Optimum Nonlinear Control for Step and Pulse Disturbances

Abstract

This paper treats the responses of a controlled system to step and pulse disturbances where the rate of change of the controlling variable is bounded. Optimum transients in the sense of minimizing the maximum error, response duration, and other variables are derived for step and pulse disturbances whose parameters, i.e., magnitude, sense of change, instant of occurrence and pulse duration, are either completely known in advance, or known at the instant the disturbance starts, or not known in advance at all. It is shown that the more that is known about the disturbance beforehand, the better the response that can be obtained. The improvement may be very great. The optimum control function for a pulse disturbance known at the initiation of the pulse contains disturbance parameters. A practical control function can be derived by eliminating these parameters so that no advance information about the disturbance is required. The resulting control function will yield optimum transients and will depend entirely on the system error and its derivatives. This practical control function yields improved response over classical theory to a train of pulse-load disturbances.