The 2nd International Conference on Control, Instrumentation and Automation, 2011
ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dyn... more ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dynamics Control system is developed for tracking desired vehicle behavior. The sliding mode controller is exploited for yaw moment controller and the fuzzy logic controller is applied for wheel slip control. Then an optimization problem is solved to find the optimum set of tire forces for generating desired yaw moment. To find out the weighting coefficients of optimization cost function, a fuzzy adaptation mechanism which based on the concept of brake intervention is used by utilizing maximum capacity of all tires. Simulation results on 8-DOF nonlinear vehicle model have shown that if the weighting coefficients of the front wheels are adopted to be greater than corresponding values of the rear wheels, the vehicle will be more responsiveness. On the other hand, if the weighting coefficients of the rear wheels are tuned to be greater than the value of front wheels, the dynamics of the vehicle becomes more stable and to achieve both of them and to use the maximum capacity of the tires an intermediate mode with fuzzy adaptation mechanism is the best case.
This thesis deals with the analysis and synthesis of piecewise smooth (PWS) systems. In general, ... more This thesis deals with the analysis and synthesis of piecewise smooth (PWS) systems. In general, PWS systems are nonsmooth systems, which means their vector fields are discontinuous functions of the state vector. Dynamic behavior of nonsmooth systems is richer than smooth systems. For example, there are phenomena such as sliding modes that occur only in nonsmooth systems. In this thesis, a Lyapunov stability theorem is proved to provide the theoretical framework for the stability analysis of PWS systems. Piecewise affine (PWA) and piecewise polynomial (PWP) systems are then introduced as important subclasses of PWS systems. The objective of this thesis is to propose efficient computational controller synthesis methods for PWA and PWP systems. Three synthesis methods are presented in this thesis. The first method extends linear controllers for uncertain nonlinear systems to PWA controllers. The result is a PWA controller that maintains the performance of the linear controller while e...
This paper introduces the dual parameter set of a piecewise affine (PWA) system. This is a key co... more This paper introduces the dual parameter set of a piecewise affine (PWA) system. This is a key concept to enable a convex formulation of PWA controller synthesis for PWA slab differential inclusions using a new convex relaxation. Another important contribution of the paper is to present PWA L2-gain analysis and synthesis results for PWA systems whose output is also a PWA function of the state (as opposed to a piecewise-linear function). Unlike other results existing in the literature, the sufficient LMI conditions in this paper are valid for synthesis, even when the PWA systems include sliding modes. A numerical example with sliding modes illustrates the new approach.
This paper addresses stability analysis of sampled-data piecewise-affine (PWA) systems consisting... more This paper addresses stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampleddata closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficientconditions for non-fragility of the stabilizing continuous-time PWA state feedback controller.
ABSTRACT A toolbox for piecewise-affine (PWA) systems called PWATOOLS is introduced in this paper... more ABSTRACT A toolbox for piecewise-affine (PWA) systems called PWATOOLS is introduced in this paper. Numerical control synthesis methodologies for PWA and nonlinear systems have been implemented in this toolbox. Although several Lyapunov-based PWA control synthesis approaches exist in the literature, to the best of our knowledge there is no software toolbox that implements these methods for continuous-time PWA systems that is also capable of analyzing nonlinear systems and synthesizing PWA controllers for them. PWATOOLS is proposed to fill this gap as a software toolbox with the ability to analyze and synthesize PWA controllers for nonlinear systems. The toolbox proposed in this paper has been written to serve as an educational as well as a modeling, analysis and synthesis tool. PWATOOLS uses Yalmip, SeDuMi and PENBMI to find solutions for the sufficient conditions for stability analysis of the models or the synthesis of PWA controllers. An example in active flutter supression illustrates the use of this new toolbox.
The 2nd International Conference on Control, Instrumentation and Automation, 2011
ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dyn... more ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dynamics Control system is developed for tracking desired vehicle behavior. The sliding mode controller is exploited for yaw moment controller and the fuzzy logic controller is applied for wheel slip control. Then an optimization problem is solved to find the optimum set of tire forces for generating desired yaw moment. To find out the weighting coefficients of optimization cost function, a fuzzy adaptation mechanism which based on the concept of brake intervention is used by utilizing maximum capacity of all tires. Simulation results on 8-DOF nonlinear vehicle model have shown that if the weighting coefficients of the front wheels are adopted to be greater than corresponding values of the rear wheels, the vehicle will be more responsiveness. On the other hand, if the weighting coefficients of the rear wheels are tuned to be greater than the value of front wheels, the dynamics of the vehicle becomes more stable and to achieve both of them and to use the maximum capacity of the tires an intermediate mode with fuzzy adaptation mechanism is the best case.
