In this paper, we propose a new approach to design output feedback regulators for bilinear system... more In this paper, we propose a new approach to design output feedback regulators for bilinear system by the mean of shifted Legendre polynomials. The proposed technique is based on the projection of the controlled system and the linear reference model that it should follow. The useful properties of the considered basis such as operational matrices combined with the Kronecker product transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. Simulation result is included to demonstrate the validity and applicability of the technique.
International Conference on Informatics in Control, Automation and Robotics, Jul 21, 2015
In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear stat... more In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear state feedback is derived using orthogonal functions and Kronecker product. The main objective is to force the controlled system output to follow that of a linear reference model. The useful properties of the considered basis transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. The efficiency of the proposed control strategy is illustrated by a single-link flexible joint robot.
This paper investigates the problem of robust tracking control for unstructured uncertain bilinea... more This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over block pulse functions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.
The present study tackles the tracking control problem for unstructured uncertain bilinear system... more The present study tackles the tracking control problem for unstructured uncertain bilinear systems with multiple time-delayed states subject to control input constraints. First, a new method is introduced to design memory state feedback controllers with compensator gain based on the use of operational properties of block-pulse functions basis. The proposed technique permits transformation of the posed control problem into a constrained and robust optimization problem. The constrained robust least squares approach is then used for determination of the control gains. Second, new sufficient conditions are proposed for the practical stability analysis of the closed-loop system, where a domain of attraction is estimated. A real-world example, the headbox control of a paper machine, demonstrates the efficiency of the proposed method.
2017 International Conference on Advanced Systems and Electric Technologies (IC_ASET), 2017
This paper investigates the problem of tracking control for nonlinear polynomial system with dela... more This paper investigates the problem of tracking control for nonlinear polynomial system with delayed state. The consider system is assumed to have a controllable linear part. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. The main contribution is to overcome the analytical complexity and to propose a controller tuned in the least square sense. Simulation results are given to demonstrate the effectiveness and advantages of the proposed control approach.
The tracking control of bilinear system with delayed state is synthesized using Block pulse funct... more The tracking control of bilinear system with delayed state is synthesized using Block pulse functions. A linear controllers are designed allowing the systems output to follow a preshaped reference model. The parameters of the feedback regulator are derived by solving a linear algebraic equation in the least square sense. Simulation results are provided to demonstrat e the merits of the proposed control approach.
2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO), 2015
In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear stat... more In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear state feedback is derived using orthogonal functions and Kronecker product. The main objective is to force the controlled system output to follow that of a linear reference model. The useful properties of the considered basis transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. The efficiency of the proposed control strategy is illustrated by a single-link flexible joint robot.
2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), 2019
This paper investigates the problem of robust tracking control for unstructured uncertain bilinea... more This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over block pulse functions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.
2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), 2014
In this paper, we propose a new approach to design output feedback regulators for bilinear system... more In this paper, we propose a new approach to design output feedback regulators for bilinear system by the mean of shifted Legendre polynomials. The proposed technique is based on the projection of the controlled system and the linear reference model that it should follow. The useful properties of the considered basis such as operational matrices combined with the Kronecker product transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. Simulation result is included to demonstrate the validity and applicability of the technique.
2015 7th International Conference on Modelling, Identification and Control (ICMIC), 2015
This article focuses on the tracking control problem for nonlinear analytical systems. A polynomi... more This article focuses on the tracking control problem for nonlinear analytical systems. A polynomial state feedback controller is designed to guarantee that the system output tracks those of linear reference model. The parameters of the feedback regulator are derived by solving a linear algebraic problem in the least square sense. The efficiency of the proposed control strategy is illustrated by mass-spring-damper benchmark.
In this paper, we propose a new approach to design output feedback regulators for bilinear system... more In this paper, we propose a new approach to design output feedback regulators for bilinear system by the mean of shifted Legendre polynomials. The proposed technique is based on the projection of the controlled system and the linear reference model that it should follow. The useful properties of the considered basis such as operational matrices combined with the Kronecker product transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. Simulation result is included to demonstrate the validity and applicability of the technique.
International Conference on Informatics in Control, Automation and Robotics, Jul 21, 2015
In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear stat... more In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear state feedback is derived using orthogonal functions and Kronecker product. The main objective is to force the controlled system output to follow that of a linear reference model. The useful properties of the considered basis transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. The efficiency of the proposed control strategy is illustrated by a single-link flexible joint robot.
This paper investigates the problem of robust tracking control for unstructured uncertain bilinea... more This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over block pulse functions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.
The present study tackles the tracking control problem for unstructured uncertain bilinear system... more The present study tackles the tracking control problem for unstructured uncertain bilinear systems with multiple time-delayed states subject to control input constraints. First, a new method is introduced to design memory state feedback controllers with compensator gain based on the use of operational properties of block-pulse functions basis. The proposed technique permits transformation of the posed control problem into a constrained and robust optimization problem. The constrained robust least squares approach is then used for determination of the control gains. Second, new sufficient conditions are proposed for the practical stability analysis of the closed-loop system, where a domain of attraction is estimated. A real-world example, the headbox control of a paper machine, demonstrates the efficiency of the proposed method.
2017 International Conference on Advanced Systems and Electric Technologies (IC_ASET), 2017
This paper investigates the problem of tracking control for nonlinear polynomial system with dela... more This paper investigates the problem of tracking control for nonlinear polynomial system with delayed state. The consider system is assumed to have a controllable linear part. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. The main contribution is to overcome the analytical complexity and to propose a controller tuned in the least square sense. Simulation results are given to demonstrate the effectiveness and advantages of the proposed control approach.
The tracking control of bilinear system with delayed state is synthesized using Block pulse funct... more The tracking control of bilinear system with delayed state is synthesized using Block pulse functions. A linear controllers are designed allowing the systems output to follow a preshaped reference model. The parameters of the feedback regulator are derived by solving a linear algebraic equation in the least square sense. Simulation results are provided to demonstrat e the merits of the proposed control approach.
2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO), 2015
In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear stat... more In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear state feedback is derived using orthogonal functions and Kronecker product. The main objective is to force the controlled system output to follow that of a linear reference model. The useful properties of the considered basis transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. The efficiency of the proposed control strategy is illustrated by a single-link flexible joint robot.
2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), 2019
This paper investigates the problem of robust tracking control for unstructured uncertain bilinea... more This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over block pulse functions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.
2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), 2014
In this paper, we propose a new approach to design output feedback regulators for bilinear system... more In this paper, we propose a new approach to design output feedback regulators for bilinear system by the mean of shifted Legendre polynomials. The proposed technique is based on the projection of the controlled system and the linear reference model that it should follow. The useful properties of the considered basis such as operational matrices combined with the Kronecker product transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. Simulation result is included to demonstrate the validity and applicability of the technique.
2015 7th International Conference on Modelling, Identification and Control (ICMIC), 2015
This article focuses on the tracking control problem for nonlinear analytical systems. A polynomi... more This article focuses on the tracking control problem for nonlinear analytical systems. A polynomial state feedback controller is designed to guarantee that the system output tracks those of linear reference model. The parameters of the feedback regulator are derived by solving a linear algebraic problem in the least square sense. The efficiency of the proposed control strategy is illustrated by mass-spring-damper benchmark.
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