Elyes Maherzi | Université de Carthage (original) (raw)

Papers by Elyes Maherzi

International Journal of Automation and Control, 2020

This paper proposes a synthesis of a dynamic controller under constraints. It is based on model p... more This paper proposes a synthesis of a dynamic controller under constraints. It is based on model predictive control (MPC) approach and resolution of a convex optimisation problem with linear matrix inequalities (LMI). The controller guarantees the closed-loop stability for polytopic time-varying uncertain systems. Conditions are provided for the controller design based on the parameter dependent Lyapunov functions (PDLF). A new demonstration is developed based on the relaxation technique, to include a slack variables G i. The new LMI's formulation offers an additional degree of freedom for the controller design. Input and output constraints are also taken into account during the design of the controller. This approach allows varying and adjusting the dynamic of system by taking into account input/output constraints.

ABSTRACT To ensure high availability of industrial systems, recent developments in system design ... more ABSTRACT To ensure high availability of industrial systems, recent developments in system design technology like in aerospace, defense, petro-chemistry and automobiles, are represented earlier in literature by simulated models during the conception step. These developments have facilitated the integration of diagnostic-prognostic models in these industrial systems. The monitoring of degradation indicators is used indirectly in failure prognostic. It is just a measurement of an unwanted situation. Hence, the diagnostic is not only a failure detection procedure but it also indicates the actual state and the historic of the system. The subsequent prognostic model leads to a predictive maintenance. The Remaining Useful Life is estimated from a predefined threshold of degradation. We will present here a procedure to create a failure prognostic model based on a physical dynamic system. But instead of degradation abaci largely used in prognostic studies, we will adopt here analytic laws of degradation such as Paris’ law for fatigue degradation and Miner’s law for cumulative damage.

Research Journal of Applied Sciences, Engineering and Technology, 2014

This study presents a new approach for modeling and controlling of a compass gait biped robot bas... more This study presents a new approach for modeling and controlling of a compass gait biped robot based on the use of the switched systems. The linearization of the equations stemming from the formalism of Lagrange allows the construction of a set of local models used to describe the behavior of this non linear system. The selection of each model depends on its activation function depending on the system states. The synthesis of the stability of the walking robot is based on the use of second method of Lyapunov. The synthesis approach leads to a set of bilinear matrices inequalities non resolvable by actual numerical solvers. To come over these difficulties, some relaxations are brought to get useful and exploitable numerical solutions.

Research Journal of Applied Sciences, Engineering and Technology, 2014

Having regard to the large application of the inverted pendulum in robotic system, this study is ... more Having regard to the large application of the inverted pendulum in robotic system, this study is interested in controlling this process with two strategies of controls. The first proposed control is the state feedback with an observer based on the Generalized Predictive Control (GPC) algorithm. In the second proposed control we used the characteristic of predictive control GPC to improve the performance of the classical PID controller. The obtained results have been discussed and compared; the simulation results obtained by the predictive PID control are mentioned.

International Journal of Advanced Computer Science and Applications, 2016

the analysis and control of delayed systems are becoming more and more research topics in progres... more the analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. In other hand, the controls of humanoid walking robot present a common problem in robotics because it involves physical interaction between an articulated system and its environment. This close relationship is actually a common set of fundamental problems such as the implementation of robust stable dynamic control. This paper presents acomplete approach, based on switched system theory, for the stabilization of a compass gait robot subject to time delays transmission. The multiple feedback gains designed are based on multiple linear systems governed by a switching control law. The establishment of control law in real time is affected by the unknown pounded random delay. The results obtained from this method show that the control law stabilize the compass robot walk despite a varying delay reaching six times sampling period.

2015 World Symposium on Mechatronics Engineering & Applied Physics (WSMEAP), 2015

ABSTRACT

Procedia Computer Science, 2015

Predictive control presents a solution to the problem of the trajectory generation for a humanoid... more Predictive control presents a solution to the problem of the trajectory generation for a humanoid robot. This control strategy is introduced by Katayama 13 and improved by Kajita 1 , in those literatures, the theory of predictive control is used to calculate the trajectory of the mass center of the cart table to track a reference trajectory and give it for the ZMP. However this control has an inconvenience such as the non respect of real-time constraints, due to the computation time and the output response establishing. In this paper we propose the predictive PID controller that imitate the calculated time and reduce the complexity of the control algorithm. The aim of this new control approach for biped robot is to make walking smoother and more efficient.