The 2nd International Conference on Control, Instrumentation and Automation, 2011
ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dyn... more ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dynamics Control system is developed for tracking desired vehicle behavior. The sliding mode controller is exploited for yaw moment controller and the fuzzy logic controller is applied for wheel slip control. Then an optimization problem is solved to find the optimum set of tire forces for generating desired yaw moment. To find out the weighting coefficients of optimization cost function, a fuzzy adaptation mechanism which based on the concept of brake intervention is used by utilizing maximum capacity of all tires. Simulation results on 8-DOF nonlinear vehicle model have shown that if the weighting coefficients of the front wheels are adopted to be greater than corresponding values of the rear wheels, the vehicle will be more responsiveness. On the other hand, if the weighting coefficients of the rear wheels are tuned to be greater than the value of front wheels, the dynamics of the vehicle becomes more stable and to achieve both of them and to use the maximum capacity of the tires an intermediate mode with fuzzy adaptation mechanism is the best case.
This thesis deals with the analysis and synthesis of piecewise smooth (PWS) systems. In general, ... more This thesis deals with the analysis and synthesis of piecewise smooth (PWS) systems. In general, PWS systems are nonsmooth systems, which means their vector fields are discontinuous functions of the state vector. Dynamic behavior of nonsmooth systems is richer than smooth systems. For example, there are phenomena such as sliding modes that occur only in nonsmooth systems. In this thesis, a Lyapunov stability theorem is proved to provide the theoretical framework for the stability analysis of PWS systems. Piecewise affine (PWA) and piecewise polynomial (PWP) systems are then introduced as important subclasses of PWS systems. The objective of this thesis is to propose efficient computational controller synthesis methods for PWA and PWP systems. Three synthesis methods are presented in this thesis. The first method extends linear controllers for uncertain nonlinear systems to PWA controllers. The result is a PWA controller that maintains the performance of the linear controller while e...
This paper introduces the dual parameter set of a piecewise affine (PWA) system. This is a key co... more This paper introduces the dual parameter set of a piecewise affine (PWA) system. This is a key concept to enable a convex formulation of PWA controller synthesis for PWA slab differential inclusions using a new convex relaxation. Another important contribution of the paper is to present PWA L2-gain analysis and synthesis results for PWA systems whose output is also a PWA function of the state (as opposed to a piecewise-linear function). Unlike other results existing in the literature, the sufficient LMI conditions in this paper are valid for synthesis, even when the PWA systems include sliding modes. A numerical example with sliding modes illustrates the new approach.
This paper addresses stability analysis of sampled-data piecewise-affine (PWA) systems consisting... more This paper addresses stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampleddata closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficientconditions for non-fragility of the stabilizing continuous-time PWA state feedback controller.
ABSTRACT A toolbox for piecewise-affine (PWA) systems called PWATOOLS is introduced in this paper... more ABSTRACT A toolbox for piecewise-affine (PWA) systems called PWATOOLS is introduced in this paper. Numerical control synthesis methodologies for PWA and nonlinear systems have been implemented in this toolbox. Although several Lyapunov-based PWA control synthesis approaches exist in the literature, to the best of our knowledge there is no software toolbox that implements these methods for continuous-time PWA systems that is also capable of analyzing nonlinear systems and synthesizing PWA controllers for them. PWATOOLS is proposed to fill this gap as a software toolbox with the ability to analyze and synthesize PWA controllers for nonlinear systems. The toolbox proposed in this paper has been written to serve as an educational as well as a modeling, analysis and synthesis tool. PWATOOLS uses Yalmip, SeDuMi and PENBMI to find solutions for the sufficient conditions for stability analysis of the models or the synthesis of PWA controllers. An example in active flutter supression illustrates the use of this new toolbox.
The 2nd International Conference on Control, Instrumentation and Automation, 2011
ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dyn... more ABSTRACT In order to improve the lateral stability of the vehicles at a high speed, a Vehicle Dynamics Control system is developed for tracking desired vehicle behavior. The sliding mode controller is exploited for yaw moment controller and the fuzzy logic controller is applied for wheel slip control. Then an optimization problem is solved to find the optimum set of tire forces for generating desired yaw moment. To find out the weighting coefficients of optimization cost function, a fuzzy adaptation mechanism which based on the concept of brake intervention is used by utilizing maximum capacity of all tires. Simulation results on 8-DOF nonlinear vehicle model have shown that if the weighting coefficients of the front wheels are adopted to be greater than corresponding values of the rear wheels, the vehicle will be more responsiveness. On the other hand, if the weighting coefficients of the rear wheels are tuned to be greater than the value of front wheels, the dynamics of the vehicle becomes more stable and to achieve both of them and to use the maximum capacity of the tires an intermediate mode with fuzzy adaptation mechanism is the best case.
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