As the robot manipulators are highly nonlinear, time varying and Multiple Input Multiple Output (MIMO)
systems, one of the most important challenges in the field of robotics is robot manipulators control with
acceptable performance. In this research paper, a simple and computationally efficient Fuzzy Logic
Controller is designed based on the Fuzzy Lyapunov Synthesis (FLS) for the position control of PUMA-560
robot manipulator. The proposed methodology enables the designer to systematically derive the rule base
thereby guarantees the stability of the controller. The methodology is model free and does not require any
information about the system nonlinearities, uncertainties, time varying parameters, etc. The performance
of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. The closed-loop control
performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a
large set of rules requires more on-line computational time and more parameters need to be adjusted.
Here, a Fuzzy Logic Controller is first designed and then the controller based on FLS is designed and
simulated with a minimum rule base. Finally the simulation results of the proposed controller are
compared with that of the normal Fuzzy Logic Controller and PD controlled Computed Torque Controller
(PD-CTC). Results show that the proposed controller outperformed the other controllers.
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.
Design Novel Nonlinear Controller Applied to Robot Manipulator: Design New Fe...Waqas Tariq
In this paper, fuzzy adaptive base tuning feedback linearization fuzzy methodology to adaption gain is introduced. The system performance in feedback linearization controller and feedback linearization fuzzy controller are sensitive to the main controller coefficient. Therefore, compute the optimum value of main controller coefficient for a system is the main important challenge work. This problem has solved by adjusting main fuzzy controller continuously in real-time. In this way, the overall system performance has improved with respect to the classical feedback linearization controller and feedback linearization fuzzy controller. Adaptive feedback linearization fuzzy controller solved external disturbance as well as mathematical nonlinear equivalent part by applied fuzzy supervisory method in feedback linearization fuzzy controller. The addition of an adaptive law to a feedback linearization fuzzy controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. Refer to this research; tuning methodology can online adjust coefficient parts of the fuzzy rules. Since this algorithm for is specifically applied to a robot manipulator.
Artificial Chattering Free on-line Fuzzy Sliding Mode Algorithm for Uncertain...CSCJournals
In this research, an artificial chattering free adaptive fuzzy sliding mode control design and application to uncertain 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 logic controller and adaptive method, the output has improved. Each method by adding to the previous controller has covered negative points. The main target in this research is design of model free estimator on-line sliding mode fuzzy algorithm for robot manipulator to reach an acceptable performance. Robot manipulators are highly nonlinear, and a number of parameters are uncertain, therefore design model free controller using both analytical and empirical paradigms are the main goal. Although classical sliding mode methodology 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. To solve the chattering fuzzy logic inference applied instead of dead zone function. To solve the equivalent problems in classical sliding mode controller this paper focuses on applied fuzzy logic method in classical controller. This algorithm works very well in certain environment but in uncertain or various dynamic parameters, it has slight chattering phenomenon. The system performance in sliding mode controller and fuzzy sliding mode controller are sensitive to the sliding function. Therefore, compute the optimum value of sliding function for a system is the next challenge. This problem has solved by adjusting sliding function of the adaptive method continuously in real-time. In this way, the overall system performance has improved with respect to the classical sliding mode controller. This controller solved chattering phenomenon as well as mathematical nonlinear equivalent part by applied fuzzy supervisory method in sliding mode fuzzy controller and tuning the sliding function.
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.
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.
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.
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.
Design Novel Nonlinear Controller Applied to Robot Manipulator: Design New Fe...Waqas Tariq
In this paper, fuzzy adaptive base tuning feedback linearization fuzzy methodology to adaption gain is introduced. The system performance in feedback linearization controller and feedback linearization fuzzy controller are sensitive to the main controller coefficient. Therefore, compute the optimum value of main controller coefficient for a system is the main important challenge work. This problem has solved by adjusting main fuzzy controller continuously in real-time. In this way, the overall system performance has improved with respect to the classical feedback linearization controller and feedback linearization fuzzy controller. Adaptive feedback linearization fuzzy controller solved external disturbance as well as mathematical nonlinear equivalent part by applied fuzzy supervisory method in feedback linearization fuzzy controller. The addition of an adaptive law to a feedback linearization fuzzy controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. Refer to this research; tuning methodology can online adjust coefficient parts of the fuzzy rules. Since this algorithm for is specifically applied to a robot manipulator.
Artificial Chattering Free on-line Fuzzy Sliding Mode Algorithm for Uncertain...CSCJournals
In this research, an artificial chattering free adaptive fuzzy sliding mode control design and application to uncertain 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 logic controller and adaptive method, the output has improved. Each method by adding to the previous controller has covered negative points. The main target in this research is design of model free estimator on-line sliding mode fuzzy algorithm for robot manipulator to reach an acceptable performance. Robot manipulators are highly nonlinear, and a number of parameters are uncertain, therefore design model free controller using both analytical and empirical paradigms are the main goal. Although classical sliding mode methodology 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. To solve the chattering fuzzy logic inference applied instead of dead zone function. To solve the equivalent problems in classical sliding mode controller this paper focuses on applied fuzzy logic method in classical controller. This algorithm works very well in certain environment but in uncertain or various dynamic parameters, it has slight chattering phenomenon. The system performance in sliding mode controller and fuzzy sliding mode controller are sensitive to the sliding function. Therefore, compute the optimum value of sliding function for a system is the next challenge. This problem has solved by adjusting sliding function of the adaptive method continuously in real-time. In this way, the overall system performance has improved with respect to the classical sliding mode controller. This controller solved chattering phenomenon as well as mathematical nonlinear equivalent part by applied fuzzy supervisory method in sliding mode fuzzy controller and tuning the sliding function.
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.
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.
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.
A Comparative Analysis of Fuzzy Based Hybrid Anfis Controller for Stabilizati...ijscmcj
This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters of the IP system. The results shows that ANFIS controller provides better results in comparison to both fuzzy controller.
A COMPARATIVE ANALYSIS OF FUZZY BASED HYBRID ANFIS CONTROLLER FOR STABILIZATI...ijscmcjournal
This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted
Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller
was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy
controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro
fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy
controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters
of the IP system. The results shows that ANFIS controller provides better results in comparison to both
fuzzy controller.
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.