2015 International Conference on Solar Energy and Building (ICSoEB), 2015

ABSTRACT

ABSTRACT This paper discusses the robust stabilization of discrete switched systems, focusing on ... more ABSTRACT This paper discusses the robust stabilization of discrete switched systems, focusing on the design of a robust static output feed-back control and dynamic output control based on a switched observer. The results are derived using the direct Lyapunov approach and the polyquadratic function concept. The stabi-lization conditions are written through linear matrix inequalities relations. The polyquadratic Lyapunov approach provides a con-structive way to tackle uncertainty in the switched framework. The feasibility is illustrated on an example of discrete uncertain switched discrete time system.

This paper discusses the stabilization of discrete time, polytopic uncertain switched systems, fo... more This paper discusses the stabilization of discrete time, polytopic uncertain switched systems, focusing on the design of a robust dynamic output feedback control, based on a Luenberger observer's. The results are derived using the direct Lyapunov approach and the polyquadratic function concept. The stabilization conditions are written through linear matrix inequalities relations. The polyquadratic Lyapunov approach provides a constructive way to tackle uncertainty in the switched framework. The feasibility is illustrated on an example of discrete time uncertain switched systems, when one of used actuators broke down.

American Journal of Applied Sciences, 2010

Problem statement: The estimation of states and the unknown inputs of a nonlinear system describe... more Problem statement: The estimation of states and the unknown inputs of a nonlinear system described by a multimodel are done by a multiobserver. The stabilization of the multiobserver calls upon uses both quadratic and no quadratic functions of Lyapunov. Although the stabilization using the quadratic approach is interesting from the point of view implementation, the step showed its limits for the multimodel. However, the problem paused by the quadratic method lies in the obligation to satisfy several LMI with respect to the same Lyapunov matrix P, these results are shown very conservative. Approach: To reduce the conservatism of the quadratic approach we propose another approach which is exclusively based on Lyapunov piecewise quadratic functions. The conditions obtained by the stabilization of the multiobserver are expressed in term of matrix inequalities with constraints on the matrices rank. Results: The estimation of both states and unknown inputs of a multimodel using the quadratic approach per pieces leads to results less conservative than the quadratic approach. Academic examples illustrate the robustness of the piecewise quadratic approach. Conclusion: In this article we proposed new sufficient conditions of stability of a multiobserver able to the estimation of states and unknown inputs of a nonlinear system describes by a multimodel subjected to the influence of the unknown inputs. The study in was carried out by considering two approaches. The first approach is based on Lyapunov quadratic functions; it is significant to note the great difficulty in finding satisfying results by this approach for the multimodel systems. For this reason we proposed an approach based on piecewise quadratic functions which led to interesting results (proposition 1) and less conservative than the quadratic approach. The conditions suggested in this article concern both the multiobserver stabilization and the estimation of states and the unknown inputs of a multimodel with measurable variables of decision (µξ(k)). The synthesis of a multiobserver with no measurable variables of decision is not approached. This point can constitute an interesting prospect for this study.

Abstract: Problem statement: More advanced control techniques have been developed in recent decad... more Abstract: Problem statement: More advanced control techniques have been developed in recent decades following the great progress of calculations means. Without considering the constraints on system variables, the response of controlled system moves away from the desired response. Hence the control strategy must provide the ability to integrate these constraints in the design phase of the controller. Approach: This study presents a design of robust dynamic controller which was based on the control strategy MPC for an uncertain discrete system described by a multimodel by solving an optimization problem. The Model Predictive Control (MPC) strategy uses a dynamic model of the process in order to predict its future behavior. This control strategy, that we propose, makes it possible to integrate these constraints in the design phase of the controller. The design of the robust dynamic controller must maintain the stability and performance of the system in the presence of uncertainties. Th...

In this paper an algorithm is presented for the stabilization of a non linear and multi-inputs sy... more In this paper an algorithm is presented for the stabilization of a non linear and multi-inputs system: a blower temperature described by a multimodel. The originality of this work lies on the fact that the applied control is quantified. In the first stage, a synthesis of a multiobserver, stabilized polyquadratically, with proper characteristic values situated in a disc inside unit circle is presented. The command law, stabilized polyquadratically, is based on the multiobserver and tracing of poles. In a second stage, the computed control can not be directly applied to the plant because of the quantification imposed by the heating resistors. To go over this problem, the variation of the ventilation's speed can compensate for the errors of the command due to the quantification of the heated power. The choice of the optimal ventilation's speed is based on the minimization of a criterion evaluating the distance between the measured output and the desired output.

This paper presents a less conservative approach for the synthesis of a multiobserver able to est... more This paper presents a less conservative approach for the synthesis of a multiobserver able to estimate the states and unknown inputs of a discrete nonlinear system. The stabilization of the error observation is guaranteed by the use of the second Lyapunov approch. The stability conditions obtained are expressed in term of Linear Matrices Inequalities (LMI) and are got from the use of the Lyapunov quadratic functions in a first study and from the Lyapunov polyquadratic functions in a second study which appears less conservative and less constraining than the first. Illustrative examples are also presented in this paper.

