Robust induced ℓ 2 -ℓ ∞ optimal control of discrete-time systems having magnitude and rate-bounded actuators

• Published in: ISA transactions Vol. 129; pp. 73 - 87
• Main Authors: Kucukdemiral, Ibrahim, Han, Xiaoran, Erden, Mustafa Suphi
• Format: Journal Article
• Language: English
• Published: United States 01.10.2022
• Subjects: Discrete-time systems; Robust control; LMIs; Magnitude and rate-bounded systems
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2022.02.025

The design of robust state- and output-feedback control for uncertain discrete-time systems with physical magnitude and rate constraints on their actuator dynamics was addressed. Unlike the traditional methods such as anti-windup (AW) methods, nested ellipsoids, model predictive controllers (MPCs) and integral quadratic constraints(IQCs) formulated by sector bounded inequalities, this paper uses a transformation of the system dynamics to a form which considers control signal and its rate as controlled outputs and using discrete-time ℓ induced (peak-to-peak) norm from disturbance inputs to these outputs. To cope with the magnitude and rate bound non-linearities together, the induced ℓ norm from disturbance input to the outputs involving control signal and its rate is utilised. On the other hand, discrete-time(DT) induced ℓ norm from disturbance input to the main controlled output is used to mitigate the effects of disturbances. We can tackle this ambitious non-linear control problem in the domain of linear convex multi-objective optimal control problem, which can be solved by effective semi-definite optimisation methods by using the proposed transformation and handling the control constraints in terms of worst case peak-to-peak gain of the system. Extended Linear Matrix Inequalities (LMIs) and full block S-procedure based design conditions developed over Linear Fractional Representation(LFR) framework allow the user to obtain robust state- and output-feedback control solutions with reduced conservatism. For the first time, this paper introduces an extended LMI based robust output-feedback control design for magnitude and rate bounded (MRB) systems, using full block S-procedure. We demonstrate the performance of the proposed controller through several simulations over benchmark examples covering systems having multi-variable structures and uncertainties. Our study also involves comparison results with a recently introduced technique based on multi-stage AW technique. The simulation results show that the proposed method of this paper is much effective and less conservative compared to the recent AW method provided in the literature.