Comparison of different controllers for the improvement of Dynamic response o...IJERA Editor
As the technology is fast changing, there is more and more use of machine intelligence in modern motor controllers. These controllers are employed in advanced electric motor drives in particular, the present day Induction motor drives. These systems emulate the human logic. This is particularly useful when the application has poorly defined mathematical model. In this present paper the analysis of fuzzy logic as the artificial intelligence is used. The comparative study of Fuzzy PI, Fuzzy MRAC is made. There is always a compromise of the cost and complexity. So this paper presents a new approach and its dynamic response in comparison to the Fuzzy PI and Fuzzy MRAC. The proposed controller is Fuzzy PI with scaling factors. This approach is validated with the Speed, torque responses of Indirect vector controlled Induction motor (IVCIM) drive.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Recurrent fuzzy neural network backstepping control for the prescribed output...ISA Interchange
This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator.
Position Control of Robot Manipulator: Design a Novel SISO Adaptive Sliding M...Waqas Tariq
This research focuses on design Single Input Single Output (SISO) adaptive sliding mode fuzzy PD fuzzy sliding mode algorithm with estimates the equivalent part derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Proposed method introduces a SISO fuzzy system to compensate for the model uncertainties of the system and eliminate the chattering by linear boundary layer method. This algorithm is used a SISO fuzzy system to alleviate chattering and to estimate the control gain in the control law and presented a scheme to online tune of sliding function. To attenuate the chattering phenomenon this method developed a linear boundary layer and the parameter of the sliding function is online tuned by adaptation laws. This algorithm will be analyzed and evaluated on robotic manipulators and design adaption laws of adaptive algorithms after that writing Lyapunov function candidates and prove the asymptotic convergence of the closed-loop system using Lyapunov stability theorem mathematically. Compare and evaluate proposed method and sliding mode algorithms under disturbance. In regards to the former, we will be looking at the availability of online tuning methodology and the number of fuzzy if-then rules inherent to the fuzzy system being used and the corresponding computational load. Our analysis of the results will be limited to tracking accuracy and chattering.
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.
On line Tuning Premise and Consequence FIS: Design Fuzzy Adaptive Fuzzy Slidi...Waqas Tariq
One of the most active research areas in the field of robotics is robot manipulators control, because these systems are multi-input multi-output (MIMO), nonlinear, and uncertainty. At present, robot manipulators is used in unknown and unstructured situation and caused to provide complicated systems, consequently strong mathematical tools are used in new control methodologies to design nonlinear robust controller with satisfactory performance (e.g., minimum error, good trajectory, disturbance rejection). Robotic systems controlling is vital due to the wide range of application. Obviously stability and robustness are the most minimum requirements in control systems; even though the proof of stability and robustness is more important especially in the case of nonlinear systems. One of the best nonlinear robust controllers which can be used in uncertainty nonlinear systems is sliding mode controller (SMC). Chattering phenomenon is the most important challenge in this controller. Most of nonlinear controllers need real time mobility operation; one of the most important devices which can be used to solve this challenge is Field Programmable Gate Array (FPGA). FPGA can be used to design a controller in a single chip Integrated Circuit (IC). In this research the SMC is designed using VHDL language for implementation on FPGA device (XA3S1600E-Spartan-3E), with minimum chattering and high processing speed (63.29 MHz).
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 research is focused on novel particle swarm optimization (PSO) SISO Lyapunov based fuzzy estimator sliding mode algorithms derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. PSO SISO fuzzy compensate sliding mode method design a SISO fuzzy system to compensate for the dynamic model uncertainties of the nonlinear dynamic system and chattering also solved by nonlinear fuzzy saturation like method. Adjust the sliding function is played important role to reduce the chattering phenomenon and also design acceptable estimator applied to nonlinear classical controller so PSO method is used to off-line tuning. 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 nonlinear (fuzzy) boundary like 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 applied fuzzy inference system into sliding mode algorithm to design and estimate model-free nonlinear dynamic equivalent part. 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 PSO method to a fuzzy sliding mode controller to tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The PSO method in this algorithm is designed based on the PSO stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov.
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).
Simulation design of trajectory planning robot manipulatorjournalBEEI
Robots can be mathematically modeled with computer programs where the results can be displayed visually, so it can be used to determine the input, gain, attenuate and error parameters of the control system. In addition to the robot motion control system, to achieve the target points should need a research to get the best trajectory, so the movement of robots can be more efficient. One method that can be used to get the best path is the SOM (Self Organizing Maps) neural network. This research proposes the usage of SOM in combination with PID and Fuzzy-PD control for finding an optimal path between source and destination. SOM Neural network process is able to guide the robot manipulator through the target points. The results presented emphasize that a satisfactory trajectory tracking precision and stability could be achieved using SOM Neural networking combination with PID and Fuzzy-PD controller.The obtained average error to reach the target point when using Fuzzy-PD=2.225% and when using PID=1.965%.
Velocity control of a two-wheeled inverted pendulum mobile robot: a fuzzy mod...journalBEEI
This paper presents the design of a fuzzy tracking controller for balancing and velocity control of a Two-Wheeled Inverted Pendulum (TWIP) mobile robot based on its Takagi-Sugino (T-S) fuzzy model, fuzzy Lyapunov function and non-parallel distributed compensation (non-PDC) control law. The T-S fuzzy model of the TWIP mobile robot was developed from its nonlinear dynamical equations of motion. Stabilization conditions in a form of linear matrix inequalities (LMIs) were derived based on the T-S fuzzy model of the TWIP mobile robot, a fuzzy Lyapunov function and a non-PDC control law. Based on the derived stabilization conditions and the T-S fuzzy model of the TWIP mobile robot, a state feedback velocity tracking controller was then proposed for the TWIP mobile robot. The balancing and velocity tracking performance of the proposed controller was investigated via simulations. The simulation result shows the effectiveness of the proposed control scheme.
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).
FRACTIONAL-ORDER PROPORTIONALINTEGRAL (FOPI) CONTROLLER FOR MECANUM-WHEELED R...IAEME Publication
This study presents experimental implementation of fractional-order proportionalintegral
(FOPI) controller on a Mecanum-wheeled robot (MWR), which is a system with
nonlinearities and uncertainties, in performing tracking of a complex path i.e. ∞-shaped
path. The FOPI controller is almost as simpler as proportional-integral (PI) controller
and has supplementary advantage over PI controller due to its fractional integral. The
tracking performances of both the controllers are compared and evaluated in terms of
integral of absolute error (IAE), integral of squared error (ISE) and root-mean-square of
error (RMSE). Experimental result shows that the FOPI controller exhibits iso-damping
properties and successfully attains tracking with reduced error. Also, in this paper,
discretization of FOPI controller by using zero-order hold (ZOH) is discussed and
presented for the purpose of programming implementation on microcontroller board.
Besides that, graphical visualization of FOPI controller is presented to provide an insight
and intuitive understanding on the characteristic of the controller
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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.
