A Method of Optimizing Adjustable Parameters in a Control System

A technique is described for adjusting parameters of a control system to optimum values for given plant characteristics and input statistics. The derivative of the performance index with respect to each parameter is measured directly by a cross-correlation measurement between a signal in the control loop, and a signal in an auxiliary loop connected to the original loop containing models of the components of the original loop. The difficulties of trial-and-error hill climbing are thus avoided, and the optimum is established by a null method without the use of the technique of parameter perturbations. The technique will extend to non-linear problems and general optimization criteria. In the presence of the type of constraint in which some average is limited, the optimization procedure must be modified by introducing Lagrangian multipliers as extra variable parameters. A second-order system has been simulated on an analogue computer and used to demonstrate the optimization procedure with and without constraints. With a view to automatic adaptation to change in plant characteristics, the problem of identifying an unknown plant is treated as a special case of the general optimization problem. An important property of this is proved, which suggests fast identification of any rational transfer function of limited degree. The advantages and limitations of the general technique are discussed.