In this work a regulator for robot manipulators is proposed, it has been developed considering that the equilibrium point of the closed-loop system is globally asymptotically stable in agreement with Lyapunov’s direct method. The global asymptotic stability of the controlled system is analyzed. We present real-time experimental results to show the performance of the proposed regulator on a robot manipulator of direct drive with three degrees of freedom. The performance of the new control scheme is compared with respect to the popular PD Algorithm in terms of positioning error
The document describes research into developing a novel controller for stabilizing an inverted pendulum. It begins with reviewing previous work that derived the differential equations governing the dynamic behavior of an inverted pendulum. The researcher then uses Laplace transforms to solve these equations and derive a transfer function relating the input and output. An output-feedback PID controller is designed using this transfer function. Additionally, a stochastic method is examined for initializing the weighting matrices in linear quadratic regulation to minimize the performance index and optimize controller design. Upon simulation, the new output-feedback controller is shown to effectively control pendulum stability without integral gain.
Design Novel Nonlinear Controller Applied to Robot Manipulator: Design New Fe...Waqas Tariq
This document describes a novel adaptive feedback linearization fuzzy controller for robot manipulators. It begins by discussing limitations of traditional feedback linearization controllers, such as sensitivity to parameter uncertainty. It then proposes designing a feedback linearization fuzzy controller to address this issue. The key steps are: 1) designing the fuzzy controller, including fuzzifying inputs/outputs and developing a rule base, 2) developing an adaptive feedback linearization fuzzy controller by adding an adaptive law to tune fuzzy rule parameters online and improve disturbance rejection. The goal is to develop a robust position controller for robot manipulators that maintains acceptable performance despite nonlinearities and uncertainty.
A Mathematical Introduction to Robotic Manipulation 第6章Xinyi Zhang
The document provides an outline for a presentation on robot hand dynamics and control. It begins with recalling concepts from previous chapters, then covers Lagrange's equations with constraints. Next, it will derive the equations of motion for a multifingered hand manipulating an object, address more complex equations for redundant or nonmanipulable robot systems, describe tendon-driven actuation kinematics, and introduce control laws for constraint-involved systems. Examples throughout illustrate key concepts in robot hand dynamics and control.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
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.
Design and Implementation of Model Reference Adaptive Controller using Coeffi...IOSR Journals
This document describes the design and implementation of a model reference adaptive controller (MRAC) using the coefficient diagram method (CDM) for a nonlinear process. It begins by introducing MRAC for single-input single-output plants, developing the MRAC design and control law. It then provides basics of the CDM design approach. The document applies the CDM-MRAC to a spherical tank level process in simulation, comparing its performance to a linear PI controller. Simulation results show the CDM-MRAC has faster rise time and settling time than the PI controller.
Research Inventy : International Journal of Engineering and Scienceinventy
The document presents an adaptive tracking control method for a welding mobile manipulator. The mobile manipulator consists of a three-linked planar manipulator mounted on a two-wheeled mobile platform. Controllers are designed using Lyapunov stability analysis to guarantee the end-effector tracks a desired welding trajectory despite unknown dimensional parameters of the manipulator. Simulation and experimental results demonstrate the effectiveness of the proposed adaptive controllers.
The document describes research into developing a novel controller for stabilizing an inverted pendulum. It begins with reviewing previous work that derived the differential equations governing the dynamic behavior of an inverted pendulum. The researcher then uses Laplace transforms to solve these equations and derive a transfer function relating the input and output. An output-feedback PID controller is designed using this transfer function. Additionally, a stochastic method is examined for initializing the weighting matrices in linear quadratic regulation to minimize the performance index and optimize controller design. Upon simulation, the new output-feedback controller is shown to effectively control pendulum stability without integral gain.
Design Novel Nonlinear Controller Applied to Robot Manipulator: Design New Fe...Waqas Tariq
This document describes a novel adaptive feedback linearization fuzzy controller for robot manipulators. It begins by discussing limitations of traditional feedback linearization controllers, such as sensitivity to parameter uncertainty. It then proposes designing a feedback linearization fuzzy controller to address this issue. The key steps are: 1) designing the fuzzy controller, including fuzzifying inputs/outputs and developing a rule base, 2) developing an adaptive feedback linearization fuzzy controller by adding an adaptive law to tune fuzzy rule parameters online and improve disturbance rejection. The goal is to develop a robust position controller for robot manipulators that maintains acceptable performance despite nonlinearities and uncertainty.
A Mathematical Introduction to Robotic Manipulation 第6章Xinyi Zhang
The document provides an outline for a presentation on robot hand dynamics and control. It begins with recalling concepts from previous chapters, then covers Lagrange's equations with constraints. Next, it will derive the equations of motion for a multifingered hand manipulating an object, address more complex equations for redundant or nonmanipulable robot systems, describe tendon-driven actuation kinematics, and introduce control laws for constraint-involved systems. Examples throughout illustrate key concepts in robot hand dynamics and control.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
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.
Design and Implementation of Model Reference Adaptive Controller using Coeffi...IOSR Journals
This document describes the design and implementation of a model reference adaptive controller (MRAC) using the coefficient diagram method (CDM) for a nonlinear process. It begins by introducing MRAC for single-input single-output plants, developing the MRAC design and control law. It then provides basics of the CDM design approach. The document applies the CDM-MRAC to a spherical tank level process in simulation, comparing its performance to a linear PI controller. Simulation results show the CDM-MRAC has faster rise time and settling time than the PI controller.
Research Inventy : International Journal of Engineering and Scienceinventy
The document presents an adaptive tracking control method for a welding mobile manipulator. The mobile manipulator consists of a three-linked planar manipulator mounted on a two-wheeled mobile platform. Controllers are designed using Lyapunov stability analysis to guarantee the end-effector tracks a desired welding trajectory despite unknown dimensional parameters of the manipulator. Simulation and experimental results demonstrate the effectiveness of the proposed adaptive 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.
This document describes simulation of non-linear computed torque control for a two link SCARA type manipulator in Simulink. It begins with an introduction to SCARA manipulators and computed torque control. It then provides the inverse kinematics equations to transform between Cartesian and joint space for the manipulator. It derives the equations of motion using Lagrange's equations. It describes a pick and place task and generates trajectories between points using a third order polynomial. Finally, it introduces computed torque control which uses feedback linearization to calculate the required joint torques to control the nonlinear manipulator.
This document describes the design and implementation of a controller for an inverted pendulum on a cart system. It provides the nonlinear and linearized models of the system and designs a PID controller using root locus analysis. Simulation results show the uncompensated system is unstable but the controlled system with PID controller and pre-compensator meets design specifications with less than 0.2 seconds settling time and 8% overshoot for a unit step input.
Output feedback trajectory stabilization of the uncertainty DC servomechanism...ISA Interchange
This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.
Identification and Real Time Control of a DC MotorIOSR Journals
This document presents a method for identifying and controlling a DC motor. It describes an experimental setup using sensors to measure the motor's speed. A parametric estimation method called PEM is used to identify the dynamic model of the motor based on input-output data. The identified model is validated via simulation. Then, an optimal linear quadratic regulator (LQR) controller is designed using the identified model to control the motor's speed and position. Simulations and experiments show the controller is able to track step and square wave position and velocity commands.
The document describes a project to create a quasi-equilibrium state pendulum using a DC motor attached to a rod. The motor drives a propeller to allow the rod to swing. Angular position is measured by a potentiometer. The system is modeled and controlled using Scilab/Xcos. Initial PID tuning is done using Ziegler-Nichols method. Future work proposed includes expanding the controllable angle range and implementing advanced controllers like adaptive control to improve response. The appendix lists components used and conclusions reiterate the potential applications and limitations of PID control for this system.
On tracking control problem for polysolenoid motor model predictive approach IJECEIAES
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects due to its functions, in which a straight motion is provided directly without mediate mechanical actuators. Recently, with several commons on mathematic model, some control methods for PLM based on Rotational Motor have been applied, but position, velocity and current constraints which are important in real systems have been ignored. In this paper, position tracking control problem for PLM was considered under state-independent disturbances via min-max model predictive control. The proposed controller forces tracking position errors converge to small region of origin and satisfies state including position, velocity and currents constraints. Further, a numerical simulation was implemented to validate the performance of the proposed controller.
Intelligent Control of a Robot Manipulator Nixon Barrera
The document discusses control techniques for robot manipulators. It proposes using fuzzy logic controllers (FLCs) and artificial neural networks (ANNs) for intelligent control of a 3-joint robot arm designed for orange picking. Specifically, it describes using an FLC to provide initial feedback control based on a model of the robot. Then an ANN with a radial basis function network is used to provide adaptive feedforward compensation for nonlinearities and disturbances. Simulation results showed the proposed control scheme improved tracking accuracy over traditional independent joint control, especially when following unknown trajectories or with an inaccurate robot model.
Iaetsd modelling and controller design of cart inverted pendulum system using...Iaetsd Iaetsd
This document presents a model reference adaptive control (MRAC) scheme for stabilizing a cart-inverted pendulum system. The cart-inverted pendulum is a highly nonlinear and unstable system that is challenging to control. The proposed controller uses Lyapunov stability theory to design an MRAC controller. Simulation results show the controller is able to balance the inverted pendulum in the unstable upright position and regulate the cart position, demonstrating the effectiveness of the proposed MRAC control approach.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects because it provides a straight motion directly without mediate mechanical actuators. Some control methods for PLM based on Rotational Motor are applied to obtain several good performances, but position and velocity constraints which are important in real systems are ignored. In this paper, we analysis control problem of tracking position in PLM under state-independent disturbances via min-max model predictive control. The proposed controller brings tracking position error converge to zero and satisfies state including position and velocity and input constraints. The simulation results validity a good efficiency of the proposed controller.
