzy control of robot manipulator should be considered. Sliding mode controller (SMC) is a significant nonlinear controller in certain and uncertain dynamic parameters systems. To solve the chattering phenomenon, this paper complicated two methods to each other; boundary layer method and applied fuzzy logic in sliding mode methodology. To remove the chattering sliding surface slope also played important role so this paper focused on the auto tuning this important coefficient to have the best results by applied mathematical model free methodology. Auto tuning methodology has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 s, steady state error = 1e-9 and RMS error=0.0001632).
A New Estimate Sliding Mode Fuzzy Controller for Robotic ManipulatorWaqas Tariq
One of the most active research areas in field of robotics is control of robot manipulator because this system has highly nonlinear dynamic parameters and most of dynamic parameters are unknown so design an acceptable controller is the main goal in this work. To solve this challenge position new estimation sliding mode fuzzy controller is introduced and applied to robot manipulator. This controller can solve to most important challenge in classical sliding mode controller in presence of highly uncertainty, namely; chattering phenomenon based on fuzzy estimator and online tuning and equivalent nonlinear dynamic based on estimation. Proposed method has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 s, steady state error = 1e-9 and RMS error=0.0001632).
Design Novel Lookup Table Changed Auto Tuning FSMC: Applied to Robot ManipulatorCSCJournals
Refer to this paper, design lookup table changed adaptive fuzzy sliding mode controller with minimum rule base and good response in presence of structure and unstructured uncertainty is presented. However sliding mode controller is one of the robust nonlinear controllers but when this controller is applied to robot manipulator with highly nonlinear and uncertain dynamic function; caused to be challenged in control. Sliding mode controller in presence of uncertainty has two most important drawbacks; chattering and nonlinear equivalent part which proposed method is solved these challenges with look up table change methodology. This method is based on self tuning methodology therefore artificial intelligence (e.g., fuzzy logic method) is played important role to design proposed method. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 s, steady state error = 1e-9 and RMS error=0.00017).
Novel Artificial Control of Nonlinear Uncertain System: Design a Novel Modifi...Waqas Tariq
This document presents a novel particle swarm optimization sliding mode control algorithm using fuzzy logic to estimate uncertainties for nonlinear systems like robotic manipulators. The algorithm combines PSO, sliding mode control, and fuzzy logic to address issues like chattering and not requiring an accurate dynamic model. It estimates the equivalent dynamic term using fuzzy logic to compensate for uncertainties. PSO is used to tune parameters offline for improved performance. Stability of the closed-loop system is proved using the Lyapunov method. The algorithm aims to provide robust control of robotic manipulators without an accurate dynamic model.
Evolutionary Design of Mathematical tunable FPGA Based MIMO Fuzzy Estimator S...Waqas Tariq
In this research, a Multi Input Multi Output (MIMO) position Field Programmable Gate Array (FPGA)-based fuzzy estimator sliding mode control (SMC) design with the estimation laws derived in Lyapunov sense and application to robotic manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy inference methodology and Lyapunov based method, the controllers output has improved. The main target in this research is analyses and design of the position MIMO artificial Lyapunov FPGA-based controller for robot manipulator in order to solve uncertainty, external disturbance, nonlinear equivalent part, chattering phenomenon, time to market and controller size using FPGA. Robot manipulators are nonlinear, time variant and a number of parameters are uncertain therefore design robust and stable controller based on Lyapunov based is discussed in this research. Studies about classical sliding mode controller (SMC) show that: although this controller has acceptable performance with known dynamic parameters such as stability and robustness but there are two important disadvantages as below: chattering phenomenon and mathematical nonlinear dynamic equivalent controller part. The first challenge; nonlinear dynamic part; is applied by inference estimator method in sliding mode controller in order to solve the nonlinear problems in classical sliding mode controller. And the second challenge; chattering phenomenon; is removed by linear method. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov. In the last part it can find the implementation of MIMO fuzzy estimator sliding mode controller on FPGA; FPGA-based fuzzy estimator sliding mode controller has many advantages such as high speed, low cost, short time to market and small device size. One of the most important drawbacks is limited capacity of available cells which this research focuses to solve this challenge. FPGA can be used to design a controller in a single chip Integrated Circuit (IC). In this research the SMC is designed using Very High Description Language (VHDL) for implementation on FPGA device (XA3S1600E-Spartan-3E), with minimum chattering.
Design Novel Nonlinear Controller Applied to Robot Manipulator: Design New Fe...Waqas Tariq
This document describes a novel adaptive feedback linearization fuzzy controller for robot manipulators. It begins by discussing limitations of traditional feedback linearization controllers, such as sensitivity to parameter uncertainty. It then proposes designing a feedback linearization fuzzy controller to address this issue. The key steps are: 1) designing the fuzzy controller, including fuzzifying inputs/outputs and developing a rule base, 2) developing an adaptive feedback linearization fuzzy controller by adding an adaptive law to tune fuzzy rule parameters online and improve disturbance rejection. The goal is to develop a robust position controller for robot manipulators that maintains acceptable performance despite nonlinearities and uncertainty.
Design Artificial Nonlinear Robust Controller Based on CTLC and FSMC with Tun...Waqas Tariq
The document describes research on designing artificial nonlinear robust controllers for robot manipulators. It discusses two classical nonlinear robust controllers - sliding mode controller (SMC) and computed torque controller (CTC) - and their limitations when applied to systems with uncertainties. It then proposes applying fuzzy logic methodology to these classical controllers to reduce their limitations. Specifically, it develops a fuzzy sliding mode controller with tunable gain (GTFSMC) and a computed torque-like controller with tunable gain (GTCTLC) that use fuzzy logic rules to eliminate the mathematical nonlinear dynamics and reduce chattering through optimization of the tunable gain parameter. The controllers aim to achieve satisfactory performance for robot manipulators operating in unknown environments with uncertainties and disturbances.
Evaluation Performance of 2nd Order Nonlinear System: Baseline Control Tunabl...Waqas Tariq
Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., internal combustion engine) is one of the most important challenging works. This paper focuses on the comparative study between two important nonlinear controllers namely; computed torque controller (CTC) and sliding mode controller (SMC) and applied to internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure SMC and CTC can be used to control of partly known nonlinear dynamic parameters of IC engine. Pure sliding mode controller and computed torque controller have difficulty in handling unstructured model uncertainties. To solve this problem applied linear error-based tuning method to sliding mode controller and computed torque controller for adjusting the sliding surface gain (ë ) and linear inner loop gain (K). Since the sliding surface gain (ë) and linear inner loop gain (K) are adjusted by linear error-based tuning method. In this research new ë and new K are obtained by the previous ë and K multiple gains updating factor(á). The results demonstrate that the error-based linear SMC and CTC are model-based controllers which works well in certain and uncertain system. These controllers have acceptable performance in presence of uncertainty.
Design Auto Adjust Sliding Surface Slope: Applied to Robot ManipulatorWaqas Tariq
The main target in this paper is to present the nonlinear methods in order to control the robot manipulators and also the related results. Also the important role of sliding surface slope in sliding mode fuzzy control of robot manipulator should be considered. Sliding mode controller (SMC) is a significant nonlinear controller in certain and uncertain dynamic parameters systems. To solve the chattering phenomenon, this paper complicated two methods to each other; boundary layer method and applied fuzzy logic in sliding mode methodology. To remove the chattering sliding surface slope also played important role so this paper focused on the auto tuning this important coefficient to have the best results by applied mathematical model free methodology. Auto tuning methodology has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 s, steady state error = 1e-9 and RMS error=0.0001632).
A New Estimate Sliding Mode Fuzzy Controller for Robotic ManipulatorWaqas Tariq
One of the most active research areas in field of robotics is control of robot manipulator because this system has highly nonlinear dynamic parameters and most of dynamic parameters are unknown so design an acceptable controller is the main goal in this work. To solve this challenge position new estimation sliding mode fuzzy controller is introduced and applied to robot manipulator. This controller can solve to most important challenge in classical sliding mode controller in presence of highly uncertainty, namely; chattering phenomenon based on fuzzy estimator and online tuning and equivalent nonlinear dynamic based on estimation. Proposed method has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 s, steady state error = 1e-9 and RMS error=0.0001632).
Design Novel Lookup Table Changed Auto Tuning FSMC: Applied to Robot ManipulatorCSCJournals
Refer to this paper, design lookup table changed adaptive fuzzy sliding mode controller with minimum rule base and good response in presence of structure and unstructured uncertainty is presented. However sliding mode controller is one of the robust nonlinear controllers but when this controller is applied to robot manipulator with highly nonlinear and uncertain dynamic function; caused to be challenged in control. Sliding mode controller in presence of uncertainty has two most important drawbacks; chattering and nonlinear equivalent part which proposed method is solved these challenges with look up table change methodology. This method is based on self tuning methodology therefore artificial intelligence (e.g., fuzzy logic method) is played important role to design proposed method. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 s, steady state error = 1e-9 and RMS error=0.00017).
Novel Artificial Control of Nonlinear Uncertain System: Design a Novel Modifi...Waqas Tariq
This document presents a novel particle swarm optimization sliding mode control algorithm using fuzzy logic to estimate uncertainties for nonlinear systems like robotic manipulators. The algorithm combines PSO, sliding mode control, and fuzzy logic to address issues like chattering and not requiring an accurate dynamic model. It estimates the equivalent dynamic term using fuzzy logic to compensate for uncertainties. PSO is used to tune parameters offline for improved performance. Stability of the closed-loop system is proved using the Lyapunov method. The algorithm aims to provide robust control of robotic manipulators without an accurate dynamic model.
Evolutionary Design of Mathematical tunable FPGA Based MIMO Fuzzy Estimator S...Waqas Tariq
In this research, a Multi Input Multi Output (MIMO) position Field Programmable Gate Array (FPGA)-based fuzzy estimator sliding mode control (SMC) design with the estimation laws derived in Lyapunov sense and application to robotic manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy inference methodology and Lyapunov based method, the controllers output has improved. The main target in this research is analyses and design of the position MIMO artificial Lyapunov FPGA-based controller for robot manipulator in order to solve uncertainty, external disturbance, nonlinear equivalent part, chattering phenomenon, time to market and controller size using FPGA. Robot manipulators are nonlinear, time variant and a number of parameters are uncertain therefore design robust and stable controller based on Lyapunov based is discussed in this research. Studies about classical sliding mode controller (SMC) show that: although this controller has acceptable performance with known dynamic parameters such as stability and robustness but there are two important disadvantages as below: chattering phenomenon and mathematical nonlinear dynamic equivalent controller part. The first challenge; nonlinear dynamic part; is applied by inference estimator method in sliding mode controller in order to solve the nonlinear problems in classical sliding mode controller. And the second challenge; chattering phenomenon; is removed by linear method. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov. In the last part it can find the implementation of MIMO fuzzy estimator sliding mode controller on FPGA; FPGA-based fuzzy estimator sliding mode controller has many advantages such as high speed, low cost, short time to market and small device size. One of the most important drawbacks is limited capacity of available cells which this research focuses to solve this challenge. FPGA can be used to design a controller in a single chip Integrated Circuit (IC). In this research the SMC is designed using Very High Description Language (VHDL) for implementation on FPGA device (XA3S1600E-Spartan-3E), with minimum chattering.
Design Novel Nonlinear Controller Applied to Robot Manipulator: Design New Fe...Waqas Tariq
This document describes a novel adaptive feedback linearization fuzzy controller for robot manipulators. It begins by discussing limitations of traditional feedback linearization controllers, such as sensitivity to parameter uncertainty. It then proposes designing a feedback linearization fuzzy controller to address this issue. The key steps are: 1) designing the fuzzy controller, including fuzzifying inputs/outputs and developing a rule base, 2) developing an adaptive feedback linearization fuzzy controller by adding an adaptive law to tune fuzzy rule parameters online and improve disturbance rejection. The goal is to develop a robust position controller for robot manipulators that maintains acceptable performance despite nonlinearities and uncertainty.
Design Artificial Nonlinear Robust Controller Based on CTLC and FSMC with Tun...Waqas Tariq
The document describes research on designing artificial nonlinear robust controllers for robot manipulators. It discusses two classical nonlinear robust controllers - sliding mode controller (SMC) and computed torque controller (CTC) - and their limitations when applied to systems with uncertainties. It then proposes applying fuzzy logic methodology to these classical controllers to reduce their limitations. Specifically, it develops a fuzzy sliding mode controller with tunable gain (GTFSMC) and a computed torque-like controller with tunable gain (GTCTLC) that use fuzzy logic rules to eliminate the mathematical nonlinear dynamics and reduce chattering through optimization of the tunable gain parameter. The controllers aim to achieve satisfactory performance for robot manipulators operating in unknown environments with uncertainties and disturbances.
