Ripple-free model reference adaptive control

It is shown how to change the primary control structure of a model reference adaptive control (MRAC) scheme from the usual minimum settling time-type algorithm to a ripple-free response control (RFRC) scheme. RFRC does not try to compensate process zeros, avoiding ringing effects (like intersampling ripple). The main issue in the derivation of the RFRC-MRAC scheme is the establishment of a stable adaptive law which guarantees a ripple-free behavior if the error signal tends to zero. In the original MRAC scheme, the error signal consisted of the desired error plus a transient term which tends to zero when adaptation proceeds. In this MRAC scheme, the error consists of a filtered form of the desired RFRC error. Hence, if the error used in the adaption tends to zero, the RFRC behavior is achieved. The scheme avoids ringing effects and can control nonminimum-phase processes. The cost of these advantages is a slowing down of the process response by a number of samples equal to the order of the numerator polynomial. Simulations confirm the RFRC-like characteristics, and practical results on a water level system show the usability of the method