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 tr'ansrniaaion magnitude, as a function of frequency. A non-linear 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.l. such that, from the inputs and the system output specifications. the nature of the inputs to the C.l. 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 claes. •
IntroductionA fundamental problem in control is the design of a sy~tem such that its response satisfies given tolerances despite substantial ignorance of the parameters of a vital part of the system, denoted as the plant. While the general subject of sensitivity to parameter variation has received considerable attention, there are few synthesis methods for realizing quantitative specifications in the face of given uncertainty bounds, even for linear time-invariant systems (Horowitz 1964, Cruz, Jr. and Perkins 1964, Perkins et al. 1968, Olson and Horowitz 1970, and hardly any for non-linear systems. This paper presents such a quantitative non-linear synthesis technique, albeit limited to a restricted input class.' The technique parallels in important aspects the linear synthesis theory of Horowitz andSidi (1972) andHorowitz (1973) and is strongly motivated by the general limitations of linear feedback design. Hence, the principles and limitations of the latter are first briefly reviewed.
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