Frequency based nonlinear controller design for regulating systems subjected to time domain constraints

Presented is a nonlinear controller design methodology for a class of regulating systems subjected to quantitative time domain constraints. The output performance specification is an allowable time domain tolerance and the system experiences actuator saturation. The controller design is executed in the frequency domain and is applicable when the frequency response of a linear design cannot satisfy the gain and phase characteristics required by quantitative time domain specifications. A describing function (DF) approach, automated by the Volterra Series, facilitates the nonlinear controller design. The resulting gain and phase distortions associated with the DF of the dynamic nonlinear element are used to achieve the desirable open loop gain and phase characteristics identified by the time domain constraints. The design methodology is illustrated on the idle speed control of a Ford 4.6 L V-8 fuel injected engine. The engine input is the by-pass air valve and the regulated output is engine speed. The power steering pump generates the nonmeasureable external torque load.