Speed and Torque Control of Mechanically Coupled Permanent Magnet Direct Curr...IDES Editor
A new controller is designed for speed and torque
control of a Permanent Magnet DC motor based on
measurements of speed and current. This research work
focuses on investigating the effects of control of the speed and
torque of two brushless dc motors that are mechanically
coupled. Two controller design methods: the Root Locus
method and Bode Plot method as well as two controllers:
Proportional-Integral-Derivative (PID) and Proportional-
Integral (PI) are used to obtain the control objectives of speed
control and torque control. The simulation is performed using
MATLAB/SIMULINK software. The effects of varying the
controller gains on the system performance is studied and
quantified. The simulation results show that the speed control
objectives of the motor are satisfied even in the case of torque
disturbance from the other motor.
1) An LQR controller with feedforward control and steady state error tracking was designed and simulated to control an inverted pendulum system.
2) The LQR controller stabilized the unstable system and achieved good performance for the pendulum angle and cart position with minimal overshoot and steady state error.
3) Simulation results demonstrated the robustness of the designed controller under system uncertainties, showing improved performance over existing H-infinity control methods.
Consider the following nonlinear system:
dx/dt = f(x) + g(x)u
Where x is an n-dimensional vector and f and g are sufficiently smooth vector fields.
The goal is to design a feedback control law u = α(x) that renders the origin globally asymptotically stable (GAS).
Backstepping provides a systematic approach to solve this problem by considering the system as a cascade of "pseudo" linear systems with intermediate virtual controls.
The procedure recursively constructs stabilizing functions and control laws to backstep through this cascade until the actual control input is determined.
This approach systematically cancels out the nonlinearities in f while preserving the desirable properties introduced by g
1) The document provides an overview of inverted pendulum control, focusing on mobile inverted pendulums.
2) It describes the structure of a mobile inverted pendulum system with a cart and mounted pendulum. Equations of motion are provided.
3) Two common control strategies for inverted pendulums are discussed: PID control and fuzzy logic control. Performance comparisons using simulations show fuzzy logic control provides better response.
In this paper, the optimal control problem of a nonlinear robot manipulator in absence of holonomic constraint force based on the point of view of adaptive dynamic programming (ADP) is presented. To begin with, the manipulator was intervened by exact linearization. Then the framework of ADP and Robust Integral of the Sign of the Error (RISE) was developed. The ADP algorithm employs Neural Network technique to tune simultaneously the actor-critic network to approximate the control policy and the cost function, respectively. The convergence of weight as well as position tracking control problem was considered by theoretical analysis. Finally, the numerical example is considered to illustrate the effectiveness of proposed control design.
Design Error-based Linear Model-free Evaluation Performance Computed Torque C...Waqas Tariq
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This research focuses on the design, implementation and analysis of a model-free linear error-based tuning computed torque controller for highly nonlinear dynamic second order system, in presence of uncertainties. In order to provide high performance nonlinear methodology, computed torque controller is selected. Pure computed torque controller can be used to control of partly known nonlinear dynamic parameters of nonlinear systems. Conversely, pure computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, model-free performance/error-based linear methodology with three inputs and one output is applied to pure computed torque controller. The results demonstrate that the error-based linear tuning computed torque controller is a model-based controllers which works well in certain and uncertain system. Pure computed torque controller has difficulty in handling unstructured model uncertainties. To solve this problem applied linear model-free error -based tuning method to computed torque controller for adjusting the linear inner loop gain (K ). Since the linear inner loop gain (K) is adjusted by linear error-based tuning method, it is linear and continuous. In this research new K is obtained by the previous K multiple gain updating factor (á) which is a coefficient varies between half to two.
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.
A personal account of doing a ph d 2004Jackie Taylor
This document is a personal account of the author's experience doing a PhD. It describes how the PhD has become a significant part of the author's life and priorities. Through systematic data collection including diaries, notes, and artifacts, the author analyzes how engaging in the PhD as an occupation is causing intellectual, social, and emotional changes. The analysis considers how the author's past and present life impacts their experience in the PhD process.
An Organizational Memory and Knowledge System (OMKS): Building Modern Decisio...Waqas Tariq
This document presents an approach for building modern decision support systems that integrates data warehouses and organizational memory systems. The approach uses scenarios to capture tacit knowledge from employees and ontology for organizing diverse data and knowledge sources. It is based on theoretical foundations including decision making processes, data warehousing, knowledge management, organizational memory systems, and the knowledge spiral concept. The integration of these systems is expected to enhance organizational decision making and learning.
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.
This document describes simulation of non-linear computed torque control for a two link SCARA type manipulator in Simulink. It begins with an introduction to SCARA manipulators and computed torque control. It then provides the inverse kinematics equations to transform between Cartesian and joint space for the manipulator. It derives the equations of motion using Lagrange's equations. It describes a pick and place task and generates trajectories between points using a third order polynomial. Finally, it introduces computed torque control which uses feedback linearization to calculate the required joint torques to control the nonlinear manipulator.
This document describes the design and implementation of a controller for an inverted pendulum on a cart system. It provides the nonlinear and linearized models of the system and designs a PID controller using root locus analysis. Simulation results show the uncompensated system is unstable but the controlled system with PID controller and pre-compensator meets design specifications with less than 0.2 seconds settling time and 8% overshoot for a unit step input.
Output feedback trajectory stabilization of the uncertainty DC servomechanism...ISA Interchange
This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.
Identification and Real Time Control of a DC MotorIOSR Journals
This document presents a method for identifying and controlling a DC motor. It describes an experimental setup using sensors to measure the motor's speed. A parametric estimation method called PEM is used to identify the dynamic model of the motor based on input-output data. The identified model is validated via simulation. Then, an optimal linear quadratic regulator (LQR) controller is designed using the identified model to control the motor's speed and position. Simulations and experiments show the controller is able to track step and square wave position and velocity commands.
The document describes a project to create a quasi-equilibrium state pendulum using a DC motor attached to a rod. The motor drives a propeller to allow the rod to swing. Angular position is measured by a potentiometer. The system is modeled and controlled using Scilab/Xcos. Initial PID tuning is done using Ziegler-Nichols method. Future work proposed includes expanding the controllable angle range and implementing advanced controllers like adaptive control to improve response. The appendix lists components used and conclusions reiterate the potential applications and limitations of PID control for this system.
On tracking control problem for polysolenoid motor model predictive approach IJECEIAES
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects due to its functions, in which a straight motion is provided directly without mediate mechanical actuators. Recently, with several commons on mathematic model, some control methods for PLM based on Rotational Motor have been applied, but position, velocity and current constraints which are important in real systems have been ignored. In this paper, position tracking control problem for PLM was considered under state-independent disturbances via min-max model predictive control. The proposed controller forces tracking position errors converge to small region of origin and satisfies state including position, velocity and currents constraints. Further, a numerical simulation was implemented to validate the performance of the proposed controller.
Intelligent Control of a Robot Manipulator Nixon Barrera
The document discusses control techniques for robot manipulators. It proposes using fuzzy logic controllers (FLCs) and artificial neural networks (ANNs) for intelligent control of a 3-joint robot arm designed for orange picking. Specifically, it describes using an FLC to provide initial feedback control based on a model of the robot. Then an ANN with a radial basis function network is used to provide adaptive feedforward compensation for nonlinearities and disturbances. Simulation results showed the proposed control scheme improved tracking accuracy over traditional independent joint control, especially when following unknown trajectories or with an inaccurate robot model.
Iaetsd modelling and controller design of cart inverted pendulum system using...Iaetsd Iaetsd
This document presents a model reference adaptive control (MRAC) scheme for stabilizing a cart-inverted pendulum system. The cart-inverted pendulum is a highly nonlinear and unstable system that is challenging to control. The proposed controller uses Lyapunov stability theory to design an MRAC controller. Simulation results show the controller is able to balance the inverted pendulum in the unstable upright position and regulate the cart position, demonstrating the effectiveness of the proposed MRAC control approach.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects because it provides a straight motion directly without mediate mechanical actuators. Some control methods for PLM based on Rotational Motor are applied to obtain several good performances, but position and velocity constraints which are important in real systems are ignored. In this paper, we analysis control problem of tracking position in PLM under state-independent disturbances via min-max model predictive control. The proposed controller brings tracking position error converge to zero and satisfies state including position and velocity and input constraints. The simulation results validity a good efficiency of the proposed controller.
Speed and Torque Control of Mechanically Coupled Permanent Magnet Direct Curr...IDES Editor
A new controller is designed for speed and torque
control of a Permanent Magnet DC motor based on
measurements of speed and current. This research work
focuses on investigating the effects of control of the speed and
torque of two brushless dc motors that are mechanically
coupled. Two controller design methods: the Root Locus
method and Bode Plot method as well as two controllers:
Proportional-Integral-Derivative (PID) and Proportional-
Integral (PI) are used to obtain the control objectives of speed
control and torque control. The simulation is performed using
MATLAB/SIMULINK software. The effects of varying the
controller gains on the system performance is studied and
quantified. The simulation results show that the speed control
objectives of the motor are satisfied even in the case of torque
disturbance from the other motor.
