Combined adaptive control with new adaptation laws

A combination of direct and indirect methods of adaptive control that yielded an improved performance (over its constituent methods) is considered in this paper. This combined method has been recently developed; it was considered that the improvement was due to the use of a new kind of error-called the closed-loop estimation error. Earlier papers on this combined method used a Lyapunov function and developed stable adaptation laws of integral (I) form. Using the same errors, this paper suggests a new Lyapunov function and its associated adaptation laws of proportional plus integral (P + I) form, showing that further improvement in the performance can be obtained. Digital simulation results are presented, indicating that the 'P' term improves the performance in those cases where the 'I' term alone is not adequate.