Stable Direct Adaptive Periodic Control Using Only Plant Order Knowledge

The main contribution of this paper is to put stability requirements for convergence of direct adaptive periodic controllers on equal footing with requirements for indirect adaptive periodic control, as set forth by Lozano. The resulting stability condition is simply that the plant order is known a priori. No other prior plant knowledge is used (e.g., relative degree, high-frequency gain, etc.), and persistent excitation is not required. More importantly, no assumption or knowledge is required as to whether the plant is minimum or nonminimum phase. A numerical example is given to demonstrate the method, and some guidelines are given for improving the adaptive transient response.