1) An LQR controller with feedforward control and steady state error tracking was designed and simulated to control an inverted pendulum system.
2) The LQR controller stabilized the unstable system and achieved good performance for the pendulum angle and cart position with minimal overshoot and steady state error.
3) Simulation results demonstrated the robustness of the designed controller under system uncertainties, showing improved performance over existing H-infinity control methods.
Consider the following nonlinear system:
dx/dt = f(x) + g(x)u
Where x is an n-dimensional vector and f and g are sufficiently smooth vector fields.
The goal is to design a feedback control law u = α(x) that renders the origin globally asymptotically stable (GAS).
Backstepping provides a systematic approach to solve this problem by considering the system as a cascade of "pseudo" linear systems with intermediate virtual controls.
The procedure recursively constructs stabilizing functions and control laws to backstep through this cascade until the actual control input is determined.
This approach systematically cancels out the nonlinearities in f while preserving the desirable properties introduced by g
1) The document provides an overview of inverted pendulum control, focusing on mobile inverted pendulums.
2) It describes the structure of a mobile inverted pendulum system with a cart and mounted pendulum. Equations of motion are provided.
3) Two common control strategies for inverted pendulums are discussed: PID control and fuzzy logic control. Performance comparisons using simulations show fuzzy logic control provides better response.
In this paper, the optimal control problem of a nonlinear robot manipulator in absence of holonomic constraint force based on the point of view of adaptive dynamic programming (ADP) is presented. To begin with, the manipulator was intervened by exact linearization. Then the framework of ADP and Robust Integral of the Sign of the Error (RISE) was developed. The ADP algorithm employs Neural Network technique to tune simultaneously the actor-critic network to approximate the control policy and the cost function, respectively. The convergence of weight as well as position tracking control problem was considered by theoretical analysis. Finally, the numerical example is considered to illustrate the effectiveness of proposed control design.
Design Error-based Linear Model-free Evaluation Performance Computed Torque C...Waqas Tariq
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This research focuses on the design, implementation and analysis of a model-free linear error-based tuning computed torque controller for highly nonlinear dynamic second order system, in presence of uncertainties. In order to provide high performance nonlinear methodology, computed torque controller is selected. Pure computed torque controller can be used to control of partly known nonlinear dynamic parameters of nonlinear systems. Conversely, pure computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, model-free performance/error-based linear methodology with three inputs and one output is applied to pure computed torque controller. The results demonstrate that the error-based linear tuning computed torque controller is a model-based controllers which works well in certain and uncertain system. Pure computed torque controller has difficulty in handling unstructured model uncertainties. To solve this problem applied linear model-free error -based tuning method to computed torque controller for adjusting the linear inner loop gain (K ). Since the linear inner loop gain (K) is adjusted by linear error-based tuning method, it is linear and continuous. In this research new K is obtained by the previous K multiple gain updating factor (á) which is a coefficient varies between half to two.
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.
A personal account of doing a ph d 2004Jackie Taylor
This document is a personal account of the author's experience doing a PhD. It describes how the PhD has become a significant part of the author's life and priorities. Through systematic data collection including diaries, notes, and artifacts, the author analyzes how engaging in the PhD as an occupation is causing intellectual, social, and emotional changes. The analysis considers how the author's past and present life impacts their experience in the PhD process.
An Organizational Memory and Knowledge System (OMKS): Building Modern Decisio...Waqas Tariq
This document presents an approach for building modern decision support systems that integrates data warehouses and organizational memory systems. The approach uses scenarios to capture tacit knowledge from employees and ontology for organizing diverse data and knowledge sources. It is based on theoretical foundations including decision making processes, data warehousing, knowledge management, organizational memory systems, and the knowledge spiral concept. The integration of these systems is expected to enhance organizational decision making and learning.
Online Adaptive Control for Non Linear Processes Under Influence of External ...Waqas Tariq
In this paper a novel temperature controller, for non linear processes, under the influence of external disturbance, has been proposed. The control process has been carried out by Neural Network based Proportional, Integral and Derivative (NNPID). In this controller, two experiments have been conducted with respect to the setpoint changes and load disturbance. The first experiment considers the change in setpoint temperature in steps of 10oC from 50oC to 70oC for three different rates of flow of water. In the second experiment the load disturbance in terms of addition of 100ml/min of water at three different time intervals is introduced in the system. It has been shown that, in these situations, the proposed controller adjusts NN weights which are equivalent to PID parameters in both the cases to achieve better control than conventional PID. In the proposed controller, an error less than 0.08oC have been achieved under the effect of the load disturbance. Moreover, it is also seen that the present controller gives error less than 0.11oC, 0.12oC and 0.12oC, without overshoot for 50oC, 60oC and 70oC, respectively, for all three rate of flow of water.
Assignment related to Structure analysis to determine the reactions and to draw axial force, shear force and bending moment diagrams for the members of statically indeterminate frames by moment distribution method
This document discusses the moment distribution method for analyzing statically indeterminate structures. It begins with an introduction of the method developed by Prof. Hardy Cross in 1930. Important terms are defined such as stiffness, carry over factor, and distribution factor. Fixed end moments are explained for various load cases like centric loading, eccentric loading, uniform distributed load, and uniform varying load. Two examples are provided - a simply supported beam and a two story building analyzed using the moment distribution method.
This document discusses the importance and benefits of adopting a virtual data room (VDR) technology for companies in emerging Asia Pacific markets. It outlines the risks of failing to implement a robust VDR solution, such as increased risk of data breaches, inability to meet international compliance standards, and high risk of materials disclosure litigation. The document recommends following best practices from established markets, such as choosing an enterprise-grade VDR with full security and audit features. Adopting a proven VDR like Merrill DataSite can help companies in emerging markets mitigate risks, ensure compliance, and drive faster, better transaction outcomes.
This document discusses connecting the 5 billion people who currently do not have internet access. It presents several projects and initiatives aimed at addressing this, including Project Loon which aims to provide internet access via balloons, One Laptop per Child which aims to provide affordable laptops to children, and Samasource which creates digital work opportunities in developing countries. The document concludes with a quote by Steve Jobs about influencing the future.
The document provides an outline for a presentation on the moment distribution method for structural analysis. It includes:
- An introduction to the moment distribution method and its use for analyzing statically indeterminate beams and frames.
- Definitions of important terms used in the method like stiffness, carry over factor, and distribution factor.
- Sign conventions for support moments, member rotations, and sinking of supports.
- Expressions for fixed end moments under different load cases including centric loading, eccentric loading, uniform loads, support rotations, and sinking of supports.
- Examples of applying the method to a simply supported beam and fixed supported beam with sinking support.
Dokumen tersebut membahas tentang logika matematika, mulai dari asal usul logika sejak zaman Yunani Kuno hingga perkembangan logika modern. Dokumen ini juga menjelaskan manfaat berfikir secara logika seperti membantu berpikir secara rasional dan meningkatkan kecerdasan.
Dynamics and control of a robotic arm having four linksAmin A. Mohammed
This document presents the dynamics modeling and control of a 4 degree-of-freedom robotic arm. It first derives the dynamic model of the robotic arm using the Euler-Lagrange approach. It then describes implementing two control approaches for position control of the arm joints: PID control and feedback linearization control. Simulation results show that PID control coupled with a differential evolution algorithm and feedback linearization control improve the robotic arm's performance. Increasing the arm link masses is found to not affect PID position control performance but require higher control torques.
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.
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).
PSO APPLIED TO DESIGN OPTIMAL PD CONTROL FOR A UNICYCLE MOBILE ROBOTJaresJournal
In this work, we propose a Particle Swarm Optimization (PSO) to design Proportional Derivative
controllers (PD) for the control of Unicycle Mobile Robot. To stabilize and drive the robot precisely with
the predefined trajectory, a decentralized control structure is adopted where four PD controllers are used.
Their parameters are given simultaneously by the proposed algorithm (PSO). The performance of the
system from its desired behavior is quantified by an objective function (SE). Simulation results are
presented to show the efficiency of the method. ).
The results are very conclusive and satisfactory in terms of stability and trajectory tracking of unicycle
mobile robot
This document presents a novel adaptive PID control scheme for flexible joint robot manipulators with known upper bounds on external disturbances. The control law combines PID feedback control with robust adaptive compensation of disturbances and unknown parameters. Lyapunov stability theory and Barbalat's lemma are used to prove global asymptotic stability of the closed-loop system. Simulation results on a two-degree-of-freedom flexible joint robot illustrate the effectiveness of the proposed controller in improving trajectory tracking accuracy and dynamic performance compared to existing adaptive PD control methods.
This document summarizes a research paper that presents a non-linear control law to track a reference trajectory for a mobile robot with caster wheels. The control law integrates kinematic and dynamic controllers to minimize position/orientation errors and differences between actual and reference velocities. The stability of the control law is proven using Lyapunov theory. Numerical simulations and experiments on a differential-drive mobile robot show the integrated control provides faster convergence and eliminates overshoot compared to just kinematic control.
PD plus error dependent integral nonlinear controllers for robot manipulatorsISA Interchange
In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator.
