Comparison of linear feedback systems with self-oscillating adaptive systems

This paper compares the adaptive and disturbance attenuation properties of the linear feedback system with those of the self-oscillating-adaptive system (SOAS). The purpose is to permit the designer to decide, in any specific problem, which of the two systems is preferable. In minimum-phase plants, the system sensitivity to feedback transducer noise is used as the basis for comparison. In nonminimum phase plants an additional consideration is the sheer realizability of system specifications. Due to the absence of a rational, quantitative design procedure for the SOAS, it was first necessary to develop one. This is presented for the single loop SOAS using a bistable element, and without limit cycle identifier and gain changer. The procedure may be easily applied to other kinds of nonlinear elements. The relative superiority of the linear system and the SOAS depends on the following factors: ratio of extreme output plant must deliver to maximum acceptable limit cycle amplitude, the severity of the disturbance attenuation problem, the actual extremes of parameter variations and acceptable tolerances, and the magnitude and frequency distribution of feedback transducer noise. In some problems the critical factor is the response of the SOAS nonlinear element to high-frequency noise. The problem areas in which the SOAS is superior may be increased if a minor loop is added around the nonlinear element. The possible advantages of adding a limit-cycle identifier and a gain changer to the SOAS are also considered.