Impulse Controllability: From Descriptor Systems to Higher Order DAEs

Kalaimani, Rachel Kalpana; Praagman, C.; Belur, Madhu N.

doi:10.1109/tac.2015.2497468

Cited by 3 publications

(1 citation statement)

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“…As a common descriptor system, the high-order descriptor linear system (HODLS) has a wide perspective of applications since many physical systems, including hydraulic position control systems [18], electro-mechanical and mechanical systems [19], unmanned free-swimming submersible systems [20,21], and damped vibroacoustic systems [22], are of high-order. The HODLS is always converted into the equivalent first-order form in earlier studies [23,24]. This transformation is probably the best choice for solving the problem of response analysis and estimation but not for controller design, because it may encounter the dimension explosion problem, destroy the physical meaning of original system parameters, increase excess computation load, lead to numerical unreliable phenomenon [25], and bring the extra smoothness requirement to control input [26,27].…”

Section: Introductionmentioning

confidence: 99%

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

Gao,

Duan

2023

IET Control Theory & Appl

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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.

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