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

Presented is a nonlinear controller design methodology for a class of linear regulating systems subjected to quantitative time-domain constraints. The design objective is to satisfy an output time-domain tolerance given an actuator saturation constraint despite an external step disturbance. The goal is to increase the allowable magnitude of the external disturbance beyond that achievable via linear control subject to the time-domain specifications. The controller design process is comprised of two phases. In the first phase, a linear controller is designed that balances the trade-off between output regulation and required actuation. To realize the linear design, the time-domain performance specifications are mapped into amplitude and phase constraints which are in turn imposed on the frequency response of the linear open-loop transfer function. In the second phase, the linear controller is then augmented with an odd nonlinearity. The coefficient for the nonlinear term is designed such that the gain and phase distortions (in the sense of describing functions) meet the frequency-domain constraints. The describing function calculation is automated by a recursive Volterra Series relationship. The nonlinear controller design methodology is experimentally verified on the idle speed control of a Ford 4.6L V-8 fuel injected engine.