Block Control Principle for Mechanical Systems

Abstract

In this paper, a generalized design procedure for sliding mode control of nonlinear mechanical systems is proposed. The design approach combines the essential idea of the block control principle, utilizing some of the components of the state vector as a virtual control, with the basic concept of zero dynamics. For mechanical systems governed by a set of interconnected second-order equations, the block control principle cannot be directly applied. To facilitate the controller design, we assume that control systems can be transformed into a regular form consisting of second-order equations. The proposed design approach consists of reducing the original plant into the regular form, constructing a switching manifold, and enforcing sliding mode in the manifold such that the reduced order system in sliding mode has desired dynamics. Stabilization of the mechanical system with unstable zero dynamics is taken into consideration. It is shown that the approach has the advantage of decomposing the original problem into subproblems of lower dimensions, and each of them can be handled independently. As an example, control of a rotational inverted pendulum system is examined. The performance of the proposed approach is validated by both numerical and experimental results. [S0022-0434(00)01601-4]