Design Methods for Model-Reference Adaptive Systems

Abstract

The ‘M.I.T. rule’ and two Lyapunov synthesis methods of design are critically reviewed. The latter are the input modification scheme of Grayson and Parks' method for the determination of parameter-adjusting feedback loops. For large inputs such methods are unsatisfactory: this is demonstrated by root locus plots for the step response of a second-order system with adaptive gain. A Lyapunov synthesis procedure is proposed which is a composite solution. The feedback loops of Parks are employed but an input modification signal is superimposed. This can be conveniently chosen from existing signals to add a fourth order negative definite term to V, thus promoting a greater degree of stability for large inputs. Results from an analogue computer study are included. The method is general in application.