Design Artificial Nonlinear Robust Controller Based on CTLC and FSMC with Tun...Waqas Tariq
The document describes research on designing artificial nonlinear robust controllers for robot manipulators. It discusses two classical nonlinear robust controllers - sliding mode controller (SMC) and computed torque controller (CTC) - and their limitations when applied to systems with uncertainties. It then proposes applying fuzzy logic methodology to these classical controllers to reduce their limitations. Specifically, it develops a fuzzy sliding mode controller with tunable gain (GTFSMC) and a computed torque-like controller with tunable gain (GTCTLC) that use fuzzy logic rules to eliminate the mathematical nonlinear dynamics and reduce chattering through optimization of the tunable gain parameter. The controllers aim to achieve satisfactory performance for robot manipulators operating in unknown environments with uncertainties and disturbances.
Methodology of Mathematical error-Based Tuning Sliding Mode ControllerCSCJournals
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This paper focuses on the design of a chattering free mathematical error-based tuning sliding mode controller (MTSMC) for highly nonlinear dynamic robot manipulator, in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller is selected. Pure sliding mode controller can be used to control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure sliding mode controller is used in many applications; it has an important drawback namely; chattering phenomenon which it can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers. In order to reduce the chattering this research is used the switching function in presence of mathematical error-based method instead of switching function method in pure sliding mode controller. The results demonstrate that the sliding mode controller with switching function is a model-based controllers which works well in certain and partly uncertain system. Pure sliding mode controller has difficulty in handling unstructured model uncertainties. To solve this problem applied mathematical model-free tuning method to sliding mode controller for adjusting the sliding surface gain (ë ). Since the sliding surface gain (ë) is adjusted by mathematical model free-based tuning method, it is nonlinear and continuous. In this research new ë is obtained by the previous ë multiple sliding surface slopes updating factor (á). Chattering free mathematical error-based tuning sliding mode controller is stable controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in mathematical error-based tuning sliding mode controller with switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).
This document discusses the theoretical and experimental study of dynamics and control of a two-link flexible robot arm. It presents the following:
1) A linear dynamic model of the robot arm is constructed using Ritz's approach and validated experimentally.
2) Three active control schemes are designed using pole placement technique for path tracking and vibration suppression, and tested via simulation.
3) A discrete-time state variable feedback control scheme is presented and designed to control the robot arm's motion using three sensors for position and curvature feedback.
Experimental verification of SMC with moving switching lines applied to hoisti...ISA Interchange
In this paper we propose sliding mode control strategies for the point-to-point motion control of a hoisting crane. The strategies employ time-varying switching lines (characterized by a constant angle of inclination) which move either with a constant deceleration or a constant velocity to the origin of the error state space. An appropriate design of these switching lines results in non-oscillatory convergence of the regulation error in the closed-loop system. Parameters of the lines are selected optimally in the sense of two criteria, i.e. integral absolute error (IAE) and integral of the time multiplied by the absolute error (ITAE). Furthermore, the velocity and acceleration constraints are explicitly taken into account in the optimization process. Theoretical considerations are verified by experimental tests conducted on a laboratory scale hoisting crane.
Fractional-order sliding mode controller for the two-link robot arm IJECEIAES
This study presents a control system of the two-link robot arm based on the sliding mode controller with the fractional-order. Firstly, the equations of the two-link robot arm are analyzed, then the author proposes the controller for each joint based on these equations. The controller is a sliding mode controller with its order is not an integer value. The task of the control system is controlling the torques acted on the joints so that the response angle of each link equal to the desired angle. The effectiveness of the proposed control system is demonstrated through Matlab-Simulink software. The robot model and controller are built for investigating the efficiency of the system. The result shows that the system quality is very good: there is not the chattering phenomenon of torques, the response angle of two links always follow the desired angle with the short transaction time and the static error of zero.
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.
This document discusses using PI and PID controllers to control shaking in a bus suspension system. It first describes modeling a quarter-model of the bus suspension as a mass-spring-damper system. The open-loop response shows oscillations and long settling time. PI and PID controllers are then designed and applied in closed-loop control simulations in MATLAB to improve the response by reducing oscillations and shortening settling time. The PI controller uses proportional and integral terms, while the PID adds a derivative term. Both controllers are evaluated and compared based on time and frequency response characteristics.
This document discusses Slotine's 1987 work on adaptive control of robot manipulators. It presents a globally stable adaptive controller using Lyapunov stability analysis. The controller derives control input and adaptation laws to regulate tracking error and parameter estimation error, ensuring global stability. While position error converges to zero, only velocity error is guaranteed to converge to zero. To ensure convergence of both position and velocity to zero, the document introduces a sliding variable and modified control laws. It also discusses extending the approach to Cartesian space control and dealing with model uncertainties through sliding mode control and adaptive estimation.
This document discusses algorithms for avoiding kinematic singularities in 6-DOF robotic manipulators controlled in real time using a teaching pendant. It proposes two algorithms: (1) non-redundancy avoidance using damped least squares to modify the inverse kinematic solution near singularities, and (2) redundancy avoidance using a potential function based on manipulability to incorporate singularity avoidance for redundant manipulators. The algorithms are experimentally tested on a DENSO VP-6242G robot to evaluate performance near shoulder and wrist singularities during teaching pendant controlled motion.
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).
Fractional order PID for tracking control of a parallel robotic manipulator t...ISA Interchange
This paper presents the tracking control for a robotic manipulator type delta employing fractional order PID controllers with computed torque control strategy. It is contrasted with an integer order PID controller with computed torque control strategy. The mechanical structure, kinematics and dynamic models of the delta robot are descripted. A SOLIDWORKS/MSC-ADAMS/MATLAB co-simulation model of the delta robot is built and employed for the stages of identification, design, and validation of control strategies. Identification of the dynamic model of the robot is performed using the least squares algorithm. A linearized model of the robotic system is obtained employing the computed torque control strategy resulting in a decoupled double integrating system. From the linearized model of the delta robot, fractional order PID and integer order PID controllers are designed, analyzing the dynamical behavior for many evaluation trajectories. Controllers robustness is evaluated against external disturbances employing performance indexes for the joint and spatial error, applied torque in the joints and trajectory tracking. Results show that fractional order PID with the computed torque control strategy has a robust performance and active disturbance rejection when it is applied to parallel robotic manipulators on tracking tasks.
Signature PSO: A novel inertia weight adjustment using fuzzy signature for LQ...journalBEEI
Particle swarm optimization (PSO) is an optimization algorithm that is simple and reliable to complete optimization. The balance between exploration and exploitation of PSO searching characteristics is maintained by inertia weight. Since this parameter has been introduced, there have been several different strategies to determine the inertia weight during a train of the run. This paper describes the method of adjusting the inertia weights using fuzzy signatures called signature PSO. Some parameters were used as a fuzzy signature variable to represent the particle situation in a run. The implementation to solve the tuning problem of linear quadratic regulator (LQR) control parameters is also presented in this paper. Another weight adjustment strategy is also used as a comparison in performance evaluation using an integral time absolute error (ITAE). Experimental results show that signature PSO was able to give a good approximation to the optimum control parameters of LQR in this case.
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).
Similar to Global Stability of A Regulator For Robot Manipulators (20)
The Use of Java Swing’s Components to Develop a WidgetWaqas Tariq
Widget is a kind of application provides a single service such as a map, news feed, simple clock, battery-life indicators, etc. This kind of interactive software object has been developed to facilitate user interface (UI) design. A user interface (UI) function may be implemented using different widgets with the same function. In this article, we present the widget as a platform that is generally used in various applications, such as in desktop, web browser, and mobile phone. We also describe a visual menu of Java Swing’s components that will be used to establish widget. It will assume that we have successfully compiled and run a program that uses Swing components.
3D Human Hand Posture Reconstruction Using a Single 2D ImageWaqas Tariq
Passive sensing of the 3D geometric posture of the human hand has been studied extensively over the past decade. However, these research efforts have been hampered by the computational complexity caused by inverse kinematics and 3D reconstruction. In this paper, our objective focuses on 3D hand posture estimation based on a single 2D image with aim of robotic applications. We introduce the human hand model with 27 degrees of freedom (DOFs) and analyze some of its constraints to reduce the DOFs without any significant degradation of performance. A novel algorithm to estimate the 3D hand posture from eight 2D projected feature points is proposed. Experimental results using real images confirm that our algorithm gives good estimates of the 3D hand pose. Keywords: 3D hand posture estimation; Model-based approach; Gesture recognition; human- computer interface; machine vision.
Camera as Mouse and Keyboard for Handicap Person with Troubleshooting Ability...Waqas Tariq
Camera mouse has been widely used for handicap person to interact with computer. The utmost important of the use of camera mouse is must be able to replace all roles of typical mouse and keyboard. It must be able to provide all mouse click events and keyboard functions (include all shortcut keys) when it is used by handicap person. Also, the use of camera mouse must allow users troubleshooting by themselves. Moreover, it must be able to eliminate neck fatigue effect when it is used during long period. In this paper, we propose camera mouse system with timer as left click event and blinking as right click event. Also, we modify original screen keyboard layout by add two additional buttons (button “drag/ drop” is used to do drag and drop of mouse events and another button is used to call task manager (for troubleshooting)) and change behavior of CTRL, ALT, SHIFT, and CAPS LOCK keys in order to provide shortcut keys of keyboard. Also, we develop recovery method which allows users go from camera and then come back again in order to eliminate neck fatigue effect. The experiments which involve several users have been done in our laboratory. The results show that the use of our camera mouse able to allow users do typing, left and right click events, drag and drop events, and troubleshooting without hand. By implement this system, handicap person can use computer more comfortable and reduce the dryness of eyes.
