Anti-windup and Control of Systems with Multiple Input Saturations : Tools, Solutions and Case Studies

Sammanfattning: Control of linear systems with saturating actuators are considered and anti-windup compensators for multiple-input multiple-output systems, and robust, almost time-optimal controllers for double integrators with input amplitude saturations, are proposed.Windup effects are defined and anti-windup compensators aiming at minimizing the windup effects are proposed. The design is based on 1) linear quadratic (LQ) optimization techniques and 2) heuristic design using Nyquist-like techniques and pole-placement techniques.A root-locus like technique that can, approximately, foretell possible directional problems that may be present in MIMO systems with input saturations, and that can be used for design of anti-windup compensators and for selection of appropriate static directional compensators, is proposed.The problem of control of double integrators via saturating inputs is addressed and a robust piece-wise linear controller that gives almost time-optimal performance is suggested. It is shown that time optimal control of a double integrator via an input amplitude limiter, is equivalent to time-optimal control of a single integrator having a rate limiter at the input. One such application, concerning control of hydraulic cylinders in container crane systems, is presented. An extension of the controller, allowing synchronous control of two integrators with input rate limitations, is proposed.