International Journal of Automation and Control, 2020

This paper proposes a synthesis of a dynamic controller under constraints. It is based on model p... more This paper proposes a synthesis of a dynamic controller under constraints. It is based on model predictive control (MPC) approach and resolution of a convex optimisation problem with linear matrix inequalities (LMI). The controller guarantees the closed-loop stability for polytopic time-varying uncertain systems. Conditions are provided for the controller design based on the parameter dependent Lyapunov functions (PDLF). A new demonstration is developed based on the relaxation technique, to include a slack variables G i. The new LMI's formulation offers an additional degree of freedom for the controller design. Input and output constraints are also taken into account during the design of the controller. This approach allows varying and adjusting the dynamic of system by taking into account input/output constraints.

ABSTRACT To ensure high availability of industrial systems, recent developments in system design ... more ABSTRACT To ensure high availability of industrial systems, recent developments in system design technology like in aerospace, defense, petro-chemistry and automobiles, are represented earlier in literature by simulated models during the conception step. These developments have facilitated the integration of diagnostic-prognostic models in these industrial systems. The monitoring of degradation indicators is used indirectly in failure prognostic. It is just a measurement of an unwanted situation. Hence, the diagnostic is not only a failure detection procedure but it also indicates the actual state and the historic of the system. The subsequent prognostic model leads to a predictive maintenance. The Remaining Useful Life is estimated from a predefined threshold of degradation. We will present here a procedure to create a failure prognostic model based on a physical dynamic system. But instead of degradation abaci largely used in prognostic studies, we will adopt here analytic laws of degradation such as Paris’ law for fatigue degradation and Miner’s law for cumulative damage.

Research Journal of Applied Sciences, Engineering and Technology, 2014

This study presents a new approach for modeling and controlling of a compass gait biped robot bas... more This study presents a new approach for modeling and controlling of a compass gait biped robot based on the use of the switched systems. The linearization of the equations stemming from the formalism of Lagrange allows the construction of a set of local models used to describe the behavior of this non linear system. The selection of each model depends on its activation function depending on the system states. The synthesis of the stability of the walking robot is based on the use of second method of Lyapunov. The synthesis approach leads to a set of bilinear matrices inequalities non resolvable by actual numerical solvers. To come over these difficulties, some relaxations are brought to get useful and exploitable numerical solutions.

Research Journal of Applied Sciences, Engineering and Technology, 2014

Having regard to the large application of the inverted pendulum in robotic system, this study is ... more Having regard to the large application of the inverted pendulum in robotic system, this study is interested in controlling this process with two strategies of controls. The first proposed control is the state feedback with an observer based on the Generalized Predictive Control (GPC) algorithm. In the second proposed control we used the characteristic of predictive control GPC to improve the performance of the classical PID controller. The obtained results have been discussed and compared; the simulation results obtained by the predictive PID control are mentioned.

International Journal of Advanced Computer Science and Applications, 2016

the analysis and control of delayed systems are becoming more and more research topics in progres... more the analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. In other hand, the controls of humanoid walking robot present a common problem in robotics because it involves physical interaction between an articulated system and its environment. This close relationship is actually a common set of fundamental problems such as the implementation of robust stable dynamic control. This paper presents acomplete approach, based on switched system theory, for the stabilization of a compass gait robot subject to time delays transmission. The multiple feedback gains designed are based on multiple linear systems governed by a switching control law. The establishment of control law in real time is affected by the unknown pounded random delay. The results obtained from this method show that the control law stabilize the compass robot walk despite a varying delay reaching six times sampling period.

2015 World Symposium on Mechatronics Engineering & Applied Physics (WSMEAP), 2015

ABSTRACT

Procedia Computer Science, 2015

Predictive control presents a solution to the problem of the trajectory generation for a humanoid... more Predictive control presents a solution to the problem of the trajectory generation for a humanoid robot. This control strategy is introduced by Katayama 13 and improved by Kajita 1 , in those literatures, the theory of predictive control is used to calculate the trajectory of the mass center of the cart table to track a reference trajectory and give it for the ZMP. However this control has an inconvenience such as the non respect of real-time constraints, due to the computation time and the output response establishing. In this paper we propose the predictive PID controller that imitate the calculated time and reduce the complexity of the control algorithm. The aim of this new control approach for biped robot is to make walking smoother and more efficient.

2015 International Conference on Solar Energy and Building (ICSoEB), 2015

ABSTRACT

ABSTRACT This paper discusses the robust stabilization of discrete switched systems, focusing on ... more ABSTRACT This paper discusses the robust stabilization of discrete switched systems, focusing on the design of a robust static output feed-back control and dynamic output control based on a switched observer. The results are derived using the direct Lyapunov approach and the polyquadratic function concept. The stabi-lization conditions are written through linear matrix inequalities relations. The polyquadratic Lyapunov approach provides a con-structive way to tackle uncertainty in the switched framework. The feasibility is illustrated on an example of discrete uncertain switched discrete time system.

