Asymptotically Globally Stable Multiwindow Controllers

The Popov criterion is applied to control system analysis and design. Nonlinear dynamic compensators (NDC) are int reduced which ensure absolute stability without penalizing the available feedback. 1 Multiwindow Controllers and Nonlinear Dynamic Compensation Ivlultiwindow controllers consisting of linear controllers with nonlinear windows [1,2] perform superior to linear controllers. They can be designed using frequency domain methods, and their stability can be assured by using describing functions. However, the describing function methods are only approximate. It is convenient to use the methods to prove the system stability within each window, but rather difficult to use the methods to rule out the oscillations with the signal moving from window to window. It would be preferable to use design methods based on the strict methods of absolute stability. Such methods have been previously described in [3,4] but only with examples made to illustrate the achievable performance. While these cxarnpl~s are of theoretical significance, but use inlpractical very high-order controllers. 111 this paper, a technique for suboptimal but simple, low-order controllers with greatly improved performance is presented. Here, we consider absolutely stable tw~ window controllers with local nonlinear feedback producing the windows with the responses typical in a real application. 2 Absolute Stability Many practical feedback systems consist of a linear link 7’(s) and a memoriless (i.e. nondynarnic) nonlinear link v(e) w shown in Fig. 1. m Figure 1: participation functions in composite controllers VI /’