Refer to the research, design a novel SISO adaptive fuzzy sliding algorithm inverse dynamic like method (NAIDLC) and application to robot manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in inverse dynamic controller, fuzzy logic controller and self tuning fuzzy sliding method, the output has improved. The main objective in this research is analyses and design of the adaptive robust controller based on artificial intelligence and nonlinear control. Robot manipulator is nonlinear, time variant and a number of parameters are uncertain, so design the best controller for this plant is the main target. Although inverse dynamic controller have acceptable performance with known dynamic parameters but regarding to uncertainty, this controller\'s output has fairly fluctuations. In order to solve this problem this research is focoused on two methodology the first one is design a fuzzy inference system as a estimate nonlinear part of main controller but this method caused to high computation load in fuzzy rule base and the second method is focused on design novel adaptive method to reduce the computation in fuzzy algorithm.
In this research, a model free sliding mode fuzzy adaptive inverse dynamic fuzzy controller (SMFIDFC) is designed for a robot manipulator to rich the best performance. Inverse dynamic controller is considered because of its high performance in certain system. Fuzzy methodology has been included in inverse dynamic to keep away from design nonlinear controller based on dynamic model. Sliding mode fuzzy adaptive methodology is applied to model free controller to have better result in presence of structure and unstructured uncertainties. Besides, this control method can be applied to non-linear systems easily. Today, strong mathematical tools are used in new control methodologies to design adaptive nonlinear controller with satisfactory output results (e.g., minimum error, good trajectory, disturbance rejection).
Evolutionary Design of Backstepping Artificial Sliding Mode Based Position Al...CSCJournals
This paper expands a fuzzy sliding mode based position controller whose sliding function is on-line tuned by backstepping methodology. The main goal is to guarantee acceptable position trajectories tracking between the robot manipulator end-effector and the input desired position. The fuzzy controller in proposed fuzzy sliding mode controller is based on Mamdani’s fuzzy inference system (FIS) and it has one input and one output. The input represents the function between sliding function, error and the rate of error. The second input is the angle formed by the straight line defined with the orientation of the robot, and the straight line that connects the robot with the reference cart. The outputs represent angular position, velocity and acceleration commands, respectively. The backstepping methodology is on-line tune the sliding function based on self tuning methodology. The performance of the backstepping on-line tune fuzzy sliding mode controller (TBsFSMC) is validated through comparison with previously developed robot manipulator position controller based on adaptive fuzzy sliding mode control theory (AFSMC). Simulation results signify good performance of position tracking in presence of uncertainty and external disturbance.
Design Error-based Linear Model-free Evaluation Performance Computed Torque C...Waqas Tariq
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This research focuses on the design, implementation and analysis of a model-free linear error-based tuning computed torque controller for highly nonlinear dynamic second order system, in presence of uncertainties. In order to provide high performance nonlinear methodology, computed torque controller is selected. Pure computed torque controller can be used to control of partly known nonlinear dynamic parameters of nonlinear systems. Conversely, pure computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, model-free performance/error-based linear methodology with three inputs and one output is applied to pure computed torque controller. The results demonstrate that the error-based linear tuning computed torque controller is a model-based controllers which works well in certain and uncertain system. Pure computed torque controller has difficulty in handling unstructured model uncertainties. To solve this problem applied linear model-free error -based tuning method to computed torque controller for adjusting the linear inner loop gain (K ). Since the linear inner loop gain (K) is adjusted by linear error-based tuning method, it is linear and continuous. In this research new K is obtained by the previous K multiple gain updating factor (á) which is a coefficient varies between half to two.
The developed control methodology can be used to build more efficient intelligent and precision mechatronic systems. Three degrees of freedom robot arm is controlled by adaptive sliding mode fuzzy algorithm fuzzy sliding mode controller (SMFAFSMC). This plant has 3 revolute joints allowing the corresponding links to move horizontally. Control of robotic manipulator is very important in field of robotic, because robotic manipulators are Multi-Input Multi-Output (MIMO), nonlinear and most of dynamic parameters are uncertainty. Design strong mathematical tools used in new control methodologies to design adaptive nonlinear robust controller with acceptable performance in this controller is the main challenge. Sliding mode methodology is a nonlinear robust controller which can be used in uncertainty nonlinear systems, but pure sliding mode controller has chattering phenomenon and nonlinear equivalent part in uncertain system therefore the first step is focused on eliminate the chattering and in second step controller is improved with regard to uncertainties. Sliding function is one of the most important challenging in artificial sliding mode algorithm which this problem in order to solved by on-line tuning method. This paper focuses on adjusting the sliding surface slope in fuzzy sliding mode controller by sliding mode fuzzy algorithm.
Artificial Chattering Free on-line Fuzzy Sliding Mode Algorithm for Uncertain...CSCJournals
This document proposes an artificial chattering free adaptive fuzzy sliding mode control algorithm for uncertain systems, specifically applied to robot manipulators. The algorithm combines sliding mode control, fuzzy logic control, and adaptive methods to address some limitations of each approach. Specifically, fuzzy logic is used instead of saturation functions and dead zones to eliminate chattering. Fuzzy rules are also used to estimate the nonlinear dynamic equivalent control term, reducing complexity. Adaptive methods are used to continuously adjust the sliding function in real-time for improved performance with uncertain or time-varying parameters. The algorithm is tested in simulations of a PUMA robot manipulator.
Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., Internal Combustion Engine) is one of the most important challenging works. This paper focuses on the design of a robust backstepping adaptive feedback linearization controller (FLC) for internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, feedback linearization controller is selected. Pure feedback linearization controller can be used to control of partly unknown nonlinear dynamic parameters of IC engine. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure feedback linearization controller. The results demonstrate that the error-based fuzzy feedback linearization controller is a model-free controllers which works well in certain and partly uncertain system. Pure feedback linearization controller and error-based feedback linearization like controller with have difficulty in handling unstructured model uncertainties. To solve this problem applied backstepping-based tuning method to error-based fuzzy feedback linearization controller for adjusting the feedback linearization controller gain (K_p,K_v ). This controller has acceptable performance in presence of uncertainty (e.g., overshoot=1%, rise time=0.48 second, steady state error = 1.3e-9 and RMS error=1.8e-11).
Adaptive MIMO Fuzzy Compensate Fuzzy Sliding Mode Algorithm: Applied to Secon...CSCJournals
This research is focused on proposed adaptive fuzzy sliding mode algorithms with the adaptation laws derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Adaptive MIMO fuzzy compensate fuzzy sliding mode method design a MIMO fuzzy system to compensate for the model uncertainties of the system, and chattering also solved by linear saturation method. Since there is no tuning method to adjust the premise part of fuzzy rules so we presented a scheme to online tune consequence part of fuzzy rules. Classical sliding mode control is robust to control model uncertainties and external disturbances. A sliding mode method with a switching control low guarantees the stability of the certain and/or uncertain system, but the addition of the switching control low introduces chattering into the system. One way to reduce or eliminate chattering is to insert a boundary layer method inside of a boundary layer around the sliding surface. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov.
Position Control of Robot Manipulator: Design a Novel SISO Adaptive Sliding M...Waqas Tariq
The document describes a novel adaptive sliding mode fuzzy PD fuzzy sliding mode control algorithm for position control of robot manipulators. The algorithm uses a single-input single-output fuzzy system to compensate for model uncertainties and eliminate chattering using a linear boundary layer method. It also online tunes the sliding function parameter using adaptation laws. The stability of the closed-loop system is proved mathematically using Lyapunov stability theory. The algorithm is analyzed and evaluated on a 2 degree of freedom robotic manipulator to achieve improved tracking performance compared to conventional sliding mode control approaches.
Digital Implementation of Fuzzy Logic Controller for Real Time Position Contr...IOSR Journals
Fuzzy Logic Controller (FLC) systems have emerged as one of the most promising areas for
Industrial Applications. The highly growth of fuzzy logic applications led to the need of finding efficient way to
hardware implementation. Field Programmable Gate Array (FPGA) is the most important tool for hardware
implementation due to low consumption of energy, high speed of operation and large capacity of data storage.
In this paper, instead of an introduction to fuzzy logic control methodology, we have demonstrated the
implementation of a FLC through the use of the Very high speed integrated circuits Hardware Description
Language (VHDL) code. FLC is designed for position control of BLDC Motor. VHDL has been used to develop
FLC on FPGA. A Mamdani type FLC structure has been used to obtain the controller output. The controller
algorithm developed synthesized, simulated and implemented on FPGA Spartan 3E board.
Sliding Mode Methodology Vs. Computed Torque Methodology Using MATLAB/SIMULIN...CSCJournals
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This paper focuses on the design, implementation and analysis of a chattering free sliding mode controller for highly nonlinear dynamic PUMA robot manipulator and compare to computed torque controller, in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure sliding mode controller and computed torque controller can be used to control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure sliding mode controller is used in many applications; it has an important drawback namely; chattering phenomenon which it can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers. In order to reduce the chattering this research is used the linear saturation function boundary layer method instead of switching function method in pure sliding mode controller. These simulation models are developed as a part of a software laboratory to support and enhance graduate/undergraduate robotics courses, nonlinear control courses and MATLAB/SIMULINK courses at research and development company (SSP Co.) research center, Shiraz, Iran.
IRJET- A Performance of Hybrid Control in Nonlinear Dynamic Multirotor UAVIRJET Journal
This document summarizes a research paper that models and evaluates control techniques for multirotor unmanned aerial vehicles (UAVs). It begins with an abstract that outlines the paper's contributions: developing an accurate mathematical model of a multirotor UAV using Newton-Euler dynamics, developing nonlinear control algorithms based on this model, and comparing the performance of backstepping control, sliding mode control, and fuzzy logic control through simulation. The document then provides details of the multirotor dynamic model and each control approach, evaluating their ability to stabilize the system and reject disturbances. It concludes that hybrid control systems combining advantages of different methods should be considered.
TORQUE CONTROL OF AC MOTOR WITH FOPID CONTROLLER BASED ON FUZZY NEURAL ALGORITHMijics
Nowadays in the complicated systems, design of proper and implementable controller has a most importance. With respect to ability of fractional order systems in complicated systems identification as a first order fractional system with time delay, usage of fractional order PID has a proper result. From one side flexibility of fractional calculus than integer order has been topics of interest to the researchers. From another side, PMSM motors which are one the AC motor types, has been allocated largely accounted position in industry and used in variety applications. Therefore in this paper torque direct control of PMSM motors with FOPID based on model is proposed. Also fuzzy neural controllers are widely considered. Reason of this is success of fuzzy neural controller in control and identification of uncertain and complicated systems. The proposed method in this paper is combination of FOPID controller with fuzzy neural supervision system which with coefficients setting of this controller, control operation of PMSM will improve. Results of proposed method show the ability of proposed technique in reference signal tracking, elimination of disturbances effects and functional robustness in presence of noise and uncertainty. The results show the error averagely in three condition, nominal form, step disturbance and noise and uncertainly will decrease 11.66% in proposed method (FNFOPID) with Integral Square Error criterion and 7.69% with Integral Absolute Error criterion in comparison to FOPID.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Simulation of Linear Induction Motor Using Sliding Mode Controller TechniqueIJMERJOURNAL
ABSTRACT:In the present paper, the mover speed control of a linear induction motor (LIM) using a sliding mode control design is proposed. First, the indirect field-oriented control LIM is derived. The sliding mode control design is then investigated to achieve speed- and flux-tracking under load thrust force disturbance. The numerical simulation results of the proposed scheme present good performances in comparison to that of the classical sliding mode control.In the present paper, a sliding mode controller based onindirect field orientation is proposed for LIM speed controlwhile considering end effects. The proposed controller isapplied to achieve a speed- and flux-tracking objectiveunder parameter uncertainties and disturbance of loadthrust force.
The document discusses control systems for robot manipulators. It covers open-loop and closed-loop control systems, with closed-loop being preferred using feedback. It describes using linear control techniques to approximate manipulator dynamics and designing controllers to meet stability and performance specifications. Common control techniques for manipulators are also summarized like PD, PID, state space control and adaptive/intelligent methods.
Design of Model Free Adaptive Fuzzy Computed Torque Controller for a Nonlinea...Waqas Tariq
In this study, a model free adaptive fuzzy computed torque controller (AFCTC) is designed for a two-degree-of freedom robot manipulator to rich the best performance. Computed torque controller is studied because of its high performance. AFCTC has been also included in this study because of its robust character and high performance. Besides, this control method can be applied to non-linear systems easily. Today, robot manipulators are used in unknown and unstructured environment and caused to provide sophisticated systems, therefore strong mathematical tools are used in new control methodologies to design adaptive nonlinear robust controller with acceptable performance (e.g., minimum error, good trajectory, disturbance rejection). The strategies of control robot manipulator are classified into two main groups: classical and non-classical methods, however both classical and non-classical theories have been applied successfully in many applications, but they also have some limitation. One of the most important nonlinear robust controller that can used in uncertainty nonlinear systems, are computed torque controller. This paper is focuses on applied non-classical method in robust classical method to reduce the limitations. Therefore adaptive fuzzy computed torque controller will be presented in this paper.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document discusses industrial robots including their definition, components, motions, configurations, and applications. It describes that a robot is a re-programmable manipulator designed to move parts and tools for various tasks. The key components are the manipulator, end effector, power supply, and control system. Common robot configurations include Cartesian, cylindrical, SCARA, and jointed arm. Industrial robots are widely used for automation in various industries.
