Non-linear proportional and rate feedback design for highly non-linear systems

A new procedure for the design of non-linear proportional and rate feedback controllers based on a previously proposed concept is developed. The procedure is to obtain the sinusoidal-input describing function models of the system, followed by determination of the amplitude-dependent rate feedback gains. Then, this amplitude-dependent gain function is inverted to obtain the non-linear function describing a non-linear rate feedback gain. Then, the amplitude-dependent proportional gains that desensitize the overall open-loop system are determined via optimization. Finally, the obtained amplitude-dependent proportional gains are inverted to obtain the actual non-linear function describing the required non-linear behaviour of the proportional gain. Bounded-input-bounded-output stability is demonstrated by successful generation of the closed-loop describing function models, and the procedure is applied to a servo problem; the results are compared with four other non-linear controller design procedures that were reported in the open literature.