Discretization of non-linear controls with application to robust, sliding-mode-based control systems

摘要

This thesis deals with sampled-data implementations of continuous-time, non-linear control systems. The basis for the analysis is a static, continuous-time feedback law for non-linear, affine systems with bounded input gain. The sampled-data implementation is obtained from the discretization of the control via a sample-and-hold-process. With the incorporation of the aspect of robustness, a theoretical framework is created which supersedes previous work concentrating on stability. Bounding constraints for the closed-loop differential system allow uncertainty and disturbances to be considered. Other assumptions for the continuous-time control are Lipschitz continuity, exponential decay outside a compact set and existence of a Lyapunov function. The important parameter for the discretization analysis is the sampling time; fast sampling implies robust stability. The controller sampling residual, the difference between the discretized and the original control, is of key interest within a Lyapunov-type stability analysis; suitable norms, such as the Euler norm, are chosen to find upper bounds for the sampling residual. The generalization of a result from linear to non-linear sampled-data control permits the application of the Lp-norm. The theoretical framework is also suitable for dynamic control systems and the investigation of computational delays.;The analysis approaches are demonstrated for two different robust control. strategies .based on sliding-mode approaches. A state-feedback sliding-mode-based control extends ideas for smoothing discontinuous sliding-mode control components by introducing a cone-shaped sliding-mode layer. A non-smooth Lyapunov function is used to prove stability of the discretized control. An observer-based tracking control improves a previous control scheme by considering a class of non-minimum phase and relative-degree-zero plants.;Simulation and numerical fast-sampling analysis results are provided for all developed discretization and sliding-mode-based control techniques in application to non-trivial examples. The simulation of a highly non-linear, large-scale chemical plant for benzene production with non-minimum phase and relative-degree-zero characteristics proves the effectiveness of sliding-mode output control.