This document summarizes investigations into a fuzzy logic controller for a sensorless switched reluctance motor drive. It begins by introducing switched reluctance motors and their nonlinear characteristics. It then describes designing a fuzzy logic controller to estimate rotor position with minimum steady state error and good dynamic response. The controller implementation and numerical simulation results using Matlab/Simulink are presented. Simulation results at different speeds and loads demonstrate the controller's steady state performance and ability to respond robustly under different conditions. The conclusions are that the fuzzy logic controller enables effective operation of the switched reluctance motor drive with only small errors in all tested scenarios.
This paper examines the stability of sliding mode control for underactuated nonlinear systems. It presents sliding mode control design for a class of underactuated systems using a switching control law. It then analyzes the stability of the closed-loop reaching phase and sliding phase dynamics. As an example, it applies this analysis to the stability of an inverted pendulum controlled via sliding mode control.
The document presents a sliding mode control algorithm and adaptive nonlinear observer for regulating wheel slip in anti-lock braking systems for commercial vehicles. Simulation results using an ADAMS vehicle model show the new control approach can achieve a stopping distance of 54 meters from 60 mph, satisfying new regulations requiring shorter stopping distances. The algorithm holds tire slip near its peak to maximize braking force, and the observer estimates brake forces using a LuGre tire friction model.
Refer to the research, design a novel SISO adaptive fuzzy sliding algorithm inverse dynamic like method (NAIDLC) and application to robot manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in inverse dynamic controller, fuzzy logic controller and self tuning fuzzy sliding method, the output has improved. The main objective in this research is analyses and design of the adaptive robust controller based on artificial intelligence and nonlinear control. Robot manipulator is nonlinear, time variant and a number of parameters are uncertain, so design the best controller for this plant is the main target. Although inverse dynamic controller have acceptable performance with known dynamic parameters but regarding to uncertainty, this controller\'s output has fairly fluctuations. In order to solve this problem this research is focoused on two methodology the first one is design a fuzzy inference system as a estimate nonlinear part of main controller but this method caused to high computation load in fuzzy rule base and the second method is focused on design novel adaptive method to reduce the computation in fuzzy algorithm.
In this research, a model free sliding mode fuzzy adaptive inverse dynamic fuzzy controller (SMFIDFC) is designed for a robot manipulator to rich the best performance. Inverse dynamic controller is considered because of its high performance in certain system. Fuzzy methodology has been included in inverse dynamic to keep away from design nonlinear controller based on dynamic model. Sliding mode fuzzy adaptive methodology is applied to model free controller to have better result in presence of structure and unstructured uncertainties. Besides, this control method can be applied to non-linear systems easily. Today, strong mathematical tools are used in new control methodologies to design adaptive nonlinear controller with satisfactory output results (e.g., minimum error, good trajectory, disturbance rejection).
Evolutionary Design of Backstepping Artificial Sliding Mode Based Position Al...CSCJournals
This paper expands a fuzzy sliding mode based position controller whose sliding function is on-line tuned by backstepping methodology. The main goal is to guarantee acceptable position trajectories tracking between the robot manipulator end-effector and the input desired position. The fuzzy controller in proposed fuzzy sliding mode controller is based on Mamdani’s fuzzy inference system (FIS) and it has one input and one output. The input represents the function between sliding function, error and the rate of error. The second input is the angle formed by the straight line defined with the orientation of the robot, and the straight line that connects the robot with the reference cart. The outputs represent angular position, velocity and acceleration commands, respectively. The backstepping methodology is on-line tune the sliding function based on self tuning methodology. The performance of the backstepping on-line tune fuzzy sliding mode controller (TBsFSMC) is validated through comparison with previously developed robot manipulator position controller based on adaptive fuzzy sliding mode control theory (AFSMC). Simulation results signify good performance of position tracking in presence of uncertainty and external disturbance.
Design Error-based Linear Model-free Evaluation Performance Computed Torque C...Waqas Tariq
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This research focuses on the design, implementation and analysis of a model-free linear error-based tuning computed torque controller for highly nonlinear dynamic second order system, in presence of uncertainties. In order to provide high performance nonlinear methodology, computed torque controller is selected. Pure computed torque controller can be used to control of partly known nonlinear dynamic parameters of nonlinear systems. Conversely, pure computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, model-free performance/error-based linear methodology with three inputs and one output is applied to pure computed torque controller. The results demonstrate that the error-based linear tuning computed torque controller is a model-based controllers which works well in certain and uncertain system. Pure computed torque controller has difficulty in handling unstructured model uncertainties. To solve this problem applied linear model-free error -based tuning method to computed torque controller for adjusting the linear inner loop gain (K ). Since the linear inner loop gain (K) is adjusted by linear error-based tuning method, it is linear and continuous. In this research new K is obtained by the previous K multiple gain updating factor (á) which is a coefficient varies between half to two.
The developed control methodology can be used to build more efficient intelligent and precision mechatronic systems. Three degrees of freedom robot arm is controlled by adaptive sliding mode fuzzy algorithm fuzzy sliding mode controller (SMFAFSMC). This plant has 3 revolute joints allowing the corresponding links to move horizontally. Control of robotic manipulator is very important in field of robotic, because robotic manipulators are Multi-Input Multi-Output (MIMO), nonlinear and most of dynamic parameters are uncertainty. Design strong mathematical tools used in new control methodologies to design adaptive nonlinear robust controller with acceptable performance in this controller is the main challenge. Sliding mode methodology is a nonlinear robust controller which can be used in uncertainty nonlinear systems, but pure sliding mode controller has chattering phenomenon and nonlinear equivalent part in uncertain system therefore the first step is focused on eliminate the chattering and in second step controller is improved with regard to uncertainties. Sliding function is one of the most important challenging in artificial sliding mode algorithm which this problem in order to solved by on-line tuning method. This paper focuses on adjusting the sliding surface slope in fuzzy sliding mode controller by sliding mode fuzzy algorithm.
Artificial Chattering Free on-line Fuzzy Sliding Mode Algorithm for Uncertain...CSCJournals
This document proposes an artificial chattering free adaptive fuzzy sliding mode control algorithm for uncertain systems, specifically applied to robot manipulators. The algorithm combines sliding mode control, fuzzy logic control, and adaptive methods to address some limitations of each approach. Specifically, fuzzy logic is used instead of saturation functions and dead zones to eliminate chattering. Fuzzy rules are also used to estimate the nonlinear dynamic equivalent control term, reducing complexity. Adaptive methods are used to continuously adjust the sliding function in real-time for improved performance with uncertain or time-varying parameters. The algorithm is tested in simulations of a PUMA robot manipulator.
Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., Internal Combustion Engine) is one of the most important challenging works. This paper focuses on the design of a robust backstepping adaptive feedback linearization controller (FLC) for internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, feedback linearization controller is selected. Pure feedback linearization controller can be used to control of partly unknown nonlinear dynamic parameters of IC engine. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure feedback linearization controller. The results demonstrate that the error-based fuzzy feedback linearization controller is a model-free controllers which works well in certain and partly uncertain system. Pure feedback linearization controller and error-based feedback linearization like controller with have difficulty in handling unstructured model uncertainties. To solve this problem applied backstepping-based tuning method to error-based fuzzy feedback linearization controller for adjusting the feedback linearization controller gain (K_p,K_v ). This controller has acceptable performance in presence of uncertainty (e.g., overshoot=1%, rise time=0.48 second, steady state error = 1.3e-9 and RMS error=1.8e-11).
Adaptive MIMO Fuzzy Compensate Fuzzy Sliding Mode Algorithm: Applied to Secon...CSCJournals
This research is focused on proposed adaptive fuzzy sliding mode algorithms with the adaptation laws derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Adaptive MIMO fuzzy compensate fuzzy sliding mode method design a MIMO fuzzy system to compensate for the model uncertainties of the system, and chattering also solved by linear saturation method. Since there is no tuning method to adjust the premise part of fuzzy rules so we presented a scheme to online tune consequence part of fuzzy rules. Classical sliding mode control is robust to control model uncertainties and external disturbances. A sliding mode method with a switching control low guarantees the stability of the certain and/or uncertain system, but the addition of the switching control low introduces chattering into the system. One way to reduce or eliminate chattering is to insert a boundary layer method inside of a boundary layer around the sliding surface. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov.
Position Control of Robot Manipulator: Design a Novel SISO Adaptive Sliding M...Waqas Tariq
The document describes a novel adaptive sliding mode fuzzy PD fuzzy sliding mode control algorithm for position control of robot manipulators. The algorithm uses a single-input single-output fuzzy system to compensate for model uncertainties and eliminate chattering using a linear boundary layer method. It also online tunes the sliding function parameter using adaptation laws. The stability of the closed-loop system is proved mathematically using Lyapunov stability theory. The algorithm is analyzed and evaluated on a 2 degree of freedom robotic manipulator to achieve improved tracking performance compared to conventional sliding mode control approaches.
Digital Implementation of Fuzzy Logic Controller for Real Time Position Contr...IOSR Journals
Fuzzy Logic Controller (FLC) systems have emerged as one of the most promising areas for
Industrial Applications. The highly growth of fuzzy logic applications led to the need of finding efficient way to
hardware implementation. Field Programmable Gate Array (FPGA) is the most important tool for hardware
implementation due to low consumption of energy, high speed of operation and large capacity of data storage.
In this paper, instead of an introduction to fuzzy logic control methodology, we have demonstrated the
implementation of a FLC through the use of the Very high speed integrated circuits Hardware Description
Language (VHDL) code. FLC is designed for position control of BLDC Motor. VHDL has been used to develop
FLC on FPGA. A Mamdani type FLC structure has been used to obtain the controller output. The controller
algorithm developed synthesized, simulated and implemented on FPGA Spartan 3E board.
Sliding Mode Methodology Vs. Computed Torque Methodology Using MATLAB/SIMULIN...CSCJournals
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This paper focuses on the design, implementation and analysis of a chattering free sliding mode controller for highly nonlinear dynamic PUMA robot manipulator and compare to computed torque controller, in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure sliding mode controller and computed torque controller can be used to control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure sliding mode controller is used in many applications; it has an important drawback namely; chattering phenomenon which it can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers. In order to reduce the chattering this research is used the linear saturation function boundary layer method instead of switching function method in pure sliding mode controller. These simulation models are developed as a part of a software laboratory to support and enhance graduate/undergraduate robotics courses, nonlinear control courses and MATLAB/SIMULINK courses at research and development company (SSP Co.) research center, Shiraz, Iran.
IRJET- A Performance of Hybrid Control in Nonlinear Dynamic Multirotor UAVIRJET Journal
This document summarizes a research paper that models and evaluates control techniques for multirotor unmanned aerial vehicles (UAVs). It begins with an abstract that outlines the paper's contributions: developing an accurate mathematical model of a multirotor UAV using Newton-Euler dynamics, developing nonlinear control algorithms based on this model, and comparing the performance of backstepping control, sliding mode control, and fuzzy logic control through simulation. The document then provides details of the multirotor dynamic model and each control approach, evaluating their ability to stabilize the system and reject disturbances. It concludes that hybrid control systems combining advantages of different methods should be considered.
TORQUE CONTROL OF AC MOTOR WITH FOPID CONTROLLER BASED ON FUZZY NEURAL ALGORITHMijics
Nowadays in the complicated systems, design of proper and implementable controller has a most importance. With respect to ability of fractional order systems in complicated systems identification as a first order fractional system with time delay, usage of fractional order PID has a proper result. From one side flexibility of fractional calculus than integer order has been topics of interest to the researchers. From another side, PMSM motors which are one the AC motor types, has been allocated largely accounted position in industry and used in variety applications. Therefore in this paper torque direct control of PMSM motors with FOPID based on model is proposed. Also fuzzy neural controllers are widely considered. Reason of this is success of fuzzy neural controller in control and identification of uncertain and complicated systems. The proposed method in this paper is combination of FOPID controller with fuzzy neural supervision system which with coefficients setting of this controller, control operation of PMSM will improve. Results of proposed method show the ability of proposed technique in reference signal tracking, elimination of disturbances effects and functional robustness in presence of noise and uncertainty. The results show the error averagely in three condition, nominal form, step disturbance and noise and uncertainly will decrease 11.66% in proposed method (FNFOPID) with Integral Square Error criterion and 7.69% with Integral Absolute Error criterion in comparison to FOPID.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Simulation of Linear Induction Motor Using Sliding Mode Controller TechniqueIJMERJOURNAL
ABSTRACT:In the present paper, the mover speed control of a linear induction motor (LIM) using a sliding mode control design is proposed. First, the indirect field-oriented control LIM is derived. The sliding mode control design is then investigated to achieve speed- and flux-tracking under load thrust force disturbance. The numerical simulation results of the proposed scheme present good performances in comparison to that of the classical sliding mode control.In the present paper, a sliding mode controller based onindirect field orientation is proposed for LIM speed controlwhile considering end effects. The proposed controller isapplied to achieve a speed- and flux-tracking objectiveunder parameter uncertainties and disturbance of loadthrust force.
