scholarly journals Design of an Optimal Preview Controller for a Class of Linear Discrete-Time Descriptor Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Fucheng Liao ◽  
Zhihua Xue ◽  
Jiang Wu
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Original System ◽  
Simulation Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Equivalent Transformation ◽  
Normal System ◽  
Preview Control ◽  
Error System

The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.

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.

scholarly journals Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Error ◽  
Reference Signal ◽  
Original System ◽  
Linear Matrix ◽  
Preview Control ◽  
Lipschitz Nonlinear Systems ◽  
Error System ◽  
Discrete Integrator

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

scholarly journals Impulse Elimination and Fault-Tolerant Preview Controller Design for a Class of Descriptor Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chen Jia ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Controller Design ◽  
Fault Tolerant ◽  
Original System ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Equivalent Transformation ◽  
Sensor Faults ◽  
Augmented System ◽  
Model Following ◽  
General Method

In this paper, a fault-tolerant preview controller is designed for a class of impulse controllable continuous time descriptor systems with sensor faults. Firstly, the impulse is eliminated by introducing state prefeedback; then an algebraic equation and a normal control system are obtained by restricted equivalent transformation for the descriptor system after impulse elimination. Next, the model following problem in fault-tolerant control is transformed into the optimal regulation problem of the augmented system which is constructed by a general method. And the final augmented system and its corresponding performance index function are obtained by state feedback for the augmented system constructed above. The controller with preview effect for the final augmented system is attained based on the existing conclusions of optimal preview control; then, the fault-tolerant preview controller for the original system is obtained through integral and backstepping. The relationships between the stabilisability and detectability of the final augmented system and the corresponding characteristics of the original descriptor system are also strictly discussed. The effectiveness of the proposed method is verified by numerical simulation.

Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems

2018 ◽  
Vol 6 (2) ◽  
pp. 178-192 ◽  
Author(s):  
Yujian Guo ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Sufficient Conditions ◽  
Original System ◽  
Discrete Time System ◽  
Linear Quadratic ◽  
Preview Control ◽  
Time System ◽  
Lifting Technique ◽  
Error System

Abstract A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given. Finally, simulation results 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 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 Design of preview controller for a type of discrete-time interconnected systems

2020 ◽  
Vol 53 (3-4) ◽  
pp. 719-729
Author(s):  
Hao Xie ◽  
Fucheng Liao ◽  
Usman ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Difference Operator ◽  
Interconnected Systems ◽  
Preview Control ◽  
Interconnected System ◽  
Lyapunov Function Method ◽  
System Equations ◽  
Error System ◽  
The Difference ◽  
Theoretical Results

This article proposes and studies a problem of preview control for a type of discrete-time interconnected systems. First, adopting the technique of decentralized control, isolated subsystems are constructed by splitting the correlations between the systems. Utilizing the difference operator to the system equations and error vectors, error systems are built. Then, the preview controller is designed for the error system of each isolated subsystem. The controllers of error systems of isolated subsystems are aggregated as a controller of the interconnected system. Finally, by employing Lyapunov function method and the properties of non-singular M-matrix, the guarantee conditions for the existence of preview controllers for interconnected systems are given. The numerical simulation shows that the theoretical results are effective.

scholarly journals Optimal Preview Control for Linear Discrete-Time Periodic Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Fucheng Liao ◽  
Mengyuan Sun ◽  
Usman
Keyword(s):  
Discrete Time ◽  
Original Problem ◽  
Control Method ◽  
Original System ◽  
Periodic Systems ◽  
Invariant System ◽  
Preview Control ◽  
Time Invariant ◽  
Time Periodic ◽  
Time Invariant System

In this paper, the optimal preview tracking control problem for a class of linear discrete-time periodic systems is investigated and the method to design the optimal preview controller for such systems is given. Initially, by fully considering the characteristic that the coefficient matrices are periodic functions, the system can be converted into a time-invariant system through lifting method. Then, the original problem is also transformed into the scenario of time-invariant system. Later on, the augmented system is constructed and the preview controller of the original system is obtained with the help of existing preview control method. The controller comprises integrator, state feedback, and preview feedforward. Finally, the simulation example shows the effectiveness of the proposed preview controller in improving the tracking performance of the close-loop system.

scholarly journals Discrete-TimeH∞Preview Control Problem in Finite Horizon

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hongxia Wang ◽  
Huanshui Zhang ◽  
Lihua Xie
Keyword(s):  
Game Theory ◽  
Dynamic Programming ◽  
Control Problem ◽  
Discrete Time ◽  
Finite Horizon ◽  
The Other ◽  
Preview Control ◽  
Discrete Time Systems ◽  
Other Hand ◽  
Time Systems

This paper considers theH∞preview control problem for discrete-time systems. It investigates the problem via game theory and dynamic programming. Different from the existing results, on one hand, the proposed approach is suitable for dealing with the corresponding multiple preview channels problem; on the other hand, the approach provides a possibility in explaining how the preview controller improves theH∞performance and why the performance will be saturated.

MAPPING DISCRETE-TIME MODELS FOR DESCRIPTOR-SYSTEMS WITH CONSISTENT INITIAL CONDITIONS

2016 ◽  
Vol 40 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Shin Kawai ◽  
Noriyuki Hori
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Initial Conditions ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Initial Time ◽  
Design Parameters ◽  
Time Model ◽  
Discrete Time Model ◽  
Sinusoidal Input

Discretization of a regular continuous-time descriptor-system, whose initial condition is consistent with its input, is considered using a general mapping method presented in our previous paper. The proposed mapping discrete-time model is shown to be a proper discretization under the definition explained in the paper. This assures that the response of the mapping model approaches that of the continuous-time descriptor system as the sampling period approaches zero. The consistency of initial conditions for the discrete-time model is also studied and the long-standing issue of ambiguities surrounding irregularities of discrete-time responses at the initial time are clarified with a simple solution. A proper range of design parameters are investigated and their suitable choices suggested. To illustrate the use of the proposed method, a simple circuit that cannot be expressed in the ordinary state-space form is considered. Its responses to a sinusoidal input when started from the consistent and inconsistent initial conditions are simulated to show that the irregularities at the initial time can be overcome easily. The proposed technique provides a convenient simulation and design environment for handling discrete-time systems in a unified manner with consistency and ease.

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