Frequency based nonlinear controller design for regulating systems subject to time domain constraints

John W Glass, Purdue University

Abstract

In this thesis two novel controller design methodologies are proposed for the design of regulation systems. The first methodology is a nonlinear controller design methodology for a class of regulating systems subject to quantitative time domain constraints. The time domain specifications appear as an allowable tolerance on the output deviations and allowable control effort. The design goal is to maximize the size of an external step disturbance beyond that of linear control which is also subject to time domain specifications. The controller design is executed in the frequency domain and is applicable when the frequency response of a linear design cannot satisfy the gain and phase characteristics required by the quantitative time domain specifications. The resulting gain and phase distortions associated with the sinusoidal input describing function (SIDF) of the dynamic nonlinear element are used to achieve the desirable open loop gain and phase characteristics required by the time domain constraints. The SIDF approach, automated by the Volterra Series, facilitates the nonlinear controller design. To illustrate the proposed nonlinear controller design technique, the idle speed control of a 1992 Ford 4.6 L V-8 fuel injected engine subject to a nonmeasurable external torque load disturbance is employed. The controller performance is validated through experimental implementation, and, finally, closed loop bounded-input-bounded-output stability is assessed. The second controller design methodology extends the notions of linear H∞ synthesis to a class of nonlinear systems modeled by a truncated Volterra series. The methodology is based on the selection of performance weights to trade-off between closed loop performance and the largest allowable disturbance which can enter a system. This proposed synthesis procedure is applied to the idle speed control of a nonlinear model Ford 4.6 L V-8 fuel injection engine. A performance trade-off curve is then used to synthesize a linear feedback controller. To further enhance the performance of the synthesis methodology, a precompensator design procedure is presented which acts to linearize the nonlinearities in the plant. Issues regarding the implementation of a precompensator are also addressed. The effect of the precompensator on enlarging the bound on the largest allowable disturbance injected into the closed loop system is then quantified.

Degree

Ph.D.

Advisors

Franchek, Purdue University.

Subject Area

Mechanical engineering

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