Combined adaptive control with new adaptation laws

A combination of direct and indirect methods of adaptive controlthat yielded an improved performance (over its constituent methods)is considered in this paper. This combined method has been recentlydeveloped; it was considered that the improvement was due tothe use of a new kind of error—called the closed-loopestimation error. Earlier papers on this combined method useda Lyapunov function and developed stable adaptation laws ofintegral (I) form. Using the same errors, this paper suggestsa new Lyapunov function and its associated adaptation laws ofproportional plus integral (P + I) form, showing that furtherimprovement in the performance can be obtained. Digital simulationresults are presented, indicating that the ‘P’ termimproves the performance in those cases where the ‘I’term alone is not adequate.