Robust SISO H_∞ 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 identification techniques integrated with an H_∞ 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_∞ controller is synthesized using the identified uncertain Hammerstein model and a systematic performance weighting selection process for a class of L_∞ constraints. Closed-loop performance and stability are assessed via sector bounds quantifying the maximum allowable precompensator error. Frequency domain conditions guaranteeing an L₂ output provided the system input belongs to L₂ 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.