Journal Article

Robust model reference tracking control for high‐order descriptor linear systems subject to parameter uncertainties

Gao, Ya‐Jun, Duan, Guang‐Ren

2024

Overview

This paper investigates the robust model reference tracking control problem for high‐order descriptor linear systems (HODLS) subject to norm‐bounded parameter uncertainties. The problem is divided into two subproblems: a robust proportional plus derivative state feedback stabilization (RPPDSFS) problem and a robust feed‐forward compensation (RFFC) problem. In the presence of uncertainties, by using the controller consisting of RPPDSFS part and RFFC part, all the signals of the closed‐loop system are bounded. The latter is equivalent to seeking three coefficient matrices such that a series of linear matrix equations are satisfied, and simultaneously the effect caused by uncertainties is minimized. Based on the right coprime factorization, the RFFC problem is further converted into a minimization problem with a quadratic performance index and some linear constraints. Thereafter, a linear matrix equation that determines the optimal solution is achieved. The restrictive condition that the coefficient matrix of the augmented reference system is non‐defective is relaxed, which reduces the conservativeness. A numerical example and the application of a three‐axis dynamic flight motion simulator manifest the effectiveness and the practicability of the proposed algorithm. This paper focuses on the robust model reference tracking control problem for high‐order descriptor linear systems subject to parameter uncertainties. The new robust feed‐forward compensation algorithm is proposed for high‐order descriptor linear systems, which take the first‐ or second‐order descriptor linear systems and high‐order linear systems as special cases and have a wide perspective of applications. The restrictive condition that the coefficient matrix of the augmented reference system is non‐defective is relaxed, which reduces the conservativeness.

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: Axis movements / Closed loop systems / Controllers / fully‐actuated / high‐order descriptor linear systems / Investigations / Lagrange multiplier / Linear systems / Motion simulators / Optimization / Parameter uncertainty / Performance indices / Reference systems / Robust control / robust feed‐forward compensator / robust model reference tracking / State feedback / Tracking control / uncertain parameters