H∞ synthesis of nonlinear feedback systems in a Volterra representation

Presented in this paper is a procedure for selecting the H. performance weights for a class of nonlinear feedback systems modeled by a truncated Volterra series. The performance weight selection addresses the trade-offs between closed-loop performance and closed-loop stability. The class of feedback systems considered are regulating systems subject to step disturbances. The methodology is based on two recent results concerning closed loop stability for this class of nonlinear feedback systems. These stability conditions can be formulated as an H. problem where the performance weights are systematically identified. This synthesis procedure is applied to the idle speed control of a Ford 4.6L V-8 fuel injection engine. Through this application, the design trade-off between closed-loop performance and stability is illustrated.