The document discusses control systems for robot manipulators. It covers open-loop and closed-loop control systems, with closed-loop being preferred using feedback. It describes using linear control techniques to approximate manipulator dynamics and designing controllers to meet stability and performance specifications. Common control techniques for manipulators are also summarized like PD, PID, state space control and adaptive/intelligent methods.
Design of Model Free Adaptive Fuzzy Computed Torque Controller for a Nonlinea...Waqas Tariq
In this study, a model free adaptive fuzzy computed torque controller (AFCTC) is designed for a two-degree-of freedom robot manipulator to rich the best performance. Computed torque controller is studied because of its high performance. AFCTC has been also included in this study because of its robust character and high performance. Besides, this control method can be applied to non-linear systems easily. Today, robot manipulators are used in unknown and unstructured environment and caused to provide sophisticated systems, therefore strong mathematical tools are used in new control methodologies to design adaptive nonlinear robust controller with acceptable performance (e.g., minimum error, good trajectory, disturbance rejection). The strategies of control robot manipulator are classified into two main groups: classical and non-classical methods, however both classical and non-classical theories have been applied successfully in many applications, but they also have some limitation. One of the most important nonlinear robust controller that can used in uncertainty nonlinear systems, are computed torque controller. This paper is focuses on applied non-classical method in robust classical method to reduce the limitations. Therefore adaptive fuzzy computed torque controller will be presented in this paper.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document discusses industrial robots including their definition, components, motions, configurations, and applications. It describes that a robot is a re-programmable manipulator designed to move parts and tools for various tasks. The key components are the manipulator, end effector, power supply, and control system. Common robot configurations include Cartesian, cylindrical, SCARA, and jointed arm. Industrial robots are widely used for automation in various industries.
This document summarizes investigations into a fuzzy logic controller for a sensorless switched reluctance motor drive. It begins by introducing switched reluctance motors and their nonlinear characteristics. It then describes designing a fuzzy logic controller to estimate rotor position with minimum steady state error and good dynamic response. The controller implementation and numerical simulation results using Matlab/Simulink are presented. Simulation results at different speeds and loads demonstrate the controller's steady state performance and ability to respond robustly under different conditions. The conclusions are that the fuzzy logic controller enables effective operation of the switched reluctance motor drive with only small errors in all tested scenarios.
This paper examines the stability of sliding mode control for underactuated nonlinear systems. It presents sliding mode control design for a class of underactuated systems using a switching control law. It then analyzes the stability of the closed-loop reaching phase and sliding phase dynamics. As an example, it applies this analysis to the stability of an inverted pendulum controlled via sliding mode control.
The document presents a sliding mode control algorithm and adaptive nonlinear observer for regulating wheel slip in anti-lock braking systems for commercial vehicles. Simulation results using an ADAMS vehicle model show the new control approach can achieve a stopping distance of 54 meters from 60 mph, satisfying new regulations requiring shorter stopping distances. The algorithm holds tire slip near its peak to maximize braking force, and the observer estimates brake forces using a LuGre tire friction model.
Sliding Mode Controller for Robotic Flexible Arm Jointomkarharshe
The problem of joint flexibility was of critical importance since the use of robot started in the fields such as space science and surveillance. This project addresses this issue by applying a stabilizing control law, ensuring robustness against plant uncertainties and disturbances.
This document provides an overview and table of contents for a book on advanced sliding mode control for mechanical systems. The book covers topics such as sliding mode controller design, analysis, and MATLAB simulation. It includes 11 chapters that discuss various sliding mode control approaches, such as normal sliding mode control, advanced sliding mode control, discrete sliding mode control, adaptive sliding mode control, terminal sliding mode control, and sliding mode control based on observers. Case studies and MATLAB programs are provided to illustrate practical applications of the theory.
Sliding Mode Control (SMC) is a type of Variable Structure Control that uses a discontinuous control law to drive the system states towards a switching surface, called the sliding surface, in finite time, resulting in robust behavior to disturbances and uncertainties. The summary discusses:
1) SMC involves selecting a sliding surface and designing discontinuous feedback gains such that the system trajectory intersects and stays on the sliding surface.
2) For a sliding mode to exist, the system state trajectory velocity must always be directed towards the sliding surface in its vicinity.
3) Using Lyapunov stability analysis, sufficient conditions are presented to guarantee the existence of a sliding mode and that the sliding surface is reached in finite
The sliding mode control approach is recognized as one of the
efficient tools to design robust controllers for complex high-order non-linear dynamic plant operating under uncertainty conditions.
This paper expands a sliding mode fuzzy controller which sliding surface gain is on-line tuned by minimum fuzzy inference algorithm. The main goal is to guarantee acceptable trajectories tracking between the second order nonlinear system (robot manipulator) actual and the desired trajectory. The fuzzy controller in proposed sliding mode fuzzy controller is based on Mamdani’s fuzzy inference system (FIS) and it has one input and one output. The input represents the function between sliding function, error and the rate of error. The outputs represent torque, respectively. The fuzzy inference system methodology is on-line tune the sliding surface gain based on error-based fuzzy tuning methodology. Pure sliding mode fuzzy controller has difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to sliding mode fuzzy controller for adjusting the sliding surface gain (ë ). Since the sliding surface gain (ë) is adjusted by fuzzy-based tuning method, it is nonlinear and continuous. Fuzzy-based tuning sliding mode fuzzy controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning sliding mode fuzzy controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).
PUMA-560 Robot Manipulator Position Sliding Mode Control Methods Using MATLAB...Waqas Tariq
This paper describes the MATLAB/SIMULINK realization, modeling and implementation of the PUMA 560 robot manipulator. This paper focuses on robot manipulator analysis and implementation and analyzed. This simulation models are developed as a part of a software laboratory to support and enhance graduate robotics courses, and MATLAB/SIMULINK courses at research and development company (SSP Co.) research center, Shiraz, Iran.
Design and Implementation of Sliding Mode Algorithm: Applied to Robot Manipul...Waqas Tariq
Refer to the research, review of sliding mode controller is introduced and application to robot manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy logic controller and adaptive method, the output in most of research have improved. Each method by adding to the previous algorithm has covered negative points. Obviously robot manipulator is nonlinear, and a number of parameters are uncertain, this research focuses on comparison between sliding mode algorithm which analyzed by many researcher. Sliding mode controller (SMC) is one of the nonlinear robust controllers which it can be used in uncertainty nonlinear dynamic systems. This nonlinear controller has two challenges namely nonlinear dynamic equivalent part and chattering phenomenon. A review of sliding mode controller for robot manipulator will be investigated in this research.
PUMA-560 Robot Manipulator Position Computed Torque Control Methods Using MAT...Waqas Tariq
This document describes the implementation of a computed torque controller for controlling the position of a PUMA 560 robot manipulator using MATLAB/Simulink. It first presents the dynamic equations of motion for the PUMA 560 robot. It then provides details on computed torque control, including its mathematical formulation and how it was modeled in Simulink. Simulation results are presented to validate the controller's performance in tracking desired joint positions for the robot.
On line Tuning Premise and Consequence FIS: Design Fuzzy Adaptive Fuzzy Slidi...Waqas Tariq
This document presents a study on tuning premise and consequence parts of fuzzy inference system rules online to design an adaptive fuzzy sliding mode controller for a robot manipulator. Classical sliding mode controllers are robust but suffer from chattering. Previous work has combined fuzzy systems and sliding mode control to address chattering and model uncertainties, but require large rule bases. The proposed method uses an adaptive law to tune fuzzy rule parameters online, ensuring moderate computational load while approximating the uncertain nonlinear system dynamics. Simulation results will demonstrate the effectiveness of the approach.
Intelligent swarm algorithms for optimizing nonlinear sliding mode controller...IJECEIAES
This document describes research into using intelligent swarm algorithms to optimize the parameters of a nonlinear sliding mode controller for a robot manipulator. Specifically, particle swarm optimization and social spider optimization were used to determine optimal values for the parameters of an integral sliding mode controller designed to control a 6 degree-of-freedom PUMA robot manipulator. Simulation results showed that social spider optimization achieved the best fitness value and performance in minimizing error for the robot controller parameters.
Impact analysis of actuator torque degradation on the IRB 120 robot performan...IJECEIAES
Actuators in a robot system may become faulty during their life cycle. Locked joints, free-moving joints, and the loss of actuator torque are common faulty types of robot joints where the actuators fail. Locked and free-moving joint issues are addressed by many published articles, whereas the actuator torque loss still opens attractive investigation challenges. The objectives of this study are to classify the loss of robot actuator torque, named actuator torque degradation, into three different cases: Boundary degradation of torque, boundary degradation of torque rate, and proportional degradation of torque, and to analyze their impact on the performance of a typical 6-DOF robot (i.e., the IRB 120 robot). Typically, controllers of robots are not pre-designed specifically for anticipating these faults. To isolate and focus on the impact of only actuator torque degradation faults, all robot parameters are assumed to be known precisely, and a popular closed-loop controller is used to investigate the robot’s responses under these faults. By exploiting MATLAB-the reliable simulation environment, a simscape-based quasi-physical model of the robot is built and utilized instead of an actual expensive prototype. The simulation results indicate that the robot responses cannot follow the desired path properly in most fault cases.
Optimal Design of Super Twisting Control with PSO Algorithm for Robotic Manip...CSCJournals
Robotic manipulators are nonlinear and coupling systems exposing to external disturbance. They are used in wide industrial applications; the suitable selection of a nonlinear robust controller is required. Sliding Mode Controller (SMC) was designed to achieve these requirements, but unfortunately the chattering phenomenon was the main drawback of the conventional SMC. It leads to destructive of some components of a real system and subsequent loss in its accuracy. Hence, the design of Super-Twisting Controller (STC) is suggested for chattering elimination. In previous literatures, the accomplishment of the manual adjustment for the parameters of STC was a large burden and time consuming process. Therefore, a new combination of Particle Swarm Optimization (PSO) algorithm with STC is proposed for optimal tuning of STC parameters. The simulation results demonstrate the superiority of the super twisting technique for chattering mitigation comparing to the conventional SMC. Also, STC tuned via PSO proves its effectiveness and robustness to different types of external disturbances without the needs for the knowledge of their upper boundary values. Besides, the performance of the controlled system is faster and more accurate in the criteria of overshoot, settling time and rise time compared to the manual adjusting of super twisting controllers.
Modeling and Control of a Spherical Rolling Robot Using Model Reference Adapt...IRJET Journal
The document describes modeling and control of a spherical rolling robot using model reference adaptive control (MRAC). It presents the mathematical model developed for the robot based on its nonholonomic constraints. MRAC is used to control the robot by adjusting controller parameters to minimize the error between the robot's actual output and the output of a reference model for ideal behavior. Simulation results show the proposed MRAC scheme eliminates steady state error and improves transient response without requiring knowledge of the robot's dynamic equations.
Fractional-order sliding mode controller for the two-link robot arm IJECEIAES
This study presents a control system of the two-link robot arm based on the sliding mode controller with the fractional-order. Firstly, the equations of the two-link robot arm are analyzed, then the author proposes the controller for each joint based on these equations. The controller is a sliding mode controller with its order is not an integer value. The task of the control system is controlling the torques acted on the joints so that the response angle of each link equal to the desired angle. The effectiveness of the proposed control system is demonstrated through Matlab-Simulink software. The robot model and controller are built for investigating the efficiency of the system. The result shows that the system quality is very good: there is not the chattering phenomenon of torques, the response angle of two links always follow the desired angle with the short transaction time and the static error of zero.
IRJET- Singular Identification of a Constrained Rigid RobotIRJET Journal
This document presents a singular identification procedure for identifying the parameters of a constrained rigid robot model. It begins with describing the constrained robot model and how it can be represented as a singular system. It then discusses singular equivalency, in particular strong equivalency, which transforms the original singular system into an equivalent regular state space model. This is important to reduce the number of initial conditions and improve identification. The document proposes using recursive least squares identification on the strongly equivalent model to identify the robot parameters. Simulation results on a robot arm model show that this approach provides significantly better parameter estimation convergence and output tracking compared to previous identification techniques for constrained robot models.
IRJET- Domestic Water Conservation by IoT (Smart Home)IRJET Journal
This document discusses singular system identification for a constrained rigid robot model. It begins by introducing constrained robot models and noting they can be considered singular systems. It then discusses the importance of singular system equivalency in identification, as an inappropriate equivalency can cause large errors. The document proposes using strong equivalency to transform the constrained robot model before identification. It applies recursive least squares identification to the strongly equivalent system. Simulation results show this approach improves identification error convergence and output tracking compared to previous techniques for constrained robot models.