A Proposed Web Accessibility Framework for the Arab DisabledWaqas Tariq
The Web is providing unprecedented access to information and interaction for people with disabilities. This paper presents a Web accessibility framework which offers the ease of the Web accessing for the disabled Arab users and facilitates their lifelong learning as well. The proposed framework system provides the disabled Arab user with an easy means of access using their mother language so they don’t have to overcome the barrier of learning the target-spoken language. This framework is based on analyzing the web page meta-language, extracting its content and reformulating it in a suitable format for the disabled users. The basic objective of this framework is supporting the equal rights of the Arab disabled people for their access to the education and training with non disabled people. Key Words : Arabic Moon code, Arabic Sign Language, Deaf, Deaf-blind, E-learning Interactivity, Moon code, Web accessibility , Web framework , Web System, WWW.
Real Time Blinking Detection Based on Gabor FilterWaqas Tariq
The document proposes a new method for real-time blinking detection based on Gabor filters. It begins by reviewing existing methods and their limitations in dealing with noise, variations in eye shape, and blinking speed. The proposed method uses a Gabor filter to extract the top and bottom arcs of the eye from an image. It then measures the distance between these arcs and compares it to a threshold: a distance below the threshold indicates a closed eye, while a distance above indicates an open eye. The document claims this Gabor filter-based approach is robust to noise, variations in eye shape and blinking speed. It presents experimental results showing the method can accurately detect blinking across different users.
Computer Input with Human Eyes-Only Using Two Purkinje Images Which Works in ...Waqas Tariq
A method for computer input with human eyes-only using two Purkinje images which works in a real time basis without calibration is proposed. Experimental results shows that cornea curvature can be estimated by using two light sources derived Purkinje images so that no calibration for reducing person-to-person difference of cornea curvature. It is found that the proposed system allows usersf movements of 30 degrees in roll direction and 15 degrees in pitch direction utilizing detected face attitude which is derived from the face plane consisting three feature points on the face, two eyes and nose or mouth. Also it is found that the proposed system does work in a real time basis.
Toward a More Robust Usability concept with Perceived Enjoyment in the contex...Waqas Tariq
Mobile multimedia service is relatively new but has quickly dominated people¡¯s lives, especially among young people. To explain this popularity, this study applies and modifies the Technology Acceptance Model (TAM) to propose a research model and conduct an empirical study. The goal of study is to examine the role of Perceived Enjoyment (PE) and what determinants can contribute to PE in the context of using mobile multimedia service. The result indicates that PE is influencing on Perceived Usefulness (PU) and Perceived Ease of Use (PEOU) and directly Behavior Intention (BI). Aesthetics and flow are key determinants to explain Perceived Enjoyment (PE) in mobile multimedia usage.
Collaborative Learning of Organisational KnolwedgeWaqas Tariq
This paper presents recent research into methods used in Australian Indigenous Knowledge sharing and looks at how these can support the creation of suitable collaborative envi- ronments for timely organisational learning. The protocols and practices as used today and in the past by Indigenous communities are presented and discussed in relation to their relevance to a personalised system of knowledge sharing in modern organisational cultures. This research focuses on user models, knowledge acquisition and integration of data for constructivist learning in a networked repository of or- ganisational knowledge. The data collected in the repository is searched to provide collections of up-to-date and relevant material for training in a work environment. The aim is to improve knowledge collection and sharing in a team envi- ronment. This knowledge can then be collated into a story or workflow that represents the present knowledge in the organisation.
Our research aims to propose a global approach for specification, design and verification of context awareness Human Computer Interface (HCI). This is a Model Based Design approach (MBD). This methodology describes the ubiquitous environment by ontologies. OWL is the standard used for this purpose. The specification and modeling of Human-Computer Interaction are based on Petri nets (PN). This raises the question of representation of Petri nets with XML. We use for this purpose, the standard of modeling PNML. In this paper, we propose an extension of this standard for specification, generation and verification of HCI. This extension is a methodological approach for the construction of PNML with Petri nets. The design principle uses the concept of composition of elementary structures of Petri nets as PNML Modular. The objective is to obtain a valid interface through verification of properties of elementary Petri nets represented with PNML.
Development of Sign Signal Translation System Based on Altera’s FPGA DE2 BoardWaqas Tariq
The main aim of this paper is to build a system that is capable of detecting and recognizing the hand gesture in an image captured by using a camera. The system is built based on Altera’s FPGA DE2 board, which contains a Nios II soft core processor. Image processing techniques and a simple but effective algorithm are implemented to achieve this purpose. Image processing techniques are used to smooth the image in order to ease the subsequent processes in translating the hand sign signal. The algorithm is built for translating the numerical hand sign signal and the result are displayed on the seven segment display. Altera’s Quartus II, SOPC Builder and Nios II EDS software are used to construct the system. By using SOPC Builder, the related components on the DE2 board can be interconnected easily and orderly compared to traditional method that requires lengthy source code and time consuming. Quartus II is used to compile and download the design to the DE2 board. Then, under Nios II EDS, C programming language is used to code the hand sign translation algorithm. Being able to recognize the hand sign signal from images can helps human in controlling a robot and other applications which require only a simple set of instructions provided a CMOS sensor is included in the system.
An overview on Advanced Research Works on Brain-Computer InterfaceWaqas Tariq
A brain–computer interface (BCI) is a proficient result in the research field of human- computer synergy, where direct articulation between brain and an external device occurs resulting in augmenting, assisting and repairing human cognitive. Advanced works like generating brain-computer interface switch technologies for intermittent (or asynchronous) control in natural environments or developing brain-computer interface by Fuzzy logic Systems or by implementing wavelet theory to drive its efficacies are still going on and some useful results has also been found out. The requirements to develop this brain machine interface is also growing day by day i.e. like neuropsychological rehabilitation, emotion control, etc. An overview on the control theory and some advanced works on the field of brain machine interface are shown in this paper.
Exploring the Relationship Between Mobile Phone and Senior Citizens: A Malays...Waqas Tariq
There is growing ageing phenomena with the rise of ageing population throughout the world. According to the World Health Organization (2002), the growing ageing population indicates 694 million, or 223% is expected for people aged 60 and over, since 1970 and 2025.The growth is especially significant in some advanced countries such as North America, Japan, Italy, Germany, United Kingdom and so forth. This growing older adult population has significantly impact the social-culture, lifestyle, healthcare system, economy, infrastructure and government policy of a nation. However, there are limited research studies on the perception and usage of a mobile phone and its service for senior citizens in a developing nation like Malaysia. This paper explores the relationship between mobile phones and senior citizens in Malaysia from the perspective of a developing country. We conducted an exploratory study using contextual interviews with 5 senior citizens of how they perceive their mobile phones. This paper reveals 4 interesting themes from this preliminary study, in addition to the findings of the desirable mobile requirements for local senior citizens with respect of health, safety and communication purposes. The findings of this study bring interesting insight to local telecommunication industries as a whole, and will also serve as groundwork for more in-depth study in the future.
Principles of Good Screen Design in WebsitesWaqas Tariq
Visual techniques for proper arrangement of the elements on the user screen have helped the designers to make the screen look good and attractive. Several visual techniques emphasize the arrangement and ordering of the screen elements based on particular criteria for best appearance of the screen. This paper investigates few significant visual techniques in various web user interfaces and showcases the results for better understanding and their presence.
This document discusses the progress of virtual teams in Albania. It provides context on virtual teams and how they differ from traditional teams in their reliance on technology for communication across distances. The document then examines the use of virtual teams in Albania, noting the growing infrastructure and technology usage that enables virtual collaboration. It highlights some virtual team examples in Albanian government and academic projects.
Cognitive Approach Towards the Maintenance of Web-Sites Through Quality Evalu...Waqas Tariq
It is a well established fact that the Web-Applications require frequent maintenance because of cutting– edge business competitions. The authors have worked on quality evaluation of web-site of Indian ecommerce domain. As a result of that work they have made a quality-wise ranking of these sites. According to their work and also the survey done by various other groups Futurebazaar web-site is considered to be one of the best Indian e-shopping sites. In this research paper the authors are assessing the maintenance of the same site by incorporating the problems incurred during this evaluation. This exercise gives a real world maintainability problem of web-sites. This work will give a clear picture of all the quality metrics which are directly or indirectly related with the maintainability of the web-site.
USEFul: A Framework to Mainstream Web Site Usability through Automated Evalua...Waqas Tariq
A paradox has been observed whereby web site usability is proven to be an essential element in a web site, yet at the same time there exist an abundance of web pages with poor usability. This discrepancy is the result of limitations that are currently preventing web developers in the commercial sector from producing usable web sites. In this paper we propose a framework whose objective is to alleviate this problem by automating certain aspects of the usability evaluation process. Mainstreaming comes as a result of automation, therefore enabling a non-expert in the field of usability to conduct the evaluation. This results in reducing the costs associated with such evaluation. Additionally, the framework allows the flexibility of adding, modifying or deleting guidelines without altering the code that references them since the guidelines and the code are two separate components. A comparison of the evaluation results carried out using the framework against published evaluations of web sites carried out by web site usability professionals reveals that the framework is able to automatically identify the majority of usability violations. Due to the consistency with which it evaluates, it identified additional guideline-related violations that were not identified by the human evaluators.
