Frequency-based controller design for a class of nonlinear systems

Presented in this paper is a frequency-based controller design methodology for a class of nonlinear systems that can be characterized by a class of Hammerstein models. The controller design is directed toward the disturbance rejection problem where the output performance specification appears as a time domain tolerance. The controller design process is executed in three stages. First, the system nonlinearities are quasilinearized via describing function techniques. Second, the design methodology enforces a time domain tolerance |y(t)| ≤ α via frequency domain constraints on the quasilinearized closed-loop system. Finally, the controller is designed via classical loop shaping of the quasilinearized system on the open-loop gain-phase plane. The design process is illustrated on the idle speed control of a Ford 4.6L-2 valve V-8 fuel injected engine.