IRJET- Design and Fabrication of PLC and SCADA based Robotic Arm for Material...IRJET Journal
This document describes the design and fabrication of a PLC and SCADA-controlled robotic arm for material handling. The robotic arm uses pneumatic cylinders connected by joints to move along three axes (X, Y, and Z). A mechanical gripper is attached to the end of the arm to grip objects on a conveyor belt. The movements of the pneumatic cylinders and gripper are controlled by a PLC based on sensor inputs from the conveyor belt. The PLC and robotic arm are integrated with a SCADA system for centralized control and monitoring. The robotic arm is intended to automate repetitive picking and placing tasks to reduce labor costs compared to manual operations.
Design Mathematical Tunable Gain PID-Like Sliding Mode Fuzzy Controller With ...Waqas Tariq
In this study, a mathematical tunable gain model free PID-like sliding mode fuzzy controller (GTSMFC) is designed to rich the best performance. Sliding mode fuzzy controller is studied because of its model free, stable and high performance. Today, most of systems (e.g., robot manipulators) are used in unknown and unstructured environment and caused to provide sophisticated systems, therefore strong mathematical tools (e.g., nonlinear sliding mode controller) are used in artificial intelligent control methodologies to design model free nonlinear robust controller with high performance (e.g., minimum error, good trajectory, disturbance rejection). Non linear classical theories have been applied successfully in many applications, but they also have some limitation. One of the best nonlinear robust controller which can be used in uncertainty nonlinear systems, are sliding mode controller but pure sliding mode controller has some disadvantages therefore this research focuses on applied sliding mode controller in fuzzy logic theory to solve the limitation in fuzzy logic controller and sliding mode controller. One of the most important challenging in pure sliding mode controller and sliding mode fuzzy controller is sliding surface slope. This paper focuses on adjusting the gain updating factor and sliding surface slope in PID like sliding mode fuzzy controller to have the best performance and reduce the limitation.
Synthesis of the Decentralized Control System for Robot-Manipulator with Inpu...ITIIIndustries
It is discussed the problem of synthesis of the decentralized adaptive-periodic control system for two degrees of freedom robotic manipulator which have an input limitations. The solution of the problem is based on the use of hyperstability criterion, L-dissipativity conditions and dynamic filter-corrector.
1) The document discusses using a sliding mode controller for speed control of a two phase induction motor.
2) Sliding mode control is an efficient technique for speed control due to its robustness and insensitivity to parameter variations.
3) A sliding mode controller is designed for the speed control of a two phase induction motor. The controller design involves choosing a sliding surface, establishing convergence conditions, and determining the control law. Chattering reduction is also addressed.
Kineto-Elasto Dynamic Analysis of Robot Manipulator Puma-560IOSR Journals
Current industrial robots are made very heavy to achieve high Stiffness
which increases the accuracy of their motion. However this heaviness limits the robot speed and in masses the
required energy to move the system. The requirement for higher speed and better system performance makes it
necessary to consider a new generation of light weight manipulators as an alternative to today's massive
inefficient ones. Light weight manipulators require Less energy to move and they have larger payload abilities
and more maneuverability. However due to the dynamic effects of structural flexibility, their control is much
more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such
systems.This project presents the flexibility and Kineto - Elasto dynamic analysis of robot manipulator
considering deflection. Based on the distributed parameter method, the generalized motion equations of robot
manipulator with flexible links are derived. The final formulation of the motion equations is used to model
general complex elastic manipulators with nonlinear rigid-body and elastic motion in dynamics and it can be
used in the flexibility analysis of robot manipulators and spatial mechanisms. Manipulator end-effector path
trajectory, velocity and accelerations are plotted. Joint torques is to be determined for each joint trajectory
(Dynamics) .Using joint torques, static loading due to link’s masses, masses at joints, and payload, the robot
arms elastic deformations are to be found by using ANSYS-12.0 software package. Elastic compensation is
inserted in coordinates of robotic programming to get exact end-effectors path. A comparison of paths
trajectory of the end-effector is to be plotted. Also variation of torques is plotted after considering elastic
compensation. These torque variations are included in the robotic programming for getting the accurate endeffect
or’s path trajectory
Optimization of Modified Sliding Mode Controller for an Electro-hydraulic Act...IJECEIAES
This paper presents the design of the modified sliding mode controller (MSMC) for the purpose of tracking the nonlinear system with mismatched disturbance. Provided that the performance of the designed controller depends on the value of control parameters, gravitational search algorithm (GSA), and particle swarm optimization (PSO) techniques are used to optimize these parameters in order to achieve a predefined system’s performance. In respect of system’s performance, it is evaluated based on the tracking error present between reference inputs transferred to the system and the system output. This is followed by verification of the efficiency of the designed controller in simulation environment under various values, with and without the inclusion of external disturbance. It can be seen from the simulation results that the MSMC with PSO exhibits a better performance in comparison to the performance of the similar controller with GSA in terms of output response and tracking error.
Similar to Methodology of Mathematical error-Based Tuning Sliding Mode Controller (18)
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Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
The chapter Lifelines of National Economy in Class 10 Geography focuses on the various modes of transportation and communication that play a vital role in the economic development of a country. These lifelines are crucial for the movement of goods, services, and people, thereby connecting different regions and promoting economic activities.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Methodology of Mathematical error-Based Tuning Sliding Mode Controller
1. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 96
Methodology of Mathematical Error-Based Tuning Sliding Mode
Controller
Farzin Piltan SSP.ROBOTIC@yahoo.com
Industrial Electrical and Electronic
Engineering SanatkadeheSabze
Pasargad. CO (S.S.P. Co), NO:16
,PO.Code 71347-66773, Fourth floor
Dena Apr , Seven Tir Ave , Shiraz , Iran
Bamdad Boroomand SSP.ROBOTIC@yahoo.com
Industrial Electrical and Electronic
Engineering SanatkadeheSabze
Pasargad. CO (S.S.P. Co), NO:16
,PO.Code 71347-66773, Fourth floor
Dena Apr , Seven Tir Ave , Shiraz , Iran
Arman Jahed SSP.ROBOTIC@yahoo.com
Industrial Electrical and Electronic
Engineering SanatkadeheSabze
Pasargad. CO (S.S.P. Co), NO:16
,PO.Code 71347-66773, Fourth floor
Dena Apr , Seven Tir Ave , Shiraz , Iran
Hossein Rezaie SSP.ROBOTIC@yahoo.com
Industrial Electrical and Electronic
Engineering SanatkadeheSabze
Pasargad. CO (S.S.P. Co), NO:16
,PO.Code 71347-66773, Fourth floor
Dena Apr , Seven Tir Ave , Shiraz , Iran
Abstract
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of
the most important challenging works. This paper focuses on the design of a chattering free
mathematical error-based tuning sliding mode controller (MTSMC) for highly nonlinear dynamic
robot manipulator, in presence of uncertainties. In order to provide high performance nonlinear
methodology, sliding mode controller is selected. Pure sliding mode controller can be used to
control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure
sliding mode controller is used in many applications; it has an important drawback namely;
chattering phenomenon which it can causes some problems such as saturation and heat the
mechanical parts of robot manipulators or drivers.
In order to reduce the chattering this research is used the switching function in presence of
mathematical error-based method instead of switching function method in pure sliding mode
controller. The results demonstrate that the sliding mode controller with switching function is a
model-based controllers which works well in certain and partly uncertain system. Pure sliding
mode controller has difficulty in handling unstructured model uncertainties. To solve this problem
applied mathematical model-free tuning method to sliding mode controller for adjusting the sliding
surface gain (λ ). Since the sliding surface gain (λ) is adjusted by mathematical model free-based
tuning method, it is nonlinear and continuous. In this research new λ is obtained by the previous λ
multiple sliding surface slopes updating factor ሺαሻ. Chattering free mathematical error-based
tuning sliding mode controller is stable controller which eliminates the chattering phenomenon
without to use the boundary layer saturation function. Lyapunov stability is proved in
mathematical error-based tuning sliding mode controller with switching (sign) function. This
2. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 97
controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise
time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).
Keywords: Nonlinear Controller, Chattering Free Mathematical Error-based Tuning Sliding Mode
Controller, Uncertainties, Chattering Phenomenon, Robot Arm, Sliding Mode Controller, Adaptive
Methodology.
1. INTRODUCTION
The international organization defines the robot as “an automatically controlled, reprogrammable,
multipurpose manipulator with three or more axes.” The institute of robotic in The United States
Of America defines the robot as “a reprogrammable, multifunctional manipulator design to move
material, parts, tools, or specialized devices through various programmed motions for the
performance of variety of tasks”[1]. Robot manipulator is a collection of links that connect to each
other by joints, these joints can be revolute and prismatic that revolute joint has rotary motion
around an axis and prismatic joint has linear motion around an axis. Each joint provides one or
more degrees of freedom (DOF). From the mechanical point of view, robot manipulator is divided
into two main groups, which called; serial robot links and parallel robot links. In serial robot
manipulator, links and joints is serially connected between base and final frame (end-effector).
Most of industrial robots are serial links, which in ݊ degrees of freedom serial link robot
manipulator the axis of the first three joints has a known as major axis, these axes show the
position of end-effector, the axis number four to six are the minor axes that use to calculate the
orientation of end-effector and the axis number seven to ݊ use to reach the avoid the difficult
conditions (e.g., surgical robot and space robot manipulator). Dynamic modeling of robot
manipulators is used to describe the behavior of robot manipulator such as linear or nonlinear
dynamic behavior, design of model based controller such as pure sliding mode controller and
pure computed torque controller which design these controller are based on nonlinear dynamic
equations, and for simulation. The dynamic modeling describes the relationship between joint
motion, velocity, and accelerations to force/torque or current/voltage and also it can be used to
describe the particular dynamic effects (e.g., inertia, coriolios, centrifugal, and the other
parameters) to behavior of system[1-10]. The Unimation PUMA 560 serially links robot
manipulator was used as a basis, because this robot manipulator is widely used in industry and
academic. It has a nonlinear and uncertain dynamic parameters serial link 6 degrees of freedom
(DOF) robot manipulator. A nonlinear robust controller design is major subject in this work.
Controller is a device which can sense information from linear or nonlinear system (e.g., robot
manipulator) to improve the systems performance [3]. The main targets in designing control
systems are stability, good disturbance rejection, and small tracking error[5]. Several industrial
robot manipulators are controlled by linear methodologies (e.g., Proportional-Derivative (PD)
controller, Proportional- Integral (PI) controller or Proportional- Integral-Derivative (PID)
controller), but when robot manipulator works with various payloads and have uncertainty in
dynamic models this technique has limitations. From the control point of view, uncertainty is
divided into two main groups: uncertainty in unstructured inputs (e.g., noise, disturbance) and
uncertainty in structure dynamics (e.g., payload, parameter variations). In some applications robot
manipulators are used in an unknown and unstructured environment, therefore strong
mathematical tools used in new control methodologies to design nonlinear robust controller with
an acceptable performance (e.g., minimum error, good trajectory, disturbance rejection).
Sliding mode controller (SMC) is a significant nonlinear controller under condition of partly
uncertain dynamic parameters of system. This controller is used to control of highly nonlinear
systems especially for robot manipulators, because this controller is a robust and stable [11-30].
Conversely, pure sliding mode controller is used in many applications; it has two important
drawbacks namely; chattering phenomenon, and nonlinear equivalent dynamic formulation in
uncertain dynamic parameter. The chattering phenomenon problem can be reduced by using
linear saturation boundary layer function in sliding mode control law [31-50]. Lyapunov stability is
proved in pure sliding mode controller based on switching (sign) function. The nonlinear
3. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 98
equivalent dynamic formulation problem in uncertain system can be solved by using artificial
intelligence theorem or online tuning methodology. Fuzzy logic theory is used to estimate the
system dynamic. However fuzzy logic controller is used to control complicated nonlinear dynamic
systems, but it cannot guarantee stability and robustness. Pure sliding mode controller has
difficulty in handling unstructured model uncertainties. It is possible to solve this problem by
combining sliding mode controller and adaption law which this method can helps improve the
system’s tracking performance by online tuning method [51-61].
