Robust SISOH∞ controller design for nonlinear systems

Presented in this paper is a nonlinear SISO controller design methodology for a class of Hammerstein models. The design process is composed of standard system identitication techniques integrated with an H-infinity linear controller synthesis formulation. The system identification portion of this work first identifies the static, single-valued nonlinearity capturing the nonlinear behavior of the system. This nonlinearity is then inverted and serves as a precompensator to the system input. The frequency response function is then identified with the precompensator in place to capture the linear dynamics of the system. Errors associated with the nonlinear inversion are addressed in an unstructured uncertainty formulation. A robust H-infinity controller is synthesized using the identified uncertain Hammerstein model and a systematic performance weighting selection process for a class of L-infinity constraints. Closed-loop performance and stability are assessed via sector bounds quantifying the maximum allowable precompensator error. Frequency domain conditions guaranteeing an L-2 output provided the system input belongs to L-2 are also presented. To illustrate the procedure, the design methodology is applied to synthesize a robust feedback controller to regulate the mass air flow of a 4.6 L V8 spark ignition engine equipped with an electronic throttle. (c) 2005 Elsevier Ltd. All rights reserved.