This paper discusses the stabilization of discrete time, polytopic uncertain switched systems, fo... more This paper discusses the stabilization of discrete time, polytopic uncertain switched systems, focusing on the design of a robust dynamic output feedback control, based on a Luenberger observer's. The results are derived using the direct Lyapunov approach and the polyquadratic function concept. The stabilization conditions are written through linear matrix inequalities relations. The polyquadratic Lyapunov approach provides a constructive way to tackle uncertainty in the switched framework. The feasibility is illustrated on an example of discrete time uncertain switched systems, when one of used actuators broke down.

American Journal of Applied Sciences, 2010

Problem statement: The estimation of states and the unknown inputs of a nonlinear system describe... more Problem statement: The estimation of states and the unknown inputs of a nonlinear system described by a multimodel are done by a multiobserver. The stabilization of the multiobserver calls upon uses both quadratic and no quadratic functions of Lyapunov. Although the stabilization using the quadratic approach is interesting from the point of view implementation, the step showed its limits for the multimodel. However, the problem paused by the quadratic method lies in the obligation to satisfy several LMI with respect to the same Lyapunov matrix P, these results are shown very conservative. Approach: To reduce the conservatism of the quadratic approach we propose another approach which is exclusively based on Lyapunov piecewise quadratic functions. The conditions obtained by the stabilization of the multiobserver are expressed in term of matrix inequalities with constraints on the matrices rank. Results: The estimation of both states and unknown inputs of a multimodel using the quadratic approach per pieces leads to results less conservative than the quadratic approach. Academic examples illustrate the robustness of the piecewise quadratic approach. Conclusion: In this article we proposed new sufficient conditions of stability of a multiobserver able to the estimation of states and unknown inputs of a nonlinear system describes by a multimodel subjected to the influence of the unknown inputs. The study in was carried out by considering two approaches. The first approach is based on Lyapunov quadratic functions; it is significant to note the great difficulty in finding satisfying results by this approach for the multimodel systems. For this reason we proposed an approach based on piecewise quadratic functions which led to interesting results (proposition 1) and less conservative than the quadratic approach. The conditions suggested in this article concern both the multiobserver stabilization and the estimation of states and the unknown inputs of a multimodel with measurable variables of decision (µξ(k)). The synthesis of a multiobserver with no measurable variables of decision is not approached. This point can constitute an interesting prospect for this study.

Abstract: Problem statement: More advanced control techniques have been developed in recent decad... more Abstract: Problem statement: More advanced control techniques have been developed in recent decades following the great progress of calculations means. Without considering the constraints on system variables, the response of controlled system moves away from the desired response. Hence the control strategy must provide the ability to integrate these constraints in the design phase of the controller. Approach: This study presents a design of robust dynamic controller which was based on the control strategy MPC for an uncertain discrete system described by a multimodel by solving an optimization problem. The Model Predictive Control (MPC) strategy uses a dynamic model of the process in order to predict its future behavior. This control strategy, that we propose, makes it possible to integrate these constraints in the design phase of the controller. The design of the robust dynamic controller must maintain the stability and performance of the system in the presence of uncertainties. Th...

In this paper an algorithm is presented for the stabilization of a non linear and multi-inputs sy... more In this paper an algorithm is presented for the stabilization of a non linear and multi-inputs system: a blower temperature described by a multimodel. The originality of this work lies on the fact that the applied control is quantified. In the first stage, a synthesis of a multiobserver, stabilized polyquadratically, with proper characteristic values situated in a disc inside unit circle is presented. The command law, stabilized polyquadratically, is based on the multiobserver and tracing of poles. In a second stage, the computed control can not be directly applied to the plant because of the quantification imposed by the heating resistors. To go over this problem, the variation of the ventilation's speed can compensate for the errors of the command due to the quantification of the heated power. The choice of the optimal ventilation's speed is based on the minimization of a criterion evaluating the distance between the measured output and the desired output.

This paper presents a less conservative approach for the synthesis of a multiobserver able to est... more This paper presents a less conservative approach for the synthesis of a multiobserver able to estimate the states and unknown inputs of a discrete nonlinear system. The stabilization of the error observation is guaranteed by the use of the second Lyapunov approch. The stability conditions obtained are expressed in term of Linear Matrices Inequalities (LMI) and are got from the use of the Lyapunov quadratic functions in a first study and from the Lyapunov polyquadratic functions in a second study which appears less conservative and less constraining than the first. Illustrative examples are also presented in this paper.