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.
ENERGY EFFICIENT ROUTING PROTOCOL BASED ON DSRijasuc
Energy consumption is a major concern in most of the present day devices in wireless networks. Especially
in Ad hoc networks, energy is a limited factor. Random movement in nodes add to the frequent failure of
routes which adds to the energy consumption in the network. In this paper, a routing protocol is proposed
which is based on a modification of the conventional DSR (Dynamic Source routing). A comparative
analysis is performed with respect to energy consumption, maximum throughput and delay. The routing
protocols used for reference in this analysis are DSDV, AODV and conventional DSR. Experimental results
show that the proposed modified DSR shows a reduced energy consumption, improved rate of maximum
throughput and a reduced delay compared to above mentioned routing protocols
A Comparative Analysis of Fuzzy Based Hybrid Anfis Controller for Stabilizati...ijscmcj
This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters of the IP system. The results shows that ANFIS controller provides better results in comparison to both fuzzy controller.
A COMPARATIVE ANALYSIS OF FUZZY BASED HYBRID ANFIS CONTROLLER FOR STABILIZATI...ijscmcjournal
This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted
Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller
was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy
controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro
fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy
controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters
of the IP system. The results shows that ANFIS controller provides better results in comparison to both
fuzzy controller.
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.
Comparison of different controllers for the improvement of Dynamic response o...IJERA Editor
As the technology is fast changing, there is more and more use of machine intelligence in modern motor controllers. These controllers are employed in advanced electric motor drives in particular, the present day Induction motor drives. These systems emulate the human logic. This is particularly useful when the application has poorly defined mathematical model. In this present paper the analysis of fuzzy logic as the artificial intelligence is used. The comparative study of Fuzzy PI, Fuzzy MRAC is made. There is always a compromise of the cost and complexity. So this paper presents a new approach and its dynamic response in comparison to the Fuzzy PI and Fuzzy MRAC. The proposed controller is Fuzzy PI with scaling factors. This approach is validated with the Speed, torque responses of Indirect vector controlled Induction motor (IVCIM) drive.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Recurrent fuzzy neural network backstepping control for the prescribed output...ISA Interchange
This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator.
Position Control of Robot Manipulator: Design a Novel SISO Adaptive Sliding M...Waqas Tariq
This research focuses on design Single Input Single Output (SISO) adaptive sliding mode fuzzy PD fuzzy sliding mode algorithm with estimates the equivalent part derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Proposed method introduces a SISO fuzzy system to compensate for the model uncertainties of the system and eliminate the chattering by linear boundary layer method. This algorithm is used a SISO fuzzy system to alleviate chattering and to estimate the control gain in the control law and presented a scheme to online tune of sliding function. To attenuate the chattering phenomenon this method developed a linear boundary layer and the parameter of the sliding function is online tuned by adaptation laws. This algorithm will be analyzed and evaluated on robotic manipulators and design adaption laws of adaptive algorithms after that writing Lyapunov function candidates and prove the asymptotic convergence of the closed-loop system using Lyapunov stability theorem mathematically. Compare and evaluate proposed method and sliding mode algorithms under disturbance. In regards to the former, we will be looking at the availability of online tuning methodology and the number of fuzzy if-then rules inherent to the fuzzy system being used and the corresponding computational load. Our analysis of the results will be limited to tracking accuracy and chattering.
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.
On line Tuning Premise and Consequence FIS: Design Fuzzy Adaptive Fuzzy Slidi...Waqas Tariq
One of the most active research areas in the field of robotics is robot manipulators control, because these systems are multi-input multi-output (MIMO), nonlinear, and uncertainty. At present, robot manipulators is used in unknown and unstructured situation and caused to provide complicated systems, consequently strong mathematical tools are used in new control methodologies to design nonlinear robust controller with satisfactory performance (e.g., minimum error, good trajectory, disturbance rejection). Robotic systems controlling is vital due to the wide range of application. Obviously stability and robustness are the most minimum requirements in control systems; even though the proof of stability and robustness is more important especially in the case of nonlinear systems. One of the best nonlinear robust controllers which can be used in uncertainty nonlinear systems is sliding mode controller (SMC). Chattering phenomenon is the most important challenge in this controller. Most of nonlinear controllers need real time mobility operation; one of the most important devices which can be used to solve this challenge is Field Programmable Gate Array (FPGA). FPGA can be used to design a controller in a single chip Integrated Circuit (IC). In this research the SMC is designed using VHDL language for implementation on FPGA device (XA3S1600E-Spartan-3E), with minimum chattering and high processing speed (63.29 MHz).
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 research is focused on novel particle swarm optimization (PSO) SISO Lyapunov based fuzzy estimator sliding mode algorithms derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. PSO SISO fuzzy compensate sliding mode method design a SISO fuzzy system to compensate for the dynamic model uncertainties of the nonlinear dynamic system and chattering also solved by nonlinear fuzzy saturation like method. Adjust the sliding function is played important role to reduce the chattering phenomenon and also design acceptable estimator applied to nonlinear classical controller so PSO method is used to off-line tuning. 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 nonlinear (fuzzy) boundary like 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 applied fuzzy inference system into sliding mode algorithm to design and estimate model-free nonlinear dynamic equivalent part. 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 PSO method to a fuzzy sliding mode controller to tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The PSO method in this algorithm is designed based on the PSO stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov.
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).
Simulation design of trajectory planning robot manipulatorjournalBEEI
Robots can be mathematically modeled with computer programs where the results can be displayed visually, so it can be used to determine the input, gain, attenuate and error parameters of the control system. In addition to the robot motion control system, to achieve the target points should need a research to get the best trajectory, so the movement of robots can be more efficient. One method that can be used to get the best path is the SOM (Self Organizing Maps) neural network. This research proposes the usage of SOM in combination with PID and Fuzzy-PD control for finding an optimal path between source and destination. SOM Neural network process is able to guide the robot manipulator through the target points. The results presented emphasize that a satisfactory trajectory tracking precision and stability could be achieved using SOM Neural networking combination with PID and Fuzzy-PD controller.The obtained average error to reach the target point when using Fuzzy-PD=2.225% and when using PID=1.965%.
