高阶系统方法-I. 全驱系统与参数化设计

In this paper, the drawback of the first-order system approaches which are widely used in the field of control systems is firstly pointed out, meanwhile the concept of high-order fully-actuated systems and, in particular, its advantage in controller design are introduced. The type of systems is demonstrated to be of wide existence by examining a number of basic physical laws and a few examples, including the common cascaded systems, the well-known strict-feedback systems, and those which can be linearized through feedback, and thus can be taken as a description of dynamical systems, more precisely, as a model for control. Then, a parametric design approach for the type of high-order fully-actuated systems is presented. With a proper nonlinear state feedback controller, a linear constant closed-loop system with desired eigenstructure can be derived, and complete parametric presentations for the closed-loop eigenvectors and the feedback law are given. Conditions of existence of solutions as well as the density of the set of design parameters are discussed. Finally, some further comments are made about future problems existing in the field of high-order fully-actuated systems.