Empirical Optimization of Non-linear Control Systems with Random Inputs. Part II †

Abstract

ABSTRACT This paper gives the results of the optimization of five second and third-order systems with saturating and relay controllers and with random Inputs. They were optimized using an approximate empirical method which was described in Part I. For a system with a double integrator plant and a Brownian Motion input signal, the optimum relay controller with quadratic switching is found to be rather different from the relay controller which minimizes the response time to a deterministic input, in that the former gives some undershoot in response to a step input. Linear switching gives slightly smaller mean squared error than quadratic switching, and no combination of linear and quadratic switching is found to be better than linear switching alone. The third-order systems which are examined have in one case a double integrator plant and a smoothed white noise input, and in the other, a triple integrator plant and a Brownian Motion input.