Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen

Neglecting actuator limitations when designing a feedback control may cause a severe malfunctioning of the control loop during operation. This faulty behavior is often termed windup and manifests itself in intense oscillations, a significantly prolonged settling time or even instability. The main objective of this work is the development of systematic design methods for anti-windup strategies, guaranteeing – in cooperation with the pre-designed controller – a safe and efficient operation of the control loop. Concerning the design approaches, three objectives are targeted. Stability of the control loop as well as a high performance, i.e. a significant reduction of windup, are desired characteristics. Furthermore, the procedure to parameterize the anti-windup should be as user-friendly as possible. Therefore, all design methods in this work are based on convex optimization. The primary contribution of this thesis consists in a systematic design method for Hippe’s observer technique, preventing controller windup, and the development of three new design methods suited for different linear and nonlinear model-based anti-windup structures. The first method uses piecewise quadratic Ljapunov functions to establish global stability of the closed-loop system with a linear anti-windup. A local performance criterion is exploited to achieve a drastic reduction of windup compared to existing approaches. The second design strategy parameterizes a newly developed soft variable-structure anti-windup by solving a convex optimization problem. Due to its variable structure, the anti-windup outperforms linear state-of-the-art approaches. The third design algorithm aims at local stability results for linear anti-windup structures. Therefore, it is suited for control loops with marginally stable or unstable plants. The main difference compared to existing approaches is the precise characterization of the stability region in combination with a performance-oriented design. Both aspects are necessary and important for a practical implementation of the proposed method.