the form of the system equations to modify the （系统方程的形式修改）.pdf

Last Update: 30.05.2011 24 Feedback Linearization Similarly to the approach taken in sliding mode control, in this section we wish to exploit the form of the system equations to modify the dynamics to something more convenient. We consider a class of nonlinear systems of the form x f x G x u     y h x   where f :D n and G : D np are defined on a domain D n , which contains the origin, and pose the question whether there exists a state feedback control u  x  x v     and a change of variables z T x   that transforms the nonlinear system into an equivalent linear system. If the answer to this question is positive, we can induce linear behavior in nonlinear systems and apply the large number of tools and the well established theory of linear control to develop stabilizing controllers. 24.1 Motivation Example 24.1: To introduce the idea of feedback linearization, let us start with the problem of stabilizing the origin of the pendulum equation. x x 1 2   x a sin x  sin bx cu 2   1   2 If we choose the control u a sin x  sin   v  1  c c We can cancel the nonlinear term a sin x  sin . This cancellation results in the  1  linear syst