Literature Review
Chattering phenomenon can causes some problems such as saturation and heats the
mechanical parts of robot arm or drivers. To reduce or eliminate the oscillation, various papers
have been reported by many researchers which one of the best method is; boundary layer
saturation method [1]. In boundary layer linear saturation method, the basic idea is the
discontinuous method replacement by linear continuous saturation method with small
neighborhood of the switching surface. This replacement caused to considerable chattering
reduction. Slotine and Sastry have introduced boundary layer method instead of discontinuous
method to reduce the chattering[21]. Slotine has presented sliding mode controller with boundary
layer to improve the industry application [22]. Palm has presented a fuzzy method to nonlinear
approximation instead of linear approximation inside the boundary layer to improve the chattering
and control the result performance[23]. Moreover, Weng and Yu improved the previous method
by using a new method in fuzzy nonlinear approximation inside the boundary layer and adaptive
method[24]. Control of robot arms using conventional controllers are based on robot arm dynamic
modelling. These controllers often have many problems for modelling. Conventional controllers
require accurate information of dynamic model of robot arms. When the system model is
unknown or when it is known but complicated, it is difficult or impossible to use conventional
mathematics to process this model[32]. In various dynamic parameters systems that need to be
training on-line, adaptive control methodology is used. Mathematical model free adaptive method
is used in systems which want to training parameters by performance knowledge. In this research
in order to solve disturbance rejection and uncertainty dynamic parameter, adaptive method is
applied to sliding mode controller. Mohan and Bhanot [40] have addressed comparative study
between some adaptive fuzzy, and a new hybrid fuzzy control algorithm for robot arm control.
They found that self-organizing fuzzy logic controller and proposed hybrid integrator fuzzy give
the best performance as well as simple structure. Temeltas [46] has proposed fuzzy adaption
techniques for VSC to achieve robust tracking of nonlinear systems and solves the chattering
problem. Conversely system’s performance is better than sliding mode controller; it is depended
on nonlinear dynamic equqation. Hwang et al. [47]have proposed a Tagaki-Sugeno (TS) fuzzy
model based sliding mode controller based on N fuzzy based linear state-space to estimate the
uncertainties. A MIMO FVSC reduces the chattering phenomenon and reconstructs the
approximate the unknown system has been presented for a nonlinear system [42]. Yoo and Ham
[58]have proposed a MIMO fuzzy system to help the compensation and estimation the torque
coupling. This method can only tune the consequence part of the fuzzy rules. Medhafer et al. [59]
have proposed an indirect adaptive fuzzy sliding mode controller to control nonlinear system. This
MIMO algorithm, applies to estimate the nonlinear dynamic parameters. Compared with the
previous algorithm the numbers of fuzzy rules have reduced by introducing the sliding surface as
inputs of fuzzy systems. Guo and Woo [60]have proposed a SISO fuzzy system compensate and
reduce the chattering. Lin and Hsu [61] can tune both systems by fuzzy rules. Eksin et. al [83]
have designed mathematical model-free sliding surface slope in fuzzy sliding mode controller. In
above method researchers are used saturation function instead of switching function therefore
the proof of stability is very difficult.
Problem Statements
One of the significant challenges in control algorithms is a linear behavior controller design for
nonlinear systems (e.g., robot manipulator). Some of robot manipulators which work in industrial
processes are controlled by linear PID controllers, but the design of linear controller for robot
manipulators is extremely difficult because they are hardly nonlinear and uncertain [1-2, 6]. To
reduce the above challenges, the nonlinear robust controller is used to control of robot
4. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 99
manipulator. Sliding mode controller is a powerful nonlinear robust controller under condition of
partly uncertain dynamic parameters of system [7]. This controller is used to control of highly
nonlinear systems especially for robot manipulators. Chattering phenomenon and nonlinear
equivalent dynamic formulation in uncertain dynamic parameter are two main drawbacks in pure
sliding mode controller [20]. The chattering phenomenon problem in pure sliding mode controller
is reduced by using linear saturation boundary layer function but prove the stability is very
difficult. In this research the nonlinear equivalent dynamic formulation problem and chattering
phenomenon in uncertain system is solved by using on-line tuning theorem [8]. To estimate the
system dynamics, mathematical error-based sliding mode controller is designed. Pure sliding
mode controller has difficulty in handling unstructured model uncertainties. It is possible to solve
this problem by combining sliding mode controller and mathematical error-based tuning. This
method is based on resolve the on line sliding surface gain (ߣ) as well as improve the output
performance by tuning the sliding surface slope updating factor (ߙ). Mathematical error-based
tuning sliding mode controllers is stable model-free controller and eliminates the chattering
phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in
mathematical error-based tuning fuzzy sliding mode controller based on switching (sign) function.
Section 2, is served as an introduction to the sliding mode controller formulation algorithm and its
application to control of robot manipulator. Part 3, introduces and describes the methodology
(design mathematical error-based sliding mode controller) algorithms and proves Lyapunov
stability. Section 4 presents the simulation results and discussion of this algorithm applied to a
robot arm and the final section is describing the conclusion.
2. THEOREM: DYNAMIC FORMULATION OF ROBOTIC MANIPULATOR,
SLIDING MODE FORMULATION APPLIED TO ROBOT ARM AND PROOF OF
STABILITY
Dynamic of robot arm: The equation of an n-DOF robot manipulator governed by the following
equation [1, 4, 15-29, 63-74]:
ࡹሺሻሷ ࡺሺ, ሶ ሻ ൌ ࣎ (1)
Where τ is actuation torque, M (q) is a symmetric and positive define inertia matrix, ܰሺ,ݍ ݍሶሻ is the
vector of nonlinearity term. This robot manipulator dynamic equation can also be written in a
following form [1-29]:
࣎ ൌ ࡹሺሻሷ ሺሻሾሶ ሶ ሿ ሺሻሾሶ ሿ
ࡳሺሻ (2)
Where B(q) is the matrix of coriolios torques, C(q) is the matrix of centrifugal torques, and G(q) is
the vector of gravity force. The dynamic terms in equation (2) are only manipulator position. This
is a decoupled system with simple second order linear differential dynamics. In other words, the
component ݍሷ influences, with a double integrator relationship, only the joint variableݍ,
independently of the motion of the other joints. Therefore, the angular acceleration is found as to
be [3, 41-62]:
ሷ ൌ ࡹିሺሻ. ሼ࣎ െ ࡺሺ, ሶ ሻሽ (3)
This technique is very attractive from a control point of view.
Sliding Mode methodology: Consider a nonlinear single input dynamic system is defined by [6]:
࢞ሺሻ
ൌ ࢌሺ࢞ሬሬԦሻ ࢈ሺ࢞ሬሬԦሻ࢛ (4)
Where u is the vector of control input, ࢞ሺሻ
is the ࢚ࢎ
derivation of ࢞, ࢞ ൌ ሾ࢞, ࢞ሶ, ࢞ሷ, … , ࢞ሺିሻ
ሿࢀ
is
the state vector, ࢌሺ࢞ሻ is unknown or uncertainty, and ࢈ሺ࢞ሻ is of known sign function. The main
goal to design this controller is train to the desired state; ࢞ࢊ ൌ ሾ࢞ࢊ, ࢞ሶࢊ, ࢞ሷࢊ, … , ࢞ࢊ
ሺିሻ
ሿࢀ
, and
trucking error vector is defined by [6]:
࢞ ൌ ࢞ െ ࢞ࢊ ൌ ሾ࢞, … , ࢞ሺିሻ
ሿࢀ (5)
A time-varying sliding surface ࢙ሺ࢞, ࢚ሻ in the state space ࡾ
is given by [6]:
5. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 100
࢙ሺ࢞, ࢚ሻ ൌ ሺ
ࢊ
ࢊ࢚
ࣅሻି
࢞ ൌ
(6)
where λ is the positive constant. To further penalize tracking error, integral part can be used in
sliding surface part as follows [6]:
࢙ሺ࢞, ࢚ሻ ൌ ሺ
݀
݀ݐ
ࣅሻି ቆන ࢞
࢚
ࢊ࢚ቇ ൌ
(7)
The main target in this methodology is kept the sliding surface slope ࢙ሺ࢞, ࢚ሻ near to the zero.
Therefore, one of the common strategies is to find input ࢁ outside of ࢙ሺ࢞, ࢚ሻ [6].
ࢊ
ࢊ࢚
࢙ሺ࢞, ࢚ሻ െࣀ|࢙ሺ࢞, ࢚ሻ|
(8)
where ζ is positive constant.
If S(0)>0՜
܌
ܜ܌
܁ሺܜሻ െા (9)
To eliminate the derivative term, it is used an integral term from t=0 to t=࢚࢘ࢋࢇࢉࢎ
න
ࢊ
ࢊ࢚
࢚ୀ࢚࢘ࢋࢇࢉࢎ
࢚ୀ
ࡿሺ࢚ሻ െ න ࣁ ՜ ࡿ
࢚ୀ࢚࢘ࢋࢇࢉࢎ
࢚ୀ
ሺ࢚࢘ࢋࢇࢉࢎሻ െ ࡿሺሻ െࣀሺ࢚࢘ࢋࢇࢉࢎ െ ሻ
(10)
Where ݐ is the time that trajectories reach to the sliding surface so, suppose S(ݐ ൌ 0ሻ
defined as
െ ࡿሺሻ െࣁሺ࢚࢘ࢋࢇࢉࢎሻ ՜ ࢚࢘ࢋࢇࢉࢎ
ࡿሺሻ
ࣀ
(11)
and
ࢌ ࡿሺሻ ൏ 0 ՜ 0 െ ܵሺሻ െࣁሺ࢚࢘ࢋࢇࢉࢎሻ ՜ ࡿሺሻ െࣀሺ࢚࢘ࢋࢇࢉࢎሻ ՜ ࢚࢘ࢋࢇࢉࢎ
|ࡿሺሻ|
ࣁ
(12)
Equation (12) guarantees time to reach the sliding surface is smaller than
|ࡿሺሻ|
ࣀ
since the
trajectories are outside of ܵሺݐሻ.
ࢌ ࡿ࢚࢘ࢋࢇࢉࢎ
ൌ ࡿሺሻ ՜ ࢋ࢘࢘࢘ሺ࢞ െ ࢞ࢊሻ ൌ (13)
suppose S is defined as
࢙ሺ࢞, ࢚ሻ ൌ ሺ
ࢊ
ࢊ࢚
ࣅሻ ࢞ ൌ ሺܠሶ െ ܠሶ܌ሻ ૃሺܠ െ ܠ܌ሻ
(14)
The derivation of S, namely, ܵሶ can be calculated as the following;
ࡿሶ ൌ ሺܠሷ െ ܠሷ܌ሻ ૃሺܠሶ െ ܠሶ܌ሻ (15)
suppose the second order system is defined as;
࢞ሷ ൌ ࢌ ࢛ ՜ ࡿሶ ൌ ࢌ ࢁ െ ࢞ሷࢊ ૃሺܠሶ െ ܠሶ܌ሻ (16)
Where ࢌ is the dynamic uncertain, and also since ܵ ൌ 0 ܽ݊݀ ܵሶ ൌ 0, to have the best
approximation ,ࢁ is defined as
ࢁ ൌ െࢌ ࢞ሷࢊ െ ࣅሺܠሶ െ ܠሶ܌ሻ (17)
A simple solution to get the sliding condition when the dynamic parameters have uncertainty is
the switching control law:
ࢁࢊ࢙ ൌ ࢁ െ ࡷሺ࢞ሬሬԦ, ࢚ሻ · ܖܛሺ࢙ሻ (18)
where the switching function ܖܛሺ܁ሻ is defined as [1, 6]
࢙ࢍሺ࢙ሻ ൌ ൝
࢙ 0
െ ࢙ ൏ 0
࢙ ൌ
(19)
and the ࡷሺ࢞ሬሬԦ, ࢚ሻ is the positive constant. Suppose by (8) the following equation can be written as,
6. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 101
ࢊ
ࢊ࢚
࢙ሺ࢞, ࢚ሻ ൌ ܁ ·ሶ ܁ ൌ ൣࢌ െ ࢌ െ ࡷܖܛሺ࢙ሻ൧ · ࡿ ൌ ൫ࢌ െ ࢌ൯ · ࡿ െ ࡷ|ࡿ|
(20)
and if the equation (12) instead of (11) the sliding surface can be calculated as
࢙ሺ࢞, ࢚ሻ ൌ ሺ
ࢊ
ࢊ࢚
ࣅሻ ቆන ࢞
࢚
ࢊ࢚ቇ ൌ ሺܠሶ െ ܠሶ܌ሻ ࣅሺܠሶ െ ܠሶ܌ሻ െ ૃሺܠ െ ܠ܌ሻ
(21)
in this method the approximation of ࢁ is computed as [6]
ࢁ ൌ െࢌ ࢞ሷࢊ െ ࣅሺܠሶ െ ܠሶ܌ሻ ૃሺܠ െ ܠ܌ሻ (22)
Based on above discussion, the sliding mode control law for a multi degrees of freedom robot
manipulator is written as [1, 6]:
࣎ ൌ ࣎ࢋ ࣎ࢊ࢙ (23)
Where, the model-based component ࣎ࢋ is the nominal dynamics of systems and ࣎ࢋ for first 3
DOF PUMA robot manipulator can be calculate as follows [1]:
࣎ࢋ ൌ ൣࡹିሺ ࡳሻ ࡿሶ൧ࡹ (24)
and ࣎ࢊ࢙ is computed as [1];
࣎ࢊ࢙ ൌ ࡷ · ܖܛሺࡿሻ (25)
by replace the formulation (25) in (23) the control output can be written as;
࣎ ൌ ࣎ࢋ ࡷ. ܖܛሺࡿሻ (26)
By (26) and (24) the sliding mode control of PUMA 560 robot manipulator is calculated as;
࣎ ൌ ൣࡹିሺ ࡳሻ ࡿሶ൧ࡹ ࡷ · ܖܛሺࡿሻ (27)
where ܵ ൌ ߣ݁ ݁ሶ in PD-SMC and ܵ ൌ ߣ݁ ݁ሶ ሺ
ఒ
ଶ
ሻଶ ∑ ݁ in PID-SMC.
