The design and performance of a model, second-order, nonlinear servomechanism

This paper discusses the design and performance characteristics of a model, second-order, nonlinear servomechanism. The design procedure stems from principles laid down in the authors´ previous paper, in which the nonlinear differential equation characterizing this servo was synthesized. The physical aspects of the various building blocks needed for nonlinear servo construction are considered. Schemes for generating nonlinear functions are described, along with methods for accomplishing the multiplication and differentiation of the control system´s variables. Schematic diagrams of the nonlinear servo are presented, in addition to instructions for adjusting the parameters to obtain the proper response behavior. The results of a comparison of equivalent nonlinear and linear servo operation are given in the form of photographs illustrating the control system´s error response for various magnitudes of step inputs of position. The nonlinear system´s error response is shown to be superior to the linear system´s error response in that the nonlinear response exhibits no overshoot and reduces the system error to zero in approximately the time required for the linear system´s error response to pass through zero for the first time. The response time of the nonlinear, model servo corresponds closely to the predicted response time.