An experimental treatment of nonlinear servomechanisms

AN EXPERIMENTAL method of achieving appropriate first switching points for certain nonlinear single-loop servomechanisms is described. The servomechanism is assumed to be a positioning device. For control intelligence, nonlinear corrective functions of output velocity, static error, or error velocity are assumed continuously available. Since the method is experimental, either the actual device or a reasonably accurate analogue model can be used, and thus is not subjected to the same limitations as those imposed by simplified mathematical models. Here the basic device may be of high order and include many unintentional nonlinearities. One principal limitation accepted by the method is that the system input can be described by a limited Taylor series; i.e., at time t = 0, the quiescent system is confronted with an input consisting of an arbitrary position step plus an arbitrary velocity step, or ramp, plus an arbitrary acceleration step, etc. Switching points subsequent to the first are assumed to be compacted into the terminal region of the response, either to be absorbed by allowing the terminal region to be unsaturated, and perhaps linear, or to be determined by other methods. This assumption might be interpreted in practice as the requirement that the system components such as amplifiers, actuators, and sensing elements be in themselves relatively well damped. A highly underdamped element that tends to wiggle or ring during the positioning operation might well require a more elaborate experimental treatment.