Proof of Stability: the lyapunov formulation can be written as follows,
ࢂ ൌ
ࡿࢀ
. ࡹ. ࡿ
(28)
the derivation of ܸ can be determined as,
ࢂሶ ൌ
ࡿࢀ
. ࡹሶ . ࡿ ࡿࢀ
ࡹࡿሶ (29)
the dynamic equation of IC engine can be written based on the sliding surface as
ࡹࡿሶ ൌ െࢂࡿ ࡹࡿሶ ࡳ (30)
it is assumed that
ࡿࢀ൫ࡹሶ െ ࡳ൯ࡿ ൌ (31)
by substituting (30) in (29)
ࢂሶ ൌ
ࡿࢀ
ࡹሶ ࡿ െ ࡿࢀ
ࡿ ࡿࢀ൫ࡹࡿሶ ࡿ ࡳ൯ ൌ ࡿࢀ൫ࡹࡿሶ ࡿ ࡳ൯
(32)
suppose the control input is written as follows
ࢁ ൌ ࢁࡺଙࢋࢇ࢘
ࢁࢊଙ࢙
ൌ ൣࡹିሺ ࡳሻ ࡿሶ൧ࡹ ࡷ. ࢙ࢍሺࡿሻ ࡿ ࡳ (33)
by replacing the equation (33) in (32)
ࢂሶ ൌ ࡿࢀ
ሺࡹࡿሶ ࡳ െ ࡹ ࡿሶ െ ࡿ ࡳ െ ࡷ࢙ࢍሺࡿሻ ൌ ࡿࢀ ቀࡹ෩ ࡿሶ ෫ ࡿ ࡳ െ
ࡷ࢙ࢍሺࡿሻ൯
(34)
7. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 102
it is obvious that
หࡹ෩ ࡿሶ ෫ ࡿ ࡳห หࡹ෩ ࡿሶห ห ෫ ࡿ ࡳห (35)
the Lemma equation in robot arm system can be written as follows
ࡷ࢛ ൌ ൣหࡹ෩ ࡿሶห | ࡿ ࡳ| ࣁ൧
, ൌ , , , , … (36)
the equation (11) can be written as
ࡷ࢛ ቚൣࡹ෩ ࡿሶ ࡿ ࡳ൧
ቚ ࣁ
(37)
therefore, it can be shown that
ࢂሶ െ ࣁ
ୀ
|ࡿ|
(38)
Consequently the equation (38) guaranties the stability of the Lyapunov equation. Figure 1 is
shown pure sliding mode controller, applied to robot arm.
FIGURE 1: Block diagram of a sliding mode controller: applied to robot arm
2. METHODOLOGY: DESIGN MATHEMATICAL ERROR-BASED
CHATTERING FREE SLIDING MODE CONTROLLER WITH SWITCHING
FUNCTION
Sliding mode controller has difficulty in handling unstructured model uncertainties. It is possible to
solve this problem by combining sliding mode controller and mathematical error-based tuning
method which this method can helps to eliminate the chattering in presence of switching function
method and improves the system’s tracking performance by online tuning method. In this
research the nonlinear equivalent dynamic (equivalent part) formulation problem in uncertain
system is solved by using on-line mathematical error-based tuning theorem. In this method
mathematical error-based theorem is applied to sliding mode controller to estimate the nonlinear
equivalent part. Sliding mode controller has difficulty in handling unstructured model
uncertainties and this controller’s performance is sensitive to sliding surface slope coefficient. It is
possible to solve above challenge by combining mathematical error-based tuning method and
8. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 103
sliding mode controller which this methodology can help to improve system’s tracking
performance by on-line tuning (mathematical error-based tuning) method. Based on above
discussion, compute the best value of sliding surface slope coefficient has played important role
to improve system’s tracking performance especially when the system parameters are unknown
or uncertain. This problem is solved by tuning the surface slope coefficient (ࣅ) of the sliding mode
controller continuously in real-time. In this methodology, the system’s performance is improved
with respect to the classical sliding mode controller. Figure 2 shows the mathematical error-based
tuning sliding mode controller. Based on (23) and (27) to adjust the sliding surface slope
coefficient we define ݂መሺߣ|ݔሻ as the fuzzy based tuning.
FIGURE 2: Block diagram of a mathematical error-based sliding mode controller: applied to
robot arm
ࢌሺ࢞|ࣅሻ ൌ ࣅࢀ
ࢻ (39)
If minimum error (ࣅכ
) is defined by;
ࣅכ
ൌ ࢇ࢘ࢍ ሾቀࡿ࢛ቚࢌሺ࢞|ࣅሻ െ ࢌሺ࢞ሻቁሿ (40)
Where ߣ்
is adjusted by an adaption law and this law is designed to minimize the error’s
parameters of ࣅ െ ࣅכ
. adaption law in mathematical error-based tuning sliding mode controller is
used to adjust the sliding surface slope coefficient. Mathematical error-based tuning part is a
supervisory controller based on the following formulation methodology. This controller has three
inputs namely; error ሺ݁ሻ, change of error (݁ሶ) and the second derivative of error (݁ሷ) and an output
namely; gain updating factorሺߙሻ. As a summary design a mathematical error-based tuning is
based on the following formulation:
ࢻ ൌ ࢋ
െ
ሺቀ
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
ቁିሻ
ା|ࢋ|
+C
ࢋሶሺכሻ ൌ ࢋሶሺ࢚ሻ ࢌ ࢋሶሺ࢚ሻ ࢋሶሺ࢚ െ ሻ
ࢋሶሺכሻ ൌ ࢋሶሺ࢚ െ ሻ ࢌ ࢋሶሺ࢚ െ ሻ ࢋሶሺ࢚ሻ
(41)
Where ሺߙሻ is gain updating factor, (݁ሷ) is the second derivative of error, (݁ሶ) is change of error, ሺ݁ሻ
is error and C is a coefficient.
Proof of Stability: The Lyapunov function in this design is defined as
9. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 104
ࢂ ൌ
ࡿࢀ
ࡹࡿ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘ
(42)
where ߛ௦ is a positive coefficient, ࣘ ൌ ࣅכ
െ ࣅ, ࣂכ
is minimum error and ߣ is adjustable parameter.
Since ܯሶ െ 2ܸ is skew-symetric matrix;
ࡿࢀ
ࡹࡿሶ
ࡿࢀ
ࡹሶ ࡿ ൌ ࡿࢀ
ሺࡹࡿሶ ࢂࡿሻ
(43)
If the dynamic formulation of robot manipulator defined by
࣎ ൌ ࡹሺሻሷ ࢂሺ, ሶ ሻሶ ࡳሺሻ (44)
the controller formulation is defined by
࣎ ൌ ࡹ ሷ ࢘ ࢂሶ ࢘ ࡳ െ ࣅࡿ െ ࡷ (45)
According to (43) and (44)
ࡹሺሻሷ ࢂሺ, ሶ ሻሶ ࡳሺሻ ൌ ࡹ ሷ ࢘ ࢂሶ ࢘ ࡳ െ ࣅࡿ െ ࡷ (46)
Since ሶ ࢘ ൌ ሶ െ ࡿ and ሷ ࢘ ൌ ሷ െ ࡿሶ
ࡹࡿሶ ሺࢂ ࣅሻࡿ ൌ ∆ࢌ െ ࡷ (47)
ࡹࡿሶ ൌ ઢࢌ െ ࡷ െ ࢂࡿ െ ࣅࡿ
The derivation of V is defined
ࢂሶ ൌ ࡿࢀ
ࡹࡿሶ
ࡿࢀ
ࡹሶ ࡿ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘሶ
(48)
ࢂሶ ൌ ࡿࢀ
ሺࡹࡿሶ ࢂࡿሻ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘሶ
Based on (46) and (47)
ࢂሶ ൌ ࡿࢀ
ሺઢࢌ െ ࡷ െ ࢂࡿ െ ࣅࡿ ࢂࡿሻ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘሶ
(49)
where ∆݂ ൌ ሾܯሺݍሻݍሷ ܸሺ,ݍ ݍሶሻݍሶ ܩሺݍሻሿ െ ∑ ࣅࢀெ
ୀଵ ࢻ
ࢂሶ ൌ ൣࡿሺઢࢌܒ െ ࡷሻ൧
ࡹ
ࡶୀ
െࡿࢀ
ࣅࡿ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘሶ
suppose ߙ is defined as follows
ࢻ ൌ ࢋ
െ
ሺ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ሻ
|ࢋ|
۱
(50)
according to 48 and 49;
ࢂሶ ൌ
ۏ
ێ
ێ
ێ
ۍ
ࡿሺઢࢌܒ െ ࣅࢀ
ሾࢋ
െ
ቆ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ቇ
|ࢋ|
۱ሿ
ے
ۑ
ۑ
ۑ
ېࡹ
ࡶୀ
െࡿࢀ
ࣅࡿ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘሶ
(51)
Based on ࣘ ൌ ࣂכ
െ ࣂ ՜ ࣂ ൌ ࣂכ
െ ࣘ
10. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 105
ࢂሶ ൌ
ۏ
ێ
ێ
ێ
ۍ
ࡿሺઢࢌܒ െ ࣂࢀכ
ሾࢋ
െ
ቆ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ቇ
|ࢋ|
۱ሿ ࣘࢀ
ሾࢋ
െ
ቆ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ቇ
|ࢋ|
۱ሿ
ے
ۑ
ۑ
ۑ
ېࡹ
ࡶୀ
െࡿࢀ
ࣅࡿ
ࢽ࢙
ࡹ
ࡶୀ
ࣘࢀ
. ࣘሶ
(52)
ࢂሶ ൌ
ۏ
ێ
ێ
ێ
ۍ
ࡿሺઢࢌܒ െ ሺࣅכ
ሻࢀ
ሾࢋ
െ
ቆ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ቇ
|ࢋ|
۱ሿ
ے
ۑ
ۑ
ۑ
ېࡹ
ࡶୀ
െࡿࢀ
ࣅࡿ
ࢽ࢙
ࡹ
ࡶୀ
ࣘ
ࢀ
ሾࢋ
െ
ሺ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ሻ
|ࢋ|
۱
ࣘሶ ሿሻ
where ࣂሶ ൌ ࢋ
െ
ሺቀ
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
ቁିሻ
ା|ࢋ|
۱ is adaption law, ଚ
ሶ ൌ െࣂሶ ൌ െሾࢋ
െ
ሺቀ
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
ቁିሻ
ା|ࢋ|
۱ሿ
ࢂሶ is considered by
ࢂሶ ൌ ሾࡿ
ୀ
∆ࢌ െ ൮ሺࣅ
כ
ሻࢀ
ࢋ
െ
ሺ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ሻ
|ࢋ|
۱൲ሿ െ ࡿࢀ
ࣅࡿ
(53)
The minimum error is defined by
ࢋ ൌ ∆ࢌ െ ൮ሺࣅ
כ
ሻࢀ
ࢋ
െ
ሺ൬
ࢋሷሺ࢚ሻ
ࢋሶሺכሻ
൰ െ ሻ
|ࢋ|
۱൲
(54)
Therefore ࢂሶ is computed as
ࢂሶ ൌ ሾࡿ
ୀ
ࢋሿ െ ࡿࢀ
ࣅࡿ
(55)
∑ |ࡿ
ୀ ||ࢋ| െ ࡿࢀ
ࣅࡿ
ൌ |ࡿ
ୀ
||ࢋ| െ ࣅࡿ
ൌ |ࡿ
ୀ
|൫หࢋห െ ࣅࡿ൯
(56)
For continuous function ݃ሺݔሻ, and suppose ߝ 0 it is defined the fuzzy logic
system in form of
ࡿ࢛࢞ࢁא|ࢌሺ࢞ሻ െ ࢍሺ࢞ሻ| ൏ ߳ (57)
the minimum approximation error ሺ݁ሻ is very small.
ࢌ ࣅ ൌ ࢻ ࢚ࢎࢇ࢚ ࢻหࡿห ࢋ ൫ࡿ ് ൯ ࢚ࢎࢋ ࢂሶ ൏ 0 ݂ݎ ൫ࡿ ് ൯ (58)
3. RESULTS
Pure sliding mode controller has difficulty in handling unstructured model uncertainties. It is
possible to solve this problem by combining sliding mode controller and mathematical error-based
tuning in a single IC chip or combining sliding mode controller by fuzzy logic method (FSMC).
