scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

2018 ◽  
Author(s):  
Yong-Hong Lan ◽  
Xia Jun-Jun
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

A robust guaranteed cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, the repetitive controller combined with preview compensator is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed cost preview repetitive control problem is transformed into the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included to show the effectiveness of the proposed method.

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

Algorithms ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Yong-Hong Lan ◽  
Jun-Jun Xia ◽  
Yue-Xiang Shi
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

scholarly journals Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fucheng Liao ◽  
Yingxue Wu ◽  
Xiao Yu ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Tracking Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Error System ◽  
Finite Time Boundedness ◽  
Boundedness Problem ◽  
Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

scholarly journals State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Wentao Chen ◽  
Yechun Lin ◽  
Qingping Wu
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Cost Control ◽  
Repetitive Control ◽  
Guaranteed Cost Control ◽  
State Feedback Control ◽  
Control Law ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.

scholarly journals Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Fucheng Liao ◽  
Yujian Guo
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Original System ◽  
Preview Control ◽  
Lifting Technique ◽  
Discrete Time Systems ◽  
Error System ◽  
Existence Conditions ◽  
Time Systems ◽  
Discrete Integrator

This paper studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.

Observer-Based H∞ Feedback Control for Arbitrarily Time-Varying Discrete-Time Systems With Intermittent Measurements and Input Constraints

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Hui Zhang ◽  
Yang Shi
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time Systems ◽  
Intermittent Measurements ◽  
Time Systems ◽  
Intermittent Measurement

In this paper, we investigate the observer-based H∞ feedback control problem for discrete-time systems subject intermittent measurements and constrained control inputs. To characterize the practical scenario of the intermittent measurement phenomenon, we model it using a stochastic Bernoulli approach. We assume that the control action is constrained to be below a prescribed level. Sufficient conditions are obtained for the observer-based H∞ feedback control problem. The estimator and the controller are derived by solving a linear matrix inequality (LMI)-based optimization problem. Moreover, the proposed method is extended to systems with arbitrarily time-varying parameters within a polytope with unknown vertices. Three examples are given to illustrate the effectiveness and efficacy of the proposed method.

scholarly journals Design of Robust Output Feedback Guaranteed Cost Control for a Class of Nonlinear Discrete-Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yan Zhang ◽  
Yali Dong ◽  
Tianrui Li
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Cost Control ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Output Measurement ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper investigates static output feedback guaranteed cost control for a class of nonlinear discrete-time systems where the delay in state vector is inconsistent with the delay in nonlinear perturbations. Based on the output measurement, the controller is designed to ensure the robust exponentially stability of the closed-loop system and guarantee the performance of system to achieve an adequate level. By using the Lyapunov-Krasovskii functional method, some sufficient conditions for the existence of robust output feedback guaranteed cost controller are established in terms of linear matrix inequality. A numerical example is provided to show the effectiveness of the results obtained.

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