Robot Arm Utilized Having Meal Support System Based on Computer Input by Huma...Waqas Tariq
A robot arm utilized having meal support system based on computer input by human eyes only is proposed. The proposed system is developed for handicap/disabled persons as well as elderly persons and tested with able persons with several shapes and size of eyes under a variety of illumination conditions. The test results with normal persons show the proposed system does work well for selection of the desired foods and for retrieve the foods as appropriate as usersf requirements. It is found that the proposed system is 21% much faster than the manually controlled robotics.
Dynamic Construction of Telugu Speech Corpus for Voice Enabled Text EditorWaqas Tariq
In recent decades speech interactive systems have gained increasing importance. Performance of an ASR system mainly depends on the availability of large corpus of speech. The conventional method of building a large vocabulary speech recognizer for any language uses a top-down approach to speech. This approach requires large speech corpus with sentence or phoneme level transcription of the speech utterances. The transcriptions must also include different speech order so that the recognizer can build models for all the sounds present. But, for Telugu language, because of its complex nature, a very large, well annotated speech database is very difficult to build. It is very difficult, if not impossible, to cover all the words of any Indian language, where each word may have thousands and millions of word forms. A significant part of grammar that is handled by syntax in English (and other similar languages) is handled within morphology in Telugu. Phrases including several words (that is, tokens) in English would be mapped on to a single word in Telugu.Telugu language is phonetic in nature in addition to rich in morphology. That is why the speech technology developed for English cannot be applied to Telugu language. This paper highlights the work carried out in an attempt to build a voice enabled text editor with capability of automatic term suggestion. Main claim of the paper is the recognition enhancement process developed by us for suitability of highly inflecting, rich morphological languages. This method results in increased speech recognition accuracy with very much reduction in corpus size. It also adapts Telugu words to the database dynamically, resulting in growth of the corpus.
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Global Stability of A Regulator For Robot Manipulators
1. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 220
Global Stability of A Regulator For Robot Manipulators
José Manuel Cervantes mcervantesv@hotmail.com
Department of Mechatronics
Universidad Popular Autónoma del Estado de Puebla (UPAEP)
Puebla, Post code 72160, México
Fernando Reyes freyes@ece.buap.mx
Faculty of Sciences of the Electronics
Benemérita Universidad Autónoma de Puebla (BUAP)
Puebla, Post code 72530, México
Jorge Bedolla ljbedolla@cenidet.edu.mx
Instituto Tecnológico de Apizaco
Av. Instituto Tecnológico s/n, Apizaco,
Tlaxcala, México
Abstract
In this work a regulator for robot manipulators is proposed, it has been developed considering
that the equilibrium point of the closed-loop system is globally asymptotically stable in agreement
with Lyapunov’s direct method. The global asymptotic stability of the controlled system is
analyzed. We present real-time experimental results to show the performance of the proposed
regulator on a robot manipulator of direct drive with three degrees of freedom. The performance
of the new control scheme is compared with respect to the popular PD Algorithm in terms of
positioning error
Keywords: Regulator, Global asymptotic stability, Lyapunov function, position control, robot
manipulators.
1. INTRODUCTION
The position control (also called regulation) of robot manipulators plays a fundamental role in
design and analysis of the modern nonlinear robust controllers. The robot manipulators are
programmed to execute a sequence of movements, such as moving to a location ሺݔଵ, ݕଵ, ݖଵሻ்
and
later to move to a new locationሺݔଶ, ݕଶ, ݖଶሻ்
. Some theoretical results on the stabilization of robot
manipulators under bounded control actions have been reported in the open literature [1] [2].
The goal of position control is to move end-effector of the robot manipulator from any initial state
to a final desired position. In an industrial robot the direct application is point-to-point control using
the proportional-derivative control (PD) plus gravity compensation [1]; another used control is the
proportional integral derivative control(PID) further gravity compensation and modifications of the
same ones [3]. The controller design for these robots can be a linear or nonlinear model, and
many of the industrial systems are nonlinear [4]-[6]. The PID requires the gravitational torque as
partial component of the robot dynamics into its control law, it lacks of a global asymptotic stability
proof, PID has local stability only in a closed loop with robot manipulator [9]-[15]. On the other
hand, the PD has global asymptotic stability in a closed loop [7]. Finally the best feature of these
controllers is that the tuning procedure to achieve global asymptotic stability reduces to select the
proportional and derivative gains in a straightforward manner.
The compensation of gravity allows maintaining the desired position once a final position is
reached, this requires the robots to apply the proper torque on each joint. Additionally, these
regulators assume implicitly that the robot actuators are able to generate the requested torques.
2. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 221
However, in current manipulators robot, the actuators are constrained to supply limited torques
[2],[8]. Due to these disadvantages the regulators PD and PID need to develop a control
algorithm for industrial robots which does not contain their limitations, and at the same time
allows performing the same or better activities carried out within the field of robot [5][16].
The control algorithms used for the control of robot manipulators should present in the equilibrium
point of dynamic model global asymptotically stability, for this reason it is important that the
proposed Lyapunov function candidate is positive definite and its derivative satisfies the
conditions of a negative definite function [2]. To proof an appropriate performance and comply
with the Lyapunov’s stability criteria, in which it is established that the proposed function should
be definite positively and with continuous partial derivatives, also should be considered that the
candidate function fulfill the conditions of Lyapunov [2][8][9]. The Lyapunov theorem ensures that,
any system that is globally asymptotically stable, must satisfy the conditions before mentioned
[3][4]. Unfortunately, for a nonlinear control system, in order to determine a function that satisfies
such conditions is in general difficult. It consists in determining functions whose derivatives along
the trajectories can be rendered negative semi-definite. The proof of this result is made by the
LaSalle’s invariance principle [1]-[4],[19]-[27].
Kelly developed a mathematical analysis for a regulator with a polynomial function to determine
its asymptotic stability [2][18]; also Meza in [17] performs a similar analysis. Sanchez and Reyes
in [18] shows the analysis of a Cartesian controller and evaluate its performance by an
experimental proof, yielding a good performance. Other authors, for example in [25] [26], analyze
the stability of regulators, developed experimental tests and compare their results against the PD
controller. In order to evaluate the performance for regulators, they only measure the Cartesian
position error without considering the transitory, which could be evaluate by using other indicator,
for example the norm L2 is used to evaluate the performance along the trajectories [28].
In this paper, we introduce a position regulator for robots plus gravity compensation, motivated by
the practical interest in the design of regulators and its analysis with the Lyapunov’s theory, to
determine that this possesses global asymptotically stability, in order to carry out its utility and
performance in the position control. It is fundamental, especially in this case, where a regulator is
designed with stabilizing feedback, which are expressed in terms of the first derivatives of
Lyapunov’s function [1],[2].
Real-time experimental results on a direct-drive robot manipulator with three degrees of freedom
are presented. The proposed regulator performance to reach the desired position is good in
comparison with the simple PD algorithm. In order to show its utility and performance we verify
the positions errors between the initial position and final position taking into account for
characteristics of our robot.
This paper is organized by the following form. Section 2, shows the model of the dynamics of
robots and some important properties. The regulator of bounded action for position control, and
its analysis to demonstrate that it has global asymptotic stability with a Lyapunov’s theory is
presented in Section 3. In Section 4, we present results of experimental of regulators into a three
degrees-of-freedom arm, and its comparison with the control PD. Finally, we offer some
conclusions in Section 5.
2. PRELIMINARIES
The dynamics model with n degrees-of-freedom of a manipulator robot with rigid links is
represented by
߬ ൌ ܯሺݍሻݍሷ ܥሺ,ݍ ݍሶሻݍሶ ܤሶ ݃ሺݍሻ (1)
where ߬ is an ݊ x 1 vector of applied torque for the robot, ܯሺሻ is the ݊ x ݊ symmetric positive
definite inertia matrix, ܥሺ,ݍ ݍሶሻ א ܴ ୶
contains the centrifugal and Coriolis forces the size ݊ x ݊,
ܤ א ܴ ୶
, represents the viscous friction matrix of the robot joints, א ܴ
is the vector of
3. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 222
position, ሶ א ܴ
is the vector of velocities of the link, ሷ א ܴ
is the vector of acceleration and ݃ሺሻ
is the torque due to gravitational forces and, it is the ݊ x 1 vector, obtained as the gradient of the
potential energy ܷሺሻ due to gravity [1][5]:
݃ሺሻ ൌ
డሺሻ
ࣔ
. (2)
To simplify the process of analysis and compression of control law is necessary the application of
the following properties of the dynamics model (1), so to facilitate the demonstration of stability
condition(see [2]).
