Beschreibung
The stabilization of manifolds, which are typically situated in the state or output space of dynamical systems, is an important topic within the field of control theory. The controller is supposed to make the manifold attractive, render it invariant under the closed-loop dynamics, and, if possible, achieve a desired movement of the state or output on the manifold. Stabilizing a one-dimensional manifold is often referred to as path following control. This work deals with the development of three different concepts for manifold stabilization in combination with nonlinear continuous-time dynamical systems. Firstly, a controller design methodology for stabilizing manifolds in flat output spaces is presented. This methodology builds on a transformation to a so-called transverse normal form. By using the equivalence between flat systems and linear controllable ones, a straightforward design of the controller is enabled. Secondly, a tailored model predictive control scheme is developed for stabilizing manifolds in the state and output space. The controller allows for the consideration of system constraints and has a novel structure with two optimal control problems which are solved sequentially at each recalculation instant. Thirdly, the focus is directed to path following control for parameterized paths in the output space. Model predictive control is utilized for solving the problem which enables to respect constraints. Real-time feasible variants of the model predictive control formulations are developed. They are applicable to constrained path following control of complex fast systems. A point-like mass and an elaborate laboratory tower crane serve as examples for all developed control concepts underlining their feasibility, performance, and versatile applicability.
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