These methods can improve the system’s tracking performance by online tuning method or soft
computing method. Proposed method is based on resolve the on line sliding surface slope as well
11. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 106
as improve the output performance by tuning the sliding surface slope coefficient. The sliding
surface gain (ࣅ) of this controller is adjusted online depending on the last values of error ሺ݁ሻ,
change of error (݁ሶ) and power two of derivative of error (݁ሷ) by sliding surface slope updating factor
(ߙሻ. Fuzzy sliding mode controller is based on applied fuzzy logic in sliding mode controller to
estimate the dynamic formulation in equivalent part. Mathematical error-based tuning sliding
mode controller is stable model-based controller which does not need to limits the dynamic model
of robot manipulator and eliminate the chattering phenomenon without to use the boundary layer
saturation function.
This section is focused on compare between Sliding Mode Controller (SMC), Fuzzy Sliding Mode
Controller (FSMC) and mathematical error-based tuning Sliding Mode Controller (MTSMC).
These controllers were tested by step responses. In this simulation, to control position of PUMA
robot manipulator the first, second, and third joints are moved from home to final position without
and with external disturbance. The simulation was implemented in Matlab/Simulink environment.
trajectory performance, torque performance, disturbance rejection, steady state error and
RMS error are compared in these controllers. These systems are tested by band limited white
noise with a predefined 10%, 20% and 40% of relative to the input signal amplitude. This type of
noise is used to external disturbance in continuous and hybrid systems and applied to nonlinear
dynamic of these controllers.
Tracking Performances
Based on (27) in sliding mode controller; controllers performance are depended on the gain
updating factor ()ܭ and sliding surface slope coefficient (ߣ). These two coefficients are computed
by trial and error in SMC. The best possible coefficients in step FSMC are; ܭ ൌ ܭ௩ ൌ ܭ ൌ 18,
ଵ ൌ ଶ ൌ ଷ ൌ 0.1, ܽ݊݀ ߣଵ ൌ 3, ߣଶ ൌ 6, ߣଷ ൌ 6 and the best possible coefficients in step SMC are;
ߣଵ ൌ 1 , ߣଶ ൌ 6, ߣଷ ൌ 8; ܭ ൌ ܭ௩ ൌ ܭ ൌ 10; ଵ ൌ ଶ ൌ ଷ ൌ 0.1. In mathematical error-based tuning
sliding mode controller the sliding surface gain is adjusted online depending on the last values of
error ሺ݁ሻ, change of error (݁ሶ) and the second derivation of error (݁ሷ) by sliding surface slope
updating factor (ߙሻ. Figure 3 shows tracking performance in mathematical error-based tuning
sliding mode controller (MTSMC), fuzzy sliding mode controller (FSMC) and SMC without
disturbance for step trajectory.
12. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 107
FIGURE 3 FSMC, MTSMC, desired input and SMC for first, second and third link step trajectory
performance without disturbance
Based on Figure 3 it is observed that, the overshoot in MTSMC is 0%, in SMC’s is 1% and in
FSMC’s is 0%, and rise time in MTSMC’s is 0.6 seconds, in SMC’s is 0.483 second and in
FSMC’s is about 0.6 seconds. From the trajectory MATLAB simulation for MTSMC, SMC and
FSMC in certain system, it was seen that all of three controllers have acceptable performance.
Disturbance Rejection
Figures 4 to 6 show the power disturbance elimination in MTSMC, SMC and FSMC with
disturbance for step trajectory. The disturbance rejection is used to test the robustness
comparisons of these three controllers for step trajectory. A band limited white noise with
predefined of 10%, 20% and 40% the power of input signal value is applied to the step trajectory.
It found fairly fluctuations in SMC and FSMC trajectory responses.
FIGURE 4 : Desired input, MTSMC, FSMC and SMC for first, second and third link trajectory with
10%external disturbance: step trajectory
Based on Figure 4; by comparing step response trajectory with 10% disturbance of relative to the
input signal amplitude in MTSMC, FSMC and SMC, MTSMC’s overshoot about (0%) is lower than
FSMC’s (0.5%) and SMC’s (1%). SMC’s rise time (0.5 seconds) is lower than FSMC’s (0.63
second) and MTSMC’s (0.65 second). Besides the Steady State and RMS error in MTSMC,
FSMC and SMC it is observed that, error performances in MTSMC (Steady State error =1.08e-
12 and RMS error=1.5e-12) are bout lower than FSMC (Steady State error =1.08e-6 and RMS
error=1.5e-6) and SMC’s (Steady State error=1.6e-6 and RMS error=1.9e-6).
13. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 108
FIGURE 5: Desired input, MTSMC, FSMC and SMC for first, second and third link trajectory with
20%external disturbance: step trajectory
Based on Figure 5; by comparing step response trajectory with 20% disturbance of relative to the
input signal amplitude in MTSMC, FSMC and SMC, MTSMC’s overshoot about (0%) is lower than
FSMC’s (1.8%) and SMC’s (2.1%). SMC’s rise time (0.5 seconds) is lower than FSMC’s (0.63
second) and MTSMC’s (0.66 second). Besides the Steady State and RMS error in FTFSMC,
FSMC and PD-SMC it is observed that, error performances in MTSMC (Steady State error
=1.2e-12 and RMS error=1.8e-12) are about lower than FSMC (Steady State error =1.7e-5 and
RMS error=2e-5) and SMC’s (Steady State error=1.8e-5 and RMS error=2e-5). Based on
Figure 6, it was seen that, MTSMC’s performance is better than FSMC and SMC because
MTSMC can auto-tune the sliding surface slope coefficient as the dynamic manipulator
parameter’s change and in presence of external disturbance whereas FSMC and SMC cannot.
14. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 109
FIGURE 6 : Desired input, MTSMC, FSMC and SMC for first, second and third link trajectory with
40%external disturbance: step trajectory
Based on Figure 6; by comparing step response trajectory with 40% disturbance of relative to the
input signal amplitude in MTSMC, SMC and FSMC, MTSMC’s overshoot about (0%) is lower than
FSMC’s (6%) and PD-SMC’s (8%). SMC’s rise time (0.5 seconds) is lower than FSMC’s (0.7
second) and MTSMC’s (0.8 second). Besides the Steady State and RMS error in MTSMC,
FSMC and SMC it is observed that, error performances in MTSMC (Steady State error =1.3e-12
and RMS error=1.8e-12) are about lower than FSMC (Steady State error =10e-4 and RMS
error=0.69e-4) and SMC’s (Steady State error=10e-4 and RMS error=11e-4). Based on Figure
7, FSMC and SMC have moderately oscillation in trajectory response with regard to 40% of the
input signal amplitude disturbance but MTSMC has stability in trajectory responses in presence of
uncertainty and external disturbance. Based on Figure 6 in presence of 40% unstructured
disturbance, MTSMC’s is more robust than FSMC and SMC because MTSMC can auto-tune the
sliding surface slope coefficient as the dynamic manipulator parameter’s change and in presence
of external disturbance whereas FSMC and SMC cannot.
Torque Performance
Figures 7 and 8 have indicated the power of chattering rejection in MTSMC, SMC and FSMC with
40% disturbance and without disturbance.
15. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 110
FIGURE 7 : MTSMC, SMC and FSMC for first, second and third link torque performance without
disturbance
Figure 7 shows torque performance for first three links PUMA robot manipulator in MTSMC, SMC
and FSMC without disturbance. Based on Figure 7, MTSMC, SMC and FSMC give considerable
torque performance in certain system and all three of controllers eliminate the chattering
phenomenon in certain system. Figure 8 has indicated the robustness in torque performance for
first three links PUMA robot manipulator in MTSMC, SMC and FSMC in presence of 40%
disturbance. Based on Figure 8, it is observed that SMC and FSMC controllers have oscillation
but MTSMC has steady in torque performance. This is mainly because pure SMC with saturation
function and fuzzy sliding mode controller with saturation function are robust but they have
limitation in presence of external disturbance. The MTSMC gives significant chattering elimination
when compared to FSMC and SMC. This elimination of chattering phenomenon is very significant
in presence of 40% disturbance. This challenge is one of the most important objectives in this
research.
16. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 111
FIGURE 8: MTSMC, SMC and FSMC for first, second and third link torque performance with40%
disturbance
Based on Figure 8 it is observed that, however mathematical tuning error-based sliding mode
controller (MTSMC) is a model-based controller that estimate the nonlinear dynamic equivalent
formulation by system’s performance but it has significant torque performance (chattering
phenomenon) in presence of uncertainty and external disturbance. SMC and FSMC have
limitation to eliminate the chattering in presence of highly external disturbance (e.g., 40%
disturbance) but MTSMC is a robust against to highly external disturbance.
Steady State Error
Figure 9 is shown the error performance in MTSMC, SMC and FSMC for first three links of PUMA
robot manipulator. The error performance is used to test the disturbance effect comparisons of
these controllers for step trajectory. All three joint’s inputs are step function with the same step
time (step time= 1 second), the same initial value (initial value=0) and the same final value (final
value=5). Based on Figure 4, MTSMC’s rise time is about 0.6 second, SMC’s rise time is about
0.483 second and FSMC’s rise time is about 0.6 second which caused to create a needle wave in
the range of 5 (amplitude=5) and the different width. In this system this time is transient time and
this part of error introduced as a transient error. Besides the Steady State and RMS error in
MTSMC, FSMC and SMC it is observed that, error performances in MTSMC (Steady State error
=0.9e-12 and RMS error=1.1e-12) are about lower than FSMC (Steady State error =0.7e-8 and
RMS error=1e-7) and SMC’s (Steady State error=1e-8 and RMS error=1.2e-6).
17. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 112
FIGURE 9 : MTSMC, SMC and FSMC for first, second and third link steady state error without
disturbance: step trajectory
The MTSMC gives significant steady state error performance when compared to FSMC and
SMC. When applied 40% disturbances in MTSMC the RMS error increased approximately
0.0164% (percent of increase the MTSMC RMS error=
ሺସ% ௗ௦௧௨ ோெௌ
ௗ௦௧௨ோெௌ
ൌ
ଵ.଼ିଵଶ
ଵ.ଵିଵଶ
ൌ
0.0164%), in FSMC the RMS error increased approximately 6.9% (percent of increase the FSMC
RMS error=
ሺସ% ௗ௦௧௨ ோெௌ
ௗ௦௧௨ோெௌ
ൌ
.ଽିସ
ଵି
ൌ 6.9%)in SMC the RMS error increased
approximately 9.17% (percent of increase the PD-SMC RMS error=
ሺସ% ௗ௦௧௨ ோெௌ
ௗ௦௧௨ ோெௌ
ൌ
ଵଵିସ
ଵ.ଶି
ൌ 9.17%). In this part MTSMC, SMC and FSMC have been comparatively evaluation
through MATLAB simulation, for PUMA robot manipulator control. It is observed that however
MTSMC is independent of nonlinear dynamic equation of PUMA 560 robot manipulator but it can
guarantee the trajectory following and eliminate the chattering phenomenon in certain systems,
structure uncertain systems and unstructured model uncertainties by online tuning method.
4. CONCLUSION
Refer to this research, a mathematical error-based tuning sliding mode controller (MTSMC) is
proposed for PUMA robot manipulator. Pure sliding mode controller with saturation function and
fuzzy sliding mode controller with saturation function have difficulty in handling unstructured
model uncertainties. It is possible to solve this problem by combining fuzzy sliding mode
controller and mathematical error-based tuning. Since the sliding surface gain (ߣ) is adjusted by
mathematical error-based tuning method, it is nonlinear and continuous. The sliding surface slope
updating factor (ߙ) of mathematical error-based tuning part can be changed with the changes in
error, change of error and the second change of error. Sliding surface gain is adapted on-line by
sliding surface slope updating factor. In pure sliding mode controller and fuzzy sliding mode
controller the sliding surface gain is chosen by trial and error, which means pure sliding mode
controller and error-based fuzzy sliding mode controller have to have a prior knowledge of the
system uncertainty. If the knowledge is not available error performance and chattering
18. Farzin Piltan, Bamdad Boroomand, Arman Jahed & Hossein Rezaie
International Journal of Engineering (IJE), Volume (6) : Issue (2) : 2012 113
phenomenon are go up. In mathematical error-based tuning sliding mode controller the sliding
surface gain are updated on-line to compensate the system unstructured uncertainty. The stability
and convergence of the mathematical error-based tuning sliding mode controller based on
switching function is guarantee and proved by the Lyapunov method. The simulation results
exhibit that the mathematical error-based tuning sliding mode controller works well in various
situations. Based on theoretical and simulation results, it is observed that mathematical error-
based tuning sliding mode controller is a model-based stable control for robot manipulator. It is a
best solution to eliminate chattering phenomenon with saturation function in structure and
unstructured uncertainties.
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