Property 1. The inertia matrix ܯሺሻ is a positive definite symmetric matrix and its components
are a function of , satisfies the following:
ሶ ்
ቂ
ଵ
ଶ
ܯሶ ሺሻ െ ܥሺ, ሶ ሻቃ ሶ ൌ 0 ሶ ߳ ܴ
. (3)
Property 2. Other important property of inertia matrix is:
ܯሺሻ ൌ ܥሺ, ሶ ሻ ܥሺ, ሶ ሻ்
(4)
Property 3. The matrix centrifugal and Coriolis forces ܥሺ, ሶ ሻ, satisfies the following:
ܥሺ, ሶ ሻ ൌ 0 ߳ ܴ
(5)
3. REGULATOR WITH BOUNDED ACTION FOR POSITION CONTROL
The position control problem of robot manipulators can be formulated as follows: considering the
dynamics equation (1) of a robot of ݊ degree-of-freedom, given a desired joint position ݍௗ
assumed constant, trying to determine a vector function ࣎, so that the position associated with the
coordinates asymptotically reaches the robot joint ݍௗ. Formally the goal of pure position control
or simply position control, is to determine ࣎ so that:
lim
௧՜ஶ
ݍሺݐሻ
ݍሶሺݐሻ
൨ ՜ 0
Taking into account the above, we present the design and analyses of a new control scheme for
robot manipulators, the proposed regulator is an algorithm based on the energy shaping which is
written in function of the potential energy, composed of a proportional and a derivative part, in
both by adding the same function and the compensation of gravity. We propose the following
rational saturated regulator (RSR):
߬ ൌ ܭ
ଵଶ
ඥହାమ
െ ݒܭ
ଵଶሶ
ඥହାሶ
݃ሺሻ (6)
Where ܭ and ݒܭ are the diagonal positive definite ݊ x ݊ matrices and so-called proportional gain
and derivative gain, respectively; which are selected by the designer[2][5]. On the other hand,
߳ ܴ
, it is the position error between the manipulator robot’s actual position and the desired
position, defined as:
ൌ ݍௗ െ (7)
by notation is defined
4. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 223
ଵଶ
ඥହା
ൌ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶభ
ඥହାభ
మ
ଵଶమ
ඥହାమ
మ
ڭ
ଵଶ
ඥହା
మے
ۑ
ۑ
ۑ
ۑ
ې
(8)
term of the speed is given by:
ଵଶሶ
ඥହାሶ మ
ൌ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶሶభ
ඥହାሶభ
మ
ଵଶሶమ
ඥହାሶమ
మ
ڭ
ଵଶሶ
ඥହାሶ
మے
ۑ
ۑ
ۑ
ۑ
ې
. (9)
Taking into account (8) and (9), we can write the RSR- regulator (6) as:
߬ ൌ ܭ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶభ
ඥହାభ
మ
ଵଶమ
ඥହାమ
మ
ڭ
ଵଶ
ඥହା
మے
ۑ
ۑ
ۑ
ۑ
ې
െ ݒܭ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶሶభ
ඥହାሶభ
మ
ଵଶሶమ
ඥହାሶమ
మ
ڭ
ଵଶሶ
ඥହାሶ
మے
ۑ
ۑ
ۑ
ۑ
ې
െ ݃ሺሻ (10)
The closed-loop system equation formed by the robot dynamics (1) and structure control of
energy shaping (10) generates a global stable equilibrium point in the sense of Lyapunov, such
an equation expressed in terms of state variables is ሾ்
, ሶ ்ሿ்
in the following way:
ௗ
ௗ௧
ሶ
൨ ൌ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
െሶ
ܯሺሻିଵ
ۏ
ێ
ێ
ێ
ێ
ۍ
ܭ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶభ
ඥହାభ
మ
ଵଶమ
ඥହାమ
మ
ڭ
ଵଶ
ඥହା
మے
ۑ
ۑ
ۑ
ۑ
ې
െ ݒܭ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶሶభ
ඥହାሶభ
మ
ଵଶሶమ
ඥହାሶమ
మ
ڭ
ଵଶሶ
ඥହାሶ
మے
ۑ
ۑ
ۑ
ۑ
ې
െ ܥሺ, ሶ ሻሶ െ ܤሶ
ے
ۑ
ۑ
ۑ
ۑ
ې
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
(11)
In order to carry out the stability analysis, we propose the following radially unbounded positive
definite function as Lyapunov function candidate:
ܸሺ, ሶ ሻ ൌ
ଵ
ଶ
ሶ ்
ܯሺሻሶ ܷሺ,ܭ ሻ. (12)
Where the first term of this Lyapunov function candidate corresponds to the kinetic energy, which
is a positive definite function in ሶ , because inertia matrix M(q) is positive definite. The second
term ܷሺ,ܭ ሻ is the artificial potential energy, this term is a radially unbounded positive definite
function in , and design ܭ is a positive-definite matrix.
The term ܷሺ,ܭ ሻ in (12) is defined in the following way:
ܷሺ,ܭ ሻ ൌ 2
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍටඥ5 6ݍଵ
ଶ
െ √5
ටඥ5 6ݍଶ
ଶ
െ √5
ڭ
ටඥ5 6ݍ
ଶ െ √5ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
்
ܭ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍටඥ5 6ݍଵ
ଶ
െ √5
ටඥ5 6ݍଶ
ଶ
െ √5
ڭ
ටඥ5 6ݍ
ଶ െ √5ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
. (13)
5. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 224
Therefore, incorporating (13) into (12), we get
ܸሺ, ሶ ሻ ൌ
ଵ
ଶ
ሶ ்
ܯሺሻሶ 2
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍටඥ5 6ݍଵ
ଶ
െ √5
ටඥ5 6ݍଶ
ଶ
െ √5
ڭ
ටඥ5 6ݍ
ଶ െ √5ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
்
ܭ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍටඥ5 6ݍଵ
ଶ
െ √5
ටඥ5 6ݍଶ
ଶ
െ √5
ڭ
ටඥ5 6ݍ
ଶ െ √5ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
. (14)
To demonstrate that candidate function satisfies the Lyapunove’s conditions, we have (11) which
complies with the following conditions: The first term is defined positive because the inertia matrix
ܯሺሻ is positive definite. The second term is the artificial potential energy also is a positive
definite function on the position error vector . Note that the term √5 was introduced to make
ൌ 0, ܸሺ, ሶ ሻ is zero; Therefore, the Lyapunov function candidate ܸሺ, ሶ ሻ is a positive definite
function in form globally and radially unbounded.
The time derivative of the Lyapunov function candidate (14) along the trajectories of the closed-
loop system can be written as
ܸሶ ሺ, ሶ ሻ ൌ ሶ ்
ܯሺሻሷ
ଵ
ଶ
ሶ ்
ܯሶ ሺሻሶ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍටඥ5 6ݍଵ
ଶ
െ √5
ටඥ5 6ݍଶ
ଶ
െ √5
ڭ
ටඥ5 6ݍ
ଶ
െ √5ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
்
ܭ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
ଵଶభ
ටඥହାభ
మି√ହ ඥହାభ
మ
ଵଶమ
ටඥହାమ
మି√ହ ඥହାమ
మ
ڭ
ଵଶ
ටඥହା
మି√ହ ඥହା
మ
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
ሶ . (15)
Considering that the derived of the position error it is ሶ ൌ െሶ , because the desired position ݍௗ is a
constant, and substituting the value of the acceleration ሷ of the equation of closed-loop (11) into
(15), we have
ܸሶ ሺ, ሶ ሻ ൌ ሶ ்
ܯሺሻ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
ܯሺሻିଵ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
ܭ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
12ݍଵ
ඥ5 6ݍଵ
ଶ
12ݍଶ
ඥ5 6ݍଶ
ଶ
ڭ
12ݍ
ඥ5 6ݍ
ଶ
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
െ ݒܭ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
12ݍሶଵ
ඥ5 6ݍሶଵ
ଶ
12ݍሶଶ
ඥ5 6ݍሶଶ
ଶ
ڭ
12ݍሶ
ඥ5 6ݍሶ
ଶ
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
െ ܥሺ, ሶ ሻሶ െ ܤሶ
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
1
2
ሶ ்
ܯሶ ሺሻሶ െ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍටඥ5 6ݍଵ
ଶ
െ √5
ටඥ5 6ݍଶ
ଶ
െ √5
ڭ
ටඥ5 6ݍ
ଶ െ √5ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
்
ܭ
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
ଵଶభ
ටඥହାభ
మି√ହ ඥହାభ
మ
ଵଶమ
ටඥହାమ
మି√ହ ඥହାమ
మ
ڭ
ଵଶ
ටඥହା
మି√ହ ඥହା
మ
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
ሶ (16)
solving the suitable operations, we have:
7. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 226
ܸሶ ሺ, ሶ ሻ ൌ െሶ ்ݒܭ
ۏ
ێ
ێ
ێ
ێ
ۍ
ଵଶሶభ
ඥହାሶభ
మ
ଵଶሶమ
ඥହାሶమ
మ
ڭ
ଵଶሶ
ඥହାሶ
మے
ۑ
ۑ
ۑ
ۑ
ې
െ ሶ ்ܤሶ 0 (22)
Using the fact that the Lyapunov function candidate (14) is a globally positive definite function and
its time derivative is a globally negative semi-definite function, we conclude that the equilibrium of
the closed-loop system (11) is stable. Finally, we can use the LaSalle’s invariance principle to
demonstrate the global asymptotic stability of the equilibrium. Toward this end, let us defined the
set Ω as:
Ωൌ ൜
ሶ
൨ ߳ ܴଶ
ܸሶ ሺ, ሶ ሻ ൌ 0ൠ (23)
Ωൌ ሼ ߳ ܴ
, ሶ ൌ 0 ߳ ܴሽ (24)
The unique invariant is ሾ்
, ሶ ்ሿ ߳ ܴଶ
. We conclude that this equilibrium is globally asymptotically
stable.
4. EXPERIMENTAL RESULTS AND DISCUSSION
The algorithm RSR is experimentally tested in an experimental platform, which consists of a three
degree-of freedom direct-driver robot manipulator, designed and built at The Benemerita
Universidad Autónoma de Puebla to research robot control algorithms. Figure 1 shows the
manipulator robot. It is a direct-drive manipulator robot that consists of links made of 6061
aluminum actuated by brushless direct drive servo actuator from Parker Compumotor to drive the
joints without gear reduction (the motors characteristics used in the experimental robot are on the
Table 1).