Velocity control of a two-wheeled inverted pendulum mobile robot: a fuzzy mod...journalBEEI
This paper presents the design of a fuzzy tracking controller for balancing and velocity control of a Two-Wheeled Inverted Pendulum (TWIP) mobile robot based on its Takagi-Sugino (T-S) fuzzy model, fuzzy Lyapunov function and non-parallel distributed compensation (non-PDC) control law. The T-S fuzzy model of the TWIP mobile robot was developed from its nonlinear dynamical equations of motion. Stabilization conditions in a form of linear matrix inequalities (LMIs) were derived based on the T-S fuzzy model of the TWIP mobile robot, a fuzzy Lyapunov function and a non-PDC control law. Based on the derived stabilization conditions and the T-S fuzzy model of the TWIP mobile robot, a state feedback velocity tracking controller was then proposed for the TWIP mobile robot. The balancing and velocity tracking performance of the proposed controller was investigated via simulations. The simulation result shows the effectiveness of the proposed control scheme.
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).
FRACTIONAL-ORDER PROPORTIONALINTEGRAL (FOPI) CONTROLLER FOR MECANUM-WHEELED R...IAEME Publication
This study presents experimental implementation of fractional-order proportionalintegral
(FOPI) controller on a Mecanum-wheeled robot (MWR), which is a system with
nonlinearities and uncertainties, in performing tracking of a complex path i.e. ∞-shaped
path. The FOPI controller is almost as simpler as proportional-integral (PI) controller
and has supplementary advantage over PI controller due to its fractional integral. The
tracking performances of both the controllers are compared and evaluated in terms of
integral of absolute error (IAE), integral of squared error (ISE) and root-mean-square of
error (RMSE). Experimental result shows that the FOPI controller exhibits iso-damping
properties and successfully attains tracking with reduced error. Also, in this paper,
discretization of FOPI controller by using zero-order hold (ZOH) is discussed and
presented for the purpose of programming implementation on microcontroller board.
Besides that, graphical visualization of FOPI controller is presented to provide an insight
and intuitive understanding on the characteristic of the controller
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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.
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.
ENERGY EFFICIENT ROUTING PROTOCOL BASED ON DSRijasuc
Energy consumption is a major concern in most of the present day devices in wireless networks. Especially
in Ad hoc networks, energy is a limited factor. Random movement in nodes add to the frequent failure of
routes which adds to the energy consumption in the network. In this paper, a routing protocol is proposed
which is based on a modification of the conventional DSR (Dynamic Source routing). A comparative
analysis is performed with respect to energy consumption, maximum throughput and delay. The routing
protocols used for reference in this analysis are DSDV, AODV and conventional DSR. Experimental results
show that the proposed modified DSR shows a reduced energy consumption, improved rate of maximum
throughput and a reduced delay compared to above mentioned routing protocols
DESIGN OF OBSERVER BASED QUASI DECENTRALIZED FUZZY LOAD FREQUENCY CONTROLLER ...ijfls
This paper proposes Fuzzy Quasi Decentralized Functional Observers (FQDFO) for Load Frequency Control of inter-connected power systems. From the literature, it is well noticed about the need of
Functional Observers (FO’s) for power system applications. In past, conventional Functional Observers are used. Later, these conventional Functional Observers are replaced with Quasi Decentralized
Functional Observers (QDFO) to improve the system performance. In order to increase the efficacy of the
system, intelligent controllers gained importance. Due to their expertise knowledge, which is adaptive in
nature is applied successfully for FQDFO. For supporting the validity of the proposed observer FQDFO,
it is compared with full order Luenberger observer and QDFO for a two-area inter connected power system by taking parametric uncertainties into consideration. Computational results proved the robustness of the proposed observer.
WAVELET- FUZZY BASED MULTI TERMINAL TRANSMISSION SYSTEM PROTECTION SCHEME IN ...ijfls
In This Paper, A New Protection Scheme In The Areas Of Accurate Fault Detection, Classification And
Location Estimation For Multi Terminal Transmission System Compensated With Statcom Is Proposed.
The Fault Indices Of All The Phases At All The Terminals Are Obtained By Analyzing The Detail
Coefficients Of Current Signals Through Bior 1.5 Mother Wavelet. The Complete Digital Simulation Of A
Transmission System With Statcom Is Performed Using Matlab /Simulink For Fault Detection,
Classification, And Faulty Terminal Identification With Variations In Fault Distance And Fault Inception
Angle For All Types Of Faults And Fuzzy Inference System Is Used To Estimate The Fault Location. The
Protection Scheme Yielded Accurate Results Within Half Cycle And Show That The Above Scheme Is
Suitable For Multi Terminal Transmission System With And Without Statcom Compensation.
COMPARISON OF DIFFERENT APPROXIMATIONS OF FUZZY NUMBERSijfls
The notions of interval approximations of fuzzy numbers and trapezoidal approximations of fuzzy numbers have been discussed. Comparisons have been made between the close-interval approximation, valueambiguity
interval approximation and distinct approximation with the corresponding crisp and trapezoidal fuzzy numbers. A numerical example is included to justify the above mentioned notions.
In this paper, the notion a -anti fuzzy new-ideal of a PU-algebra are defined and discussed. The
homomorphic images (pre images) ofa -anti fuzzy new-ideal under homomorphism of a PU-algebras has
been obtained. Some related result have been derived.
Implementation of Fuzzy Controlled Photo Voltaic Fed Dynamic Voltage Restorer...ijfls
Power Quality(PQ) has become an area of concern in the electrical distribution system. Dynamic Voltage
Restorer(DVR) restores load voltage to a nominal balanced sinusoidal voltage, when the source voltage
has harmonic distortions, sag, swell and unbalances. In this paper a Photo Voltaic(PV) fed DVR is
proposed to mitigate PQ problems. The PV system can supply the maximum power to the load at a
particular operating point known as Maximum Power Point (MPP), at which the entire PV system operates
with maximum efficiency. A Fuzzy Controller based MPPT is implemented to generate the optimal voltage
from the photovoltaic system by modulating the duty cycle applied to the boost converter. The DVR is
implemented using a Fuzzy Logic Controller based voltage source inverter with Photovoltaic system. The
test system has been simulated and the efficacy of the proposed PV based Fuzzy controlled DVR is
compared with Proportional Integral (PI) controlled DVR.
Akmo-İnek hayvancılık sektöründeki işletmelerin verimliliğini yükseltmek ve risklerini azaltmak için tasarlanmış, kablosuz iletişim teknolojileri tabanlı bir çözümüdür.
Limited energy is the major driving factor for research on wireless sensor networks. Clustering alleviates
this energy shortage problem by reducing data traffic conveyed over the network and therefore several
clustering methods are proposed in the literature. Researchers put forward their methods by making
serious assumptions such as always locating single sink at one side of the topology or making clusters near
to the sink with smaller sizes. However, to the best of our knowledge, there is no comprehensive research
that investigates the effects of various structural alternatives on energy consumption of wireless sensor
networks. In this paper, we thoroughly analyse the impact of various structural approaches such as cluster
size, number of tiers in the topology, node density, position and number of sinks. Extensive simulation
results are provided. The results show that the best performance about lifetime prolongation is achieved by
locating a sufficient number of sinks around the network area.
