A Nonlinear Filter for Independent Gain and Phase (With Applications)

Abstract

Compensation of control systems by means of linear filters is a basic and well-known art. However, the limitations of linear compensation are also well known. In particular, the interdependence of the phase and gain characteristics of linear filters is always in conflict with the desires of the control-system designer. For example, it is impossible to introduce attenuation into a system without introducing undesirable phase lag as well. The development of a split-path nonlinear filter (SPAN filter) concept promises to yield a practical device which has independent phase and gain characteristics. These characteristics are independent of input signal amplitude. This filter can, therefore, have desirable characteristics which are unattainable with conventional linear filters. The design of the nonlinear filter to meet a desired gain-phase, describing-function specification is simplified by results given in the paper. Analysis and simulation of three sample problems has shown that a great deal of flexibility is available with this nonlinear filter. It is possible to obtain phase lead and amplitude attenuation by a proper choice of linear filtering in the two channels. Analog-computer simulation has verified the analytical work with respect to stability margins, and provided transient-response data, in the absence of analytical methods.