FIGURE 1: Robot Manipulator.
In this robot manipulator we recall the equation of the control law (10) to apply the torque in each
joint to produced the movement in every link of the robot. The proportional gains were chosen
such that ߬ ൏ ԡ߬௫ԡ, where ߬௫ represents the maximum applied torque of the ݅th joint (see
limits of actuators in Table 1).
The empirical procedure that was used to select the tunning of the proportional gain is given by:
ܭ ൌ 80%߬௫/ݍௗ, after several experimental tests and considering that the best time response
8. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and
without overshoot the minimum
saturation zone of the actuators torques.
Link
Base
Shoulder
Elbow
TABLE
The proportional and derivative gains were selected
The initial conditions for the joint positions of
Link one (Base) degrees;
degrees.
The initial conditions for the joint velocities are:
Base joint degrees/sec;
degrees/sec.
The desired final position was definite as
degrees, considered time in the experiment
positions was seconds.
The experimental results of RSR
the regulator in function of the position errors
FIGURE 2
Figure 2 shows that, as time evolves, the position
position control objective defined in equation (
tracking position error in the exponential regulato
degree in 1.757517sec.
0.123596 ± 0.0269 degree in
, Fernando Reyes & Jorge Bedolla
and Automation (IJRA), Volume (3) : Issue (4) : 2012
without overshoot the minimum steady-state position error were obtained without reach the
zone of the actuators torques.
Model Torque [Nm] p/rev
DM-1015B 15 1024000
DM-1050A 50 1024000
DM-1004C 4 1024000
TABLE 1: Servo actuators of the robot manipulator.
The proportional and derivative gains were selected as:
;
The initial conditions for the joint positions of the robot manipulator were defined as:
degrees; Link two (Shoulder) degrees; Link three (Elbow)
The initial conditions for the joint velocities are:
degrees/sec; Shoulder joint degrees/sec; Elbow joint
The desired final position was definite as: degrees, degrees
onsidered time in the experiment to that the robot arrive to the final
RSR-regulator are depicted in Figures 2-3. We analyze the acting of
in function of the position errors and the applied torque .
FIGURE 2: Position error of regulator RSR.
shows that, as time evolves, the position errors tend to zero, in agreement with
control objective defined in equation (10), in this case we can see with regard to the
ror in the exponential regulator was of approximately 0.035156
= 0.086329 ± 0.0074 degree in 0.672499
0.902499sec. The position is maintained until the end of the
227
error were obtained without reach the
the robot manipulator were defined as:
Link three (Elbow)
Elbow joint
degrees and
to that the robot arrive to the final
3. We analyze the acting of
tend to zero, in agreement with
case we can see with regard to the
0.035156±0.0087
0.672499sec.
The position is maintained until the end of the
9. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and
experiment. It can be concluded that the robot
overshoot toward the reference position
Figure 3 shows that the applied torque for each joint remain within the prescribed limits of these
actuators (see Table 1), and the magnitude of the torques stay inside physics li
state. Each joint has a smooth moving, free from irregularities; in stationary state the magnitude
of the base torque is: 2.497
2.963 Nm. Also it is observed that the applied
two links, this is because of it corresponds to the shoulder joint, which has to support the weight
of the arm, causing high oscillations of the applied torque during the first instants of time of the
movement, and later decrease until a value of 11.11396±1.23
servos to the links one and three are approximately constant during the beginning of the
movement, later on they present smaller oscillations to locate to the links in
Torque oscillates among
1.524700Nm. The value of the applied torque to the shoulder and elbow links do not decrease to
zero because they have to stay in the specified position,
apply a torque to compensate the effects of the force of gravity that it acts on them.
FIGURE 3
In order to compare the performance of the
tests with the known PD-regulator
The tunning-up for proportional and derivative gains were selected as:
Figure 4 shows that the position error
this presents a broad overshoot and when the experiment concludes his position error was
several degrees −0.72399 ± 0.000275
4.466492 ± 0.001098 degrees.
, Fernando Reyes & Jorge Bedolla
and Automation (IJRA), Volume (3) : Issue (4) : 2012
It can be concluded that the robot system moves fast and practically without
reference position .
Figure 3 shows that the applied torque for each joint remain within the prescribed limits of these
actuators (see Table 1), and the magnitude of the torques stay inside physics limits in steady
state. Each joint has a smooth moving, free from irregularities; in stationary state the magnitude
2.497 Nm; for shoulder joint 34.775 Nm; and elbow joint
. Also it is observed that the applied torque for the link two ( ) is higher than the other
two links, this is because of it corresponds to the shoulder joint, which has to support the weight
of the arm, causing high oscillations of the applied torque during the first instants of time of the
movement, and later decrease until a value of 11.11396±1.23Nm; the applied torque by the
servos to the links one and three are approximately constant during the beginning of the
movement, later on they present smaller oscillations to locate to the links in their final position.
oscillates among -0.61233Nm and 0.920216Nm; among -0.11133
. The value of the applied torque to the shoulder and elbow links do not decrease to
zero because they have to stay in the specified position, for such a reason the servo actuators
apply a torque to compensate the effects of the force of gravity that it acts on them.
FIGURE 3: Applied torque to the joints of the manipulator.
the performance of the RSR-regulator presented here, develop experimental
regulator
up for proportional and derivative gains were selected as:
;
Figure 4 shows that the position error of PD regulator falls with a tendency to zero, however,
this presents a broad overshoot and when the experiment concludes his position error was
−0.72399 ± 0.000275 degrees, 5.47241 ± 0.00386
228
fast and practically without
Figure 3 shows that the applied torque for each joint remain within the prescribed limits of these
mits in steady-
state. Each joint has a smooth moving, free from irregularities; in stationary state the magnitude
; and elbow joint
) is higher than the other
two links, this is because of it corresponds to the shoulder joint, which has to support the weight
of the arm, causing high oscillations of the applied torque during the first instants of time of the
; the applied torque by the
servos to the links one and three are approximately constant during the beginning of the
their final position.
0.11133Nm and
. The value of the applied torque to the shoulder and elbow links do not decrease to
for such a reason the servo actuators
apply a torque to compensate the effects of the force of gravity that it acts on them.
here, develop experimental
(25)
.
r falls with a tendency to zero, however,
this presents a broad overshoot and when the experiment concludes his position error was
5.47241 ± 0.00386 degrees,
10. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and
FIGURE 4: Position error and applied torque
As we can appreciate the values of the torque applied
are bigger than the maximum torque values that can give the
1; therefore they work in the saturation condition during the first instants
displacement. Applied torque by
position stays approximately constant
Previous results do not allow us to properly compare the p
PD-regulator. With this propose, the
of position error is given by:
Where is the duration of the experimental test, in our case, 5 seconds. A small
represents a better regulator performance.
The performance result of regulato
norm corresponds to RSR-regulator
regulator had the best performance when compared
norm criterion.
FIGURE 5
, Fernando Reyes & Jorge Bedolla
and Automation (IJRA), Volume (3) : Issue (4) : 2012
Position error and applied torque by means of the control PD.
As we can appreciate the values of the torque applied by the PD-regulator (see Figure
than the maximum torque values that can give the servo actuators according to
1; therefore they work in the saturation condition during the first instants of the robot’s
displacement. Applied torque by the PD when the robot manipulator approaches to the
position stays approximately constant to maintain the position.
Previous results do not allow us to properly compare the performance of proposed regulato
r. With this propose, the L2 norm criterion has error useful. The scalar value
L2
is the duration of the experimental test, in our case, 5 seconds. A small
r performance.
performance result of regulators is shown in Figure 5. It can be observed that the smaller
regulator, considering these results, we can conclude that the
r had the best performance when compared whit PD-regulator using the scalar
FIGURE 5: Performance index of regulators.
229
r (see Figure 4), they
servo actuators according to Table
of the robot’s
the PD when the robot manipulator approaches to the desired
erformance of proposed regulator and
norm criterion has error useful. The scalar value L2 norm
(26)
is the duration of the experimental test, in our case, 5 seconds. A small L2 value
rs is shown in Figure 5. It can be observed that the smaller L2
, considering these results, we can conclude that the RSR-
using the scalar-valued L2
11. José Manuel Cervantes, Fernando Reyes & Jorge Bedolla
International Journal of Robotics and Automation (IJRA), Volume (3) : Issue (4) : 2012 230
5. CONCLUSIONS & FUTURE WORK
In this paper, we have presented a simple regulator (RSR) to solve the position control problem of
robot manipulators, motivated by the practical interest of relying on control algorithms that
preserve global asymptotic stability. The RSR-regulator is analyzed, demonstrating that the origin
of the state space is asymptotically stable in Lyapunov’s sense.
We have developed experiments on a direct-drive robot system of 3 degrees-of freedom, that
demonstrate the stability and performance of the RSR regulator. We have shown that, for desired
position and under the design guidelines, the requested torques remain within the prescribed
limits of the actuators, guaranteeing their correct operation during the experiment, and the
steady-state position errors are inside an interval around zero, as shown from the results of the
experiments that are carried out. The L2 norm provided a suitable index used to compare the
performance of the RSR-regulator with the PD-regulator under de same conditions, which for the
case presented herein, it showed that the RSR-regulator has a better performance. A future work
is the generation with auto-tuning control algorithms that enable better performance and reduce
time tuning the gains.
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