Controller synthesis for systems with input saturation

Abstract

This thesis addresses the controller synthesis for systems with input saturation. Theproposed controller synthesis consists of three approaches: first approach is multi-stage γlevel H∞ control for input-saturated systems with disturbances, second approach is H∞ control of continuous-time uncertain linear systems with quantized-input saturation and external disturbances, and third approach is H2 state-feedback control for linear parameter varying (LPV) systems with input saturation and matched disturbance. First, in Chapter 2, for input-saturated systems with disturbances, states in the domain of attraction cannot converge to the origin but only to neighborhood around it. In order to design the smallest possible target invariant set and the largest possible domain of attraction, we introduce a multi-stage γ-level H∞ control for achieving a smaller target invariant set within a given H∞ performance level and a larger domain of attraction than results obtained in previous studies. In particular, for the case in which the disturbances satisfy a matched condition, this chapter introduces an H∞ control with an extra control part to perfectly reject these disturbances despite the uncertainties; the introduction of the H∞ control with an extra control part causes the target invariant set to shrink to the origin and the H∞ performance level to become zero. Second, in Chapter 3, an H∞ state-feedback controller for uncertain linear systems with quantized-input saturation and external disturbances is introduced. The proposed controller comprises two parts: a linear control part to achieve an H∞ performance against model uncertainties and the mismatched part of the disturbances and a nonlinear control part to eliminate the effect of input quantization and the matched part of the disturbances, which provides the better disturbance attenuation performance than a controller that deals with a unified disturbance regardless of the presence of matched and mismatched parts. Simulation results confirm the effectiveness of the proposed controller. Finally, in Chapter 4, a controller design for LPV systems with input saturation and a matched disturbance is proposed. On the basis of the feedback gain matrix K(θ(t)) and the Lyapunov function V(x(t)), three types of controllers are suggested under H2 performance conditions. To this end, the conditions used for designing the H2 state-feedback controller are first formulated in terms of parameterized linear matrix inequalities (PLMIs). They are then converted into linear matrix inequalities (LMIs) using a parameter relaxation technique. The simulation results illustrate the effectiveness of the proposed controllers.