The objective of this paper is to introduce a fuzzy linear programming problem with hexagonal fuzzy
numbers. Here the parameters are hexagonal fuzzy numbers and Simplex method is used to arrive an
optimal solution by a new method compared to the earlier existing method. This procedure is illustrated
with numerical example. This will further help the decision makers to come out with a feasible alternatives
with better economical viability.
Modeling the Adaption Rule in Contextaware Systemsijasuc
Context awareness is increasingly gaining applicability in interactive ubiquitous mobile computing
systems. Each context-aware application has its own set of behaviors to react to context modifications. This
paper is concerned with the context modeling and the development methodology for context-aware systems.
We proposed a rule-based approach and use the adaption tree to model the adaption rule of context-aware
systems. We illustrate this idea in an arithmetic game application.
Optimal Alternative Selection Using MOORA in Industrial Sector - A ijfls
Modern manufacturing organizations tend to face versatile challenges due to globalization, modern
lifestyle trends and rapid market requirements from both locally and globally placed competitors. The
organizations faces high stress from dual perspective namely enhancement in science and technology and
development of modern strategies. In such an instance, organizations were in a need of using an effective
decision making tool that chooses out optimal alternative that reduces time, complexity and highly
simplified. This paper explores a usage of new multi criteria decision making tool known as MOORA for
selecting the best alternatives by examining various case study. The study was covered up in two fold
manner by comparing MOORA with other MCDM and MADM approaches to identify its advantage for
selecting optimal alternative, followed by extending MOORA with interval grey numbers, crisp and interval
grey number and whitening coefficient and future scope of the present work concentrate on highlighting the
scope and gap between MOORA, Multiplicative form of MOORA(MULTIMOORA) and Multi objective
optimization on the basis of simple ratio analysis (MOOSRA) for numerous manufacturing and service
applications.
A FUZZY LOGIC BASED SCHEME FOR THE PARAMETERIZATION OF THE INTER-TROPICAL DIS...ijfls
In this paper, a Fuzzy Logic based scheme for the parameterization of the Inter-Tropical Discontinuity
(ITD) over Nigeria was presented. The scheme was developed in order to provide a computational basis for
Numerical Weather Prediction (NWP) modeling over Nigeria. The scheme uses a fuzzified 2.50 by 50
resolution grid box or 10 rows by 4 columns (10x4) matrix with the rows classified into 10 zones. The two extreme zones represented by the five (5) boundary points or two-dimensional (2-D) lattice nodes (O1 – O5), define the matrix boundaries or lattice edges, and hence, the meridional limits of the ITD position. The scheme is simple enough to be included as an ITD parameterization by NWP modelers over West Africa.
APPROXIMATE CONTROLLABILITY RESULTS FOR IMPULSIVE LINEAR FUZZY STOCHASTIC DIF...ijfls
In this paper, the approximate controllability of impulsive linear fuzzy stochastic differential equations with nonlocal conditions in Banach space is studied. By using the Banach fixed point
theorems, stochastic analysis, fuzzy process and fuzzy solution, some sufficient conditions are given for
the approximate controllability of the system.
GROUP FUZZY TOPSIS METHODOLOGY IN COMPUTER SECURITY SOFTWARE SELECTIONijfls
In today's interconnected world, the risk of malwares is a major concern for users. Antivirus software is a
device to prevent, discover, and eliminatemalwares such as, computer worm, trojan horses,computer
viruses,spyware and adware. In the competitive IT environment, due to availability of many antivirus
software and their diverse features evaluating them is an arguable and complicated issue for users which
has a significant impact on the efficiency of computers defense systems. The anti-virus selection problem
can be formulated as a multiple criteria decision making problem. This paper proposes an antivirus
evaluation model for computer users based on group fuzzy TOPSIS. We study a real world case of antivirus
software and define criteria for antivirus selection problem. Seven alternatives were selected from among
the most popular antiviruses in the market and seven criteria were determined by the experts. The study is
followed by the sensitivity analyses of the results which also gives valuable insights into the needs and
solutions for different users in different conditions.
This present paper includes the study Load Frequency Control (LFC) of power systems with several nonlinearities
like Generation Rate Constraint(GRC) and Boiler Dynamics (BD) including Superconducting
Magnetic Energy Storage (SMES) units using Type-2 Fuzzy System (T2FS) controllers . Here, Load
frequency control problem is dealt with a three – area interconnected system of Thermal-Thermal-Hydal
power system by observing the effects and variations of dynamic responses employing conventional
controller, Type-1 fuzzy controller and T2FS controller considering incremental increase of step
pertubations by 10% in the load. The salient advantage of this controller is its high insensitivity to large
load changes and plant parameter variations even in the presence of non-linearities. As the non-linearities
were considered in the system, the conventional and classical Fuzzy controllers does not provide adequate
control performance with the consideration of above nonlinearities. To overcome this drawback T2FS
Controller has been employed in the system. Therefore, the efficacy of the proposed T2FS controller is
found to be better than that of conventional controller and Type-1 Fuzzy controller in cosidreration with
overshoot, settling time and robustness.
The aim of this paper is to prove that fuzzy logic algorithm is a suitable control technique for fast processes such as electrical machines. This theory has been experimented on different kinds of electrical machines such as stepping motors, dc motors and induction machines (with 6 phases) and the experimental results show that the proposed fuzzy logic algorithm is the most suitable control technique for electrical machines since this algorithm is not time consuming and it is also robust between plant parameters variations.
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.
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).
Design Artificial Nonlinear Robust Controller Based on CTLC and FSMC with Tun...Waqas Tariq
One of the most active research areas in the field of robotics is robot manipulators control, because these systems are multi-input multi-output (MIMO), nonlinear, time variant and uncertainty. An artificial non linear robust controller design is major subject in this work. At present, robot manipulators are used in unknown and unstructured situation and caused to provide complicated systems, consequently nonlinear classical controllers are used in artificial intelligence control methodologies to design nonlinear robust controller with satisfactory performance (e.g., minimum error, good trajectory, disturbance rejection). Sliding mode controller (SMC) and computed torque controller (CTC) are the best nonlinear robust controllers which can be used in uncertainty nonlinear. Sliding mode controller has two most important challenges in uncertain systems: chattering phenomenon and nonlinear dynamic equivalent part. Computed torque controller works very well when all nonlinear dynamic parameters are known. This research is focused on the applied non-classical method (e.g., Fuzzy Logic) in robust classical method (e.g., Sliding Mode Controller and computed torque controller) in the presence of uncertainties and external disturbance to reduce the limitations. Applying the Mamdani’s error based fuzzy logic controller with minimum rules is the first goal that causes the elimination of the mathematical nonlinear dynamic in SMC and CTC. Second target focuses on the elimination of chattering phenomenon with regard to the variety of uncertainty and external disturbance in fuzzy sliding mode controller and computed torque like controller by optimization the tunable gain. Therefore fuzzy sliding mode controller with tunable gain (GTFSMC) and computed torque like controller with tunable gain (GTCTLC) will be presented in this paper.
