Modelling Dynamical Systems with Equality State-Space Constraints

摘要

A mathematical theory for modelling dynamical systems with equality state-spaceconstraints is presented. The dynamic behavior of these systems is represented by a combination of differential and algebraic equations. It is shown that the freedom offered by control is essential to obtain other, mathematically equivalent formulations. The notion of applicable control is introduced for the systems under consideration. A characterization for all applicable controls of constrained dynamical systems is presented. The theory also covers the case of mechanical systems with equality state-space constraints. The equations of motions as derived in classical mechanics can be obtained from the formulations presented in the report by a suitable choice of parameters or by further restrictions on the class of applicable controls. Furthermore, it is shown that in the case of mechanical systems, from a mathematical point of view, holonomic and nonholonomic constraints are merely special cases. The theory is illustrated by modelling constrained manipulator motions. Here the kinematic relation between joints and end-effector is treated as an additional constraint. A number of test cases are considered. Decomposition of a model in submodels as well as easy exchange of submodels, important for the development and evaluation of (sub)models, is supported by the theory presented here.