Model reference control in quasi-linear systems with a parametric feed-forward compensator and state-feedback stabilization controller

2021 ◽  
pp. 014233122110564
Author(s):  
Weizhen Liu ◽  
Guangren Duan ◽  
Dake Gu
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Matrix Equations ◽  
Parametric Solution ◽  
Model Reference ◽  
Feed Forward ◽  
Model Reference Control ◽  
Sylvester Matrix Equations

In this paper, a parametric feed-forward compensator and a parametric state-feedback stabilization controller are proposed for the model reference control to a class of quasi-linear systems. Quasi-linear systems are a special type of nonlinear systems whose coefficient matrices contain the state variables and also a time-varying parameter vector. The parametric state-feedback stabilization controller guarantees the stability of the closed-loop system and the parametric feed-forward compensator compensates the effect of the reference model state to the tracking error. The complete parametrization of the parametric feed-forward compensator is established based on a complete parametric solution to a class of generalized Sylvester matrix equations and solution of a coefficient matrix such that two matrix equations are satisfied. The established parametric state-feedback stabilization controller only needs a complete parametric solution to the same generalized Sylvester matrix equations but with different sets of freely designed parameters that represent the degrees of design freedom and may be further utilized to improve the system performance. A linear closed-loop form with the desired eigenstructure can be derived with the proposed parametric feed-forward compensator and parametric state-feedback stabilization controller, and a constant linear can even be obtained in certain cases. A numerical example and the application in spacecraft rendezvous are provided to illustrate the effectiveness of the proposed approach.

An LMI Approach to State Feedback H∞ Control for Switched Singular Linear Systems

2014 ◽  
Vol 875-877 ◽  
pp. 835-840
Author(s):  
Zhu Mu Fu ◽  
Bin Wang ◽  
Ai Yun Gao
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lmi Approach ◽  
Singular Linear Systems

In this paper, the problems of state feedback control for a class of switched singular linear systems are investigated. By constructing a novel switched Lyapunov functional and convex combinations techniques, a sufficient condition established in terms of strict linear matrix inequalities (LMIs) is presented such that the system is asymptotically stable and satisfies performance. An explicit expression for the state feedback stabilization sub-controller and switching rule are designed. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, in which the closed-loop system satisfies performance at each point in whole state-space through switching, although each sub-system doesn’t satisfy the performance and even is not asymptotically stable. A numerical example is provided to illustrate the validity of the proposed methods.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

A Reduced-Order H∞ Controller Design for Linear Structures

2012 ◽  
Vol 170-173 ◽  
pp. 3334-3337
Author(s):  
Lian Hua Hu ◽  
Xiao Feng Yang
Keyword(s):  
State Feedback ◽  
Parametric Design ◽  
Controller Design ◽  
State Feedback Control ◽  
Matrix Equations ◽  
Linear Structures ◽  
Reduced Order ◽  
Disturbance Decoupling ◽  
Necessary And Sufficient ◽  
Sylvester Matrix Equations

A robust reduced-order H∞ controller for the linear structures is investigated. This controller is with disturbance decoupling. First, a necessary and sufficient condition for the H∞ state feedback control problem is established. Second, based on the parametric design approach for generalized Sylvester matrix equations, we obtain a reduced-order H∞ controller for linear structures. Finally, numerical example is given to illustrate the validity of the results.

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