Model reference adaptive control for plants with unknown relative degree

A parameterization scheme for model reference control which guarantees stable model-plant transfer function matching is presented. This scheme has a linear dynamic feedforward block whose numerator and denominator should be stable polynomials for closed-loop stability. An adaptive law is designed to update the controller parameters in the feedback loop and the coefficients of the numerator of the feedforward block as well as some additional parameters. Since, for stability, the inverse of the polynomial differential operator defined by some of the estimated parameters has to be stable, the adaptive law is modified using a projection technique. The stability analysis of the model reference adaptive control (MRAC) scheme is given. The robustness of the MRAC scheme with respect to unmodeled dynamics is established