Robust H ∞ control for a class of uncertain mechanical systems

• Published in: International journal of control Vol. 83; no. 7; pp. 1303 - 1324
• Main Authors: Yang, Xuebo, Gao, Huijun, Shi, Peng, Duan, Guangren
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.07.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; Computer science; control theory; systems; control; Control system analysis; Control system synthesis; Control theory. Systems; Controllers; Exact sciences and technology; input delay; linear matrix inequalities; mechanical systems; parameter uncertainties; Studies; State feedback; Linear form; Linear fractional transformation; H infinite control; Feedback regulation; Control synthesis; Delay system; Spring mass system; Robust control; Uncertain system; Mechanical system; Linear matrix inequality; Lyapunov function
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170903267047

In this article, the problem of H ∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov-Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H ∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.