PUMA-560 Robot Manipulator Position Computed Torque Control Methods Using MAT...Waqas Tariq
This paper describes the MATLAB/SIMULINK realization of the PUMA 560 robot manipulator position control methodology. This paper focuses on design, analyzed and implements nonlinear computed torque control (CTC) methods. 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.
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.
Design and Implementation of Sliding Mode Algorithm: Applied to Robot Manipul...Waqas Tariq
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Design of lyapunov based fuzzy logic
1. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
DESIGN OF LYAPUNOV BASED FUZZY LOGIC
CONTROLLER FOR PUMA-560 ROBOT
MANIPULATOR
1
1
Ch Ravi kumar 2DV Pushpalatha 3K R Sudha 4KA Gopala Rao
Research Scholar, Department of Electrical Engineering, Andhra University, India
2
Professor, Department of EEE, GRIET, Hyderabad, India
3
Professor, Department of Electrical Engineering, Andhra University, India
4
Professor, Department of EEE, GVPCE, Visakhapatnam
ABSTRACT
As the robot manipulators are highly nonlinear, time varying and Multiple Input Multiple Output (MIMO)
systems, one of the most important challenges in the field of robotics is robot manipulators control with
acceptable performance. In this research paper, a simple and computationally efficient Fuzzy Logic
Controller is designed based on the Fuzzy Lyapunov Synthesis (FLS) for the position control of PUMA-560
robot manipulator. The proposed methodology enables the designer to systematically derive the rule base
thereby guarantees the stability of the controller. The methodology is model free and does not require any
information about the system nonlinearities, uncertainties, time varying parameters, etc. The performance
of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. The closed-loop control
performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a
large set of rules requires more on-line computational time and more parameters need to be adjusted.
Here, a Fuzzy Logic Controller is first designed and then the controller based on FLS is designed and
simulated with a minimum rule base. Finally the simulation results of the proposed controller are
compared with that of the normal Fuzzy Logic Controller and PD controlled Computed Torque Controller
(PD-CTC). Results show that the proposed controller outperformed the other controllers.
KEYWORDS
PUMA-560 robot manipulator, Fuzzy controller, Fuzzy Lyapunov Synthesis.
1. INTRODUCTION
Robotic arm is an important class in the robot anatomy such as manipulator of PUMA-560 robot.
These arms are widely used for mechanical handling, welding, assembling, painting, grinding and
other industrial applications. These applications may require path planning, trajectory generation
and control design. All these factors make the study of robot manipulators, interesting.
Conventional methods of controlling a nonlinear system are based on models, especially in the
field of robot control. Many controllers like LQG, Hα [1] and input shaping as well as singular
perturbation, feedback linearization, manifolds and output redefinition techniques have been used
for controlling purpose if the exact model of the system is known. Many robotic control schemes
can be considered as special cases of model-based control called computed torque approach. The
basic concept of computed torque is to linearize a nonlinear system, and then to apply linear
control theory. But these controllers suffer from the lack of an exact simple-enough model of the
system and this calls for the use of the intelligent controllers. And for these above mentioned
controllers stability also became hard task. Fuzzy inference systems [2] have been proven to be
powerful tools to deal with the nonlinear systems on the basis of fuzzy rules [3], particularly those
DOI : 10.5121/ijfls.2014.4101
1
2. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
possessing a high degree of uncertainty and nonlinearity. Thus considerable research
development has been achieved in the use of fuzzy inference system for the control of a robot
manipulator that suffers from structured and unstructured uncertainties such as load variation,
friction, and external disturbances etc. To avoid these difficulties and ensuring the stability of the
system, a model free technique Fuzzy Lyapunov Synthesis (FLS) is proposed to control the
PUMA-560 robot in this paper.
A new Fuzzy rule base is derived for stabilizing the system and minimizing the error. The basic
idea to choose Lyapunov function and derive the Fuzzy rules is to make its derivative negative.
For this, the knowledge of output relative degree of the system model is only sufficient. The basic
assumption of the fuzzy Lyapunov synthesis is that, for a Lyapunov function V (x), if the
linguistic value of (x) is Negative, then (x) < 0, so the stability can be guaranteed.
Prior to this work, the mathematical model of PUMA-560 robot manipulator is implemented in
Simulink, the normal three input Fuzzy controller is applied to the model [4], the results are
compared with the results obtained by PD controlled Computed Torque Controller (PD-CTC).
The rest of the paper is organized as follows: The mathematical model of PUMA-560 robot
manipulator is presented in section 2, The Fuzzy Lyapunov Synthesis (FLS) is presented in
section 3, the FLS Control law is explained in section 4, and Simulation results are presented in
section 5.
2. THE MATHEMATICAL MODEL OF PUMA-560 ROBOT MANIPULATOR
The mathematical model Armstrong [5] [6] [7] of PUMA-560 robot manipulator [8] model is
derived by using Lagrange’s equation considering only three links among the total six links, such
that
.
-------eq. (1)
Where
q: nx1 position vector ,
A(q): nxn inertia matrix of the manipulator,
G(q): nx1 vector of gravity terms
: nx1 vector of torques
B(q): nxn(n-1)/2 matrix of Coriolis torques
C(q): nxn matrix of Centrifugal torques
: n vector of acceleration
and
are notation for n(n-1)/2 vector of velocity products and the n-vector of squared
velocities respectively.
Where
The above model of the robot arm is derived by generating the kinetic energy matrix and gravity
vector symbolic elements by performing the summation of Lagrange’s nonlinear formulation [9].
These elements are simplified by combining inertia constants that multiply common variable
expressions. The Coriolis and centrifugal matrix elements are then calculated in terms of partial
derivatives of kinetic energy, and then reduced using four relations that hold the partial
derivatives.
