Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed system tolerances†

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Abstract
In the design of a linear feedback system to achieve prescribed response tolerances despite significant plant uncertainty, the principal price paid is in the amplification of sensor noise, which tends to saturate the plant elements. This noise amplification is due to the fixed relation between gain and phase of an analytic function, which forces relatively slow reduction of the loop transmission magnitude, as a function of frequency. A nonlinear element, the Clegg Integrator (C.I.), is used to alleviate this relation, permitting faster reduction of the loop transmission magnitude. The major difficulty is in finding a description of C.I. usable for synthesis. This is done by considering the class of step inputs, and locating the C.I. such that, from the inputs and the system output specifications, the nature of the inputs to the C.I. is known, permitting an equivalent linear characterization. A quantitative design procedure is then available to precisely design to achieve specified tolerances. A design example is included illustrating the superior features of the non-linear system, for a specific input class.

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