An Adaptive Pole Placement Controller Based on Pole-Zero Parameterization

The pule placement design principle pruvides a good way of determining a closed loop system with desired properties. The method has been used in adaptive contexts for many years. A drawback of the method is, however, that the polynomial formulation mav lead to robustness problems because of the sensitivity with respect to the coefficients of the polynomials. Further, unless all process zeros are cancelled a set of linear equations has to be solved at each step in time. In this paper an attempt is made to avoid