2
3. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
Where
a11=Im1+I1+I3CC2+I7SS23+I10SC23+I11SC2+I20(SS5(SS23(I21+CC4)–1)–2SC23C4SC5)
+I21SS23CC4+2{I5C2S23+I12C2C23+I15(SS23C5+SC23C4S5)+I16C2(S23C5+C23C4S5)+I18S4S
5+I22(SC23C5+CC23C4S5);
a12=I4S2+I8C23+I9C2+I13S23–I15C23S4S5+I16S2S4S5+I18(S23C4S5–C23C5)+I19S23SC4 +
I20S4(S23C4CC5+C23SC5)+I22S23S4S5;
a13=I8C23+I13S23–I15C23S4S5+I19S23SC4+I18(S23C4S5–C23C5)+I22S23S4S5+I20S4(S23C4
CC5+C23SC5);
a22=Im12+I2+I6+I20SS4SS5+I21SS4+2(I3S3+I12C3+I15C5+I16(S3C5+C3C4S5)+I22C4S5;
a23=I5S3+I6+I12C3+I16(S3C5+C3C4S5+I20SS4SS5+I21SS4+2{I15C5+I22C4S5};
a33=Im5 I6+I20SS4+SS5+I21SS4+2{I15C5+I22C4S5};
a34=-I15S4S5+I20S4SC5; a35=I15C4C5+I17C4+I22S5;
a36=I23S4S5; a44=Im4+I14–I20SS5; a46=I23C5;a55=Im5+I17; a66=Im6+I23;
b112=2{-I3SC2+I5C223+I7SC23–I12S223+I15(2SC23C5+(1-2SS23)C4S5+I16(C223C5S223C4S5)+I21SC23CC4+I20(1+CC4)SC23SS5-(1-2SS23)C4SC5+I22{(1–2SS23)C52SC23)C4S5)}+I10(1-2SS23)+I11(1-2SS2)
b113=2{I5C2C23+I7SC23-I12C2S23+I15(2SC23C5+(1-2SS23)C4S5)+I16C2(C23C5S23C4S5)+I21SC23CC4+I20{(1+CC4)SC23SS5-(1-2SS23)C4SC5)+I22{(1–2SS23)C52SC23)C4S5)}+I10(1-2SS23)
b114=2{-I15SC23S4S5–I16C2C23S4S5+I18C4S5–I20(SS23SS5SC4–SC23S4+SC5)+
I22CC23S4S5–I21SS23SC4);
b115=2{I20(SC5(CC4(1-CC23)CC23)-SC23C4(1-2SS5))–I15(SS23S5–SC23C4C5)I16C2(S23S5-C23C4C5)+I18S4C5+I22{CC23C4C5-SC23S5)}
b123=2{-I8S23+I13C23+I15S23S4S5+I18(C23C4S5+S23C5)+I19C23SC4+I20S4(C23C4CC5–
3
5. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
Matrix C is
Where
c12=I4C2–I8S23–I9S2+I13C23+I15S23S4S4+I16C2S4S5+I18(C23C4S5+S23C5)+I19C23SC4+
I20S4(C23CC5-S23SC5)+I22C23S4S5;
c13=0.5b123; c21=-0.5b112; c23=0.5b223; c24=-I15C4S5–I16S3C4S5+I20C4SC5;
c31=-0.5b113; c32=c23; c34=-I15C4S5+I20C4SC5;c35=-I15C4S5+I22C5;
c41=-0.5b114; c42=0.5b224; c43=0.5b423; c31=-0.5b115; c52=-0.5b225; c53=0.5b523; c34=-0.5b145.
And matrix G is:
Where
g2=g1C2+g2S23+g3S2+g4C23+g5(S23C5+C23C4S5)
g3=g2S23+g4C23+g5(S23C5+C23C4S5); g5=g5(C23S5+S23C4C5);
Where
are the inertial constants,
are the gravitational constants. And
we have abbreviated the trigonometric functions by writing S2 to mean sin( ), C23 to mean
cos(
) and CS4 to mean cos( )*sin( ).
With all the above parameters the dynamic model equation (1) can be written as follows.
-------- eq. (2)
Where
-------- eq. (3)
Selecting the Proportional-Derivative (PD) [10] feedback results in the PD-Computed Torque
Controller (PD-CTC) Nguyen [11], this forms equation (4).
-------- eq. (4)
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6. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
From the equation (4), we can separate the mathematical model into linear and nonlinear parts.
The schematic diagram of a 6DOF PUMA-560 robot manipulator is shown in Fig. 1.
Figure 1. The 6DOF PUMA-560 robot manipulator
3. FUZZY LYAPUNIV SYNTHESIS (FLS)
The FLS, Margaliot [12] is fuzzy model-free approach based on selecting a Lyapunov function
candidate [13] [14] and make its derivative negative by designing fuzzy control rules [15]. The
FLS was applied to some minimum phase single input single output plants where some fuzzy
rules describing the linguistic relation between the input and the output and the output relative
degree were known [16]. And in this process there is no direct insight to the system dynamic and
structural properties was given there, so that the applicability of the FLS and the study of stability
analysis were less tractable. Here, the reviewed formulation is to show the essentials of the theory
and its control rules [12] are clearly modified to illustrate applicability of the FLS to the
nonminimum phase systems and improve the system performance. Consider the nonlinear system
p
, u
n
, y
-------eq. (5)
y = h(x)
The control objective is that the error e = y – yd goes to zero asymptotically where yd is the
desired reference trajectory. First we had chosen a positive definite function V as a lyapunov
function candidate and then design u to make its time-derivative as negative along the system
trajectory, i.e.
,
--------eq. (6)
If the knowledge about (5) is limited to fuzzy descriptions of the proposed system, (6) may be
used again, but here this time as a linguistic inequality yielding u in terms of fuzzy mamdani IFTHEN rules. This methodology is called Fuzzy Lyapunov Synthesis. The control strategy of FLS
is based on designing u to make negative.
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7. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
4. FLS CONTROL LAW
The Lyapunov function candidate [17] can be selected in several approaches based on some
specific controlling objectives. The following are some possible approaches in them.
1. Select a Lyapunov function candidate in order to guarantee the system stability and to meet the
performance measures. And this approach often becomes more complex.
2. The Lyapunov function candidate parameters are tuned accordingly by observing the
performance measures and the internal stability of system dynamics so that system stability [18]
is guaranteed.
3. Add all control terms to the main system controller, such that each control term that satisfies
the performance measures pertaining to the internal stability.
In this section, to derive the control rules two Lyapunov function candidates are proposed. Even
though these two Lyapunov functions are simple easy functions of output error e, with their
integral and derivative, these also give good insight to the problem. These Lyapunov functions
and corresponding derived FLS control rules are modified and reviewed to improve the
performance and to stabilize the internal dynamics of the system. Let us consider the first
Lyapunov function candidate and its time derivative are
The FLS control rules are derived assuming ë is proportional to u with e and ė. And the premise
variables are summarized in the Table 1. Using
and, can be rewritten as:
-------- eq. (7)
The FLS control rules framed based on equation (7) do not generate effective control signals
when the steady state error is large. Under these conditions, the second Lyapunov function can be
chosen which gives effective control. The equation is:
2
)
-----eq. (8)
The related control rules corresponding equation (8) are given below in the Table 1.
Table 1. Fuzzy Lyapunov control rules
+
+
-
+
-
+
-
+
+
-
-
+
+
-
-
+
U
-
+
+
+
-
-
-
-
nb
nm
z
ns
ps
z
pm
pb
Where
nb- negative big, nm- negative medium, z- zero, ns- negative small, ps- positive small, pmpositive medium, pb- positive big.
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8. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
5. RESULTS
The Fuzzy Lyapunov Synthesis (FLS) controller was designed by means of selecting appropriate
rule base such that the system stability was also guaranteed and tested to step and ramp inputs. At
first the mathematical model of PUMA-560 robot manipulator was implemented in simulation. In
this simulation the first, second and third joints are moved from home to final position with and
without uncertainties. The simulation was implemented in MATLAB/SIMULINK environment.
The results obtained for Fuzzy Lyapunov Synthesis (FLS) controller were compared with the
results obtained for PD controlled Computed Torque Controller (PD-CTC) Nguyen [4] and
normal Fuzzy controller. From the figures from Fig. 2 to Fig. 12 it was observed that the FLS
controller gave better results in all cases when compared with PD-CTC and Fuzzy controllers.
Error in theta3 of link3 for ramp input without uncertainties
0
PD-CTC
Fuzzy
Ref
Fuzzy Lyap
-1
-2
Error
-3
-4
-5
-6
-7
0
1
2
3
4
5
Time
6
7
8
9
10
Fig. 2 Response of error in angle at link3 for ramp input without uncertainties
Error in theta3 of link3 for ramp input with uncertainties (positive)
0
Reference
PD-CTC
Fuzzy
Fuzzy Lyap
-1
Error
-2
-3
-4
-5
-6
-7
0
1
2
3
4
5
Time
6
7
8
9
10
Fig. 3 Response of error in angle at link3 for ramp input with uncertainties (positive)
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9. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
Error in theta3 of link3 for step input without uncertainties
1.2
1
Reference
PD-CTC
Fuzzy
Fuzzy Lyap
0.8
Error
0.6
0.4
0.2
0
-0.2
0
1
2
3
4
5
Time
6
7
8
9
10
9
10
Fig. 4 Response of error in angle at link3 for step input without uncertainties
E rror in theta3 of link 3 for s tep input with unc ertainties (pos itive)
1.2
1
Referenc e
P D-CTC
Fuz z y
Fuz z y Ly ap
0.8
E rror
0.6
0.4
0.2
0
-0.2
0
1
2
3
4
5
Tim e
6
7
8
Fig. 5 Response of error in angle at link3 for step input with uncertainties (positive)
Error in theta2 of link2 for ramp input without uncertainties
7
6
PD-CTC
Ref
Fuzzy
Fuzzy Lyap
5
Error
4
3
2
1
0
0
1
2
3
4
5
Time
6
7
8
9
10
Fig. 6 Response of error in angle at link2 for ramp input without uncertainties
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10. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
Error in theta2 of link2 for ramp input with uncertainties (positive)
7
Reference
PD-CTC
Fuzzy
Fuzzy Lyap
6
5
Error
4
3
2
1
0
0
1
2
3
4
5
Time
6
7
8
9
10
Fig. 7 Response of error in angle at link2 for ramp input with uncertainties (positive)
E rror in theta2 of link 2 for s tep input without unc ertainties
2
1
E rror
0
Referenc e
P D-CTC
Fuz z y
Fuz z y Ly ap
-1
-2
-3
-4
0
1
2
3
4
5
Tim e
6
7
8
9
10
Fig. 8 Response of error in angle at link2 for step input without uncertainties
Error in theta1 of link1 for ramp input without uncertainties
0.005
0
PD-CTC
Fuzzy
Ref
FUZZY LYAP
-0.005
Error
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
-0.04
0
1
2
3
4
5
Time
6
7
8
9
10
Fig.9 Response of error in angle at link1 for ramp input without uncertainties
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11. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
Error in theta1 of link1 for ramp input with uncertainties (positive)
0.005
0
Reference
PD-CTC
Fuzzy
Fuzzy Lyap
-0.005
Error
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
0
1
2
3
4
5
Time
6
7
8
9
10
Fig. 10 Response of error in angle at link2 for ramp input with uncertainties (positive)
E rror in theta1 of link 1 for s tep input without unc ertainties
0.01
0
Referenc e
P D-CTC
Fuz z y
Fuz z y Ly ap
-0.01
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
0
1
2
3
4
5
Tim e
6
7
8
9
10
Fig.11 Response of error in angle at link1 for step input without uncertainties
-5
12
Error in theta1 of link1 for step input with uncertainties (positive)
x 10
10
Fuzzy Lyap
Reference
8
6
Error
E rror
-0.02
4
2
0
-2
0
2
4
6
8
10
Time
12
14
16
18
20
Fig. 12 Response of error in angle at link1 for step input with uncertainties (positive)
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12. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014
6. CONCLUSIONS
In this paper, a novel approach for determining the rule base of a Fuzzy lyapunov Synthesis (FLS)
controller is proposed. Starting with minimal knowledge concerning the plant’s behavior, a
lyapunov function candidate V is chosen and determines conditions so that V will indeed be a
lyapunov function. These conditions provide us the rule base of the fuzzy controller.
Our proposed FLS approach combines two works here. On one hand, the plant is model-free in
the sense only minimal fuzzy knowledge is available. On the other hand, it follows the classical
Lyapunov Synthesis method. This combination provides us with a solid analytical basis from
which the rules are obtained and justified. And now the concept of Fuzzy Lyapunov Synthesis
(FLS) is applied to a PUMA-560 robot manipulator, the effectiveness of the control is observed
when compared with PD controlled Computed Torque Controller (PD-CTC) and the normal
Fuzzy controller. Only with the knowledge of output relative degree and some structural
properties of the robot manipulator model the framework of stability and performance analysis of
the system was done.
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