scholarly journals Optimal Preview Controller for Linear Discrete-Time Systems: A Virtual System Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jiang Wu ◽  
Huali Zhang ◽  
Denggui Fan
Keyword(s):  
Discrete Time ◽  
Minimum Principle ◽  
Reference Signal ◽  
Positive Semidefinite ◽  
Algebraic Riccati Equation ◽  
Controlled System ◽  
Discrete Time Systems ◽  
Error System ◽  
Virtual System ◽  
Time Systems

In this paper, a new method for the design of the preview controller for a class of discrete-time systems is proposed based on the virtual system. Firstly, by taking the known future reference signal as the output, the virtual system with similar structures to the controlled system is constructed. Then, the augmented error system is received by translating the controlled system to it and by integrating the error equation. Thus, the tracking problem of the controlled system is transformed into the regulation problem of the augmented error system. Secondly, in view of the minimum principle, the optimal controller of the augmented error system is acquired, and the preview controller of the controlled system is also gained. Further, by discussing the stabilizability and detectability of the augmented error system, the conditions for the existence of the unique positive semidefinite solution to an algebraic Riccati equation are obtained. By using the method in this paper, making difference and dimension expansion for the state equation in designing the augmented error system is avoided and the output can track the reference signals better. Finally, the numerical simulation shows the effectiveness of the proposed controller.

Design of a robust H∞ preview controller for a class of uncertain discrete-time systems

2017 ◽  
Vol 40 (8) ◽  
pp. 2639-2650 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Lyapunov Stability Theory ◽  
Interference Rejection ◽  
Discrete Time Systems ◽  
Controller Gain ◽  
Error System ◽  
The Difference ◽  
System States ◽  
Time Systems

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

scholarly journals Optimal Robust Fault Detection for Linear Discrete Time Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Nike Liu ◽  
Kemin Zhou
Keyword(s):  
Fault Detection ◽  
Discrete Time ◽  
Filter Design ◽  
Algebraic Riccati Equation ◽  
Optimization Criteria ◽  
Robust Detection ◽  
Discrete Time Systems ◽  
Robust Fault Detection ◽  
Time Systems ◽  
Detection Filter

This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such asℋ−/ℋ∞,ℋ2/ℋ∞, andℋ∞/ℋ∞problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal) but useless fault-detection filters.

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 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 Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaobo Li ◽  
Hugh H. T. Liu
Keyword(s):  
Fault Detection ◽  
Riccati Equation ◽  
Discrete Time ◽  
Time Horizon ◽  
Linear Time ◽  
Sensitivity Study ◽  
Algebraic Riccati Equation ◽  
System Sensitivity ◽  
Discrete Time Systems ◽  
Time Systems

Fault detection is a critical step in the fault diagnosis of modern complex systems. An important notion in fault detection is the smallest gain of system sensitivity, denoted asℋ−index, which measures the worst fault sensitivity. This paper is concerned with characterizingℋ−index for linear discrete time systems. First, a necessary and sufficient condition on the lower bound ofℋ−index in finite time horizon for linear discrete time-varying systems is developed. It is characterized in terms of the existence of solution to a backward difference Riccati equation with an inequality constraint. The result is further extended to systems with unknown initial condition based on a modifiedℋ−index. In addition, for linear time-invariant systems in infinite time horizon, based on the definition of theℋ−index in frequency domain, a condition in terms of algebraic Riccati equation is developed. In comparison with the well-known bounded real lemma, it is found thatℋ−index is not completely dual toℋ∞norm. Finally, several numerical examples are given to illustrate the main results.

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