Nonlinear Controller Design for Regulating Systems
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Presented in this dissertation is a nonlinear controller synthesis methodology based on the inverse Sinusoidal Input Describing Function (SIDF) for a class of regulating systems. The design goal is to improve regulating performance beyond what is achievable by a linear control for a predicted level of disturbance step size. The controller design is executed using open loop frequency domain information and is applicable when the frequency response of a linear design cannot satisfy the designed open loop gain and phase characteristics. The gain and phase differences between the designed open loop frequency response and that of a linear design is treated as SIDF distortions. The inverse describing function approach is employed to identify an isolated explicit nonlinearity that is associated with obtained gain and phase distortions. For this, a computational solution to the inverse SIDF for a broad class of hysteresis or memoryless explicit nonlinearities is developed. The proposed numerical solution uses gain and phase distortions as a function of input amplitude size to identify the nonlinearity, and does not require a priori knowledge of the nonlinearity in the estimation process. The output from the algorithm is a non-parametric model of the nonlinearity from which a parametric model can be recovered. To illustrate the proposed nonlinear controller design technique, the idle speed control of a V-6 fuel injected engine model subject to an external torque load disturbance is considered. The closed loop performance is validated through simulation and the closed loop stability in the sense of the bounded-input-bounded-output (BIBO) is assessed using Circle Theorem.