Adaptive servomechanisms

A generalized approach is developed to aid in the synthesis of servomechanisms exhibiting adaptive behavior. The design methods described in this paper permit the synthesis of adaptive systems to follow polynomial signals up to any predetermined degree in the presence of Gaussian noise of known autocorrelation function. The basis of the method is the requirement that the servo loop adjust its parameters so as to minimize the steady-state root-mean-square error resulting from a polynomial input in the presence of noise. This condition specifies the functional relation between the servo parameters and the polynomial input. The physical realization of these functional relationships is treated in the paper and leads to the adaptation loops necessary to produce the adaptive behavior. As an example of the synthesis procedure, the design of a second-order adaptive system is presented. Analog computer results demonstrating that the adaptive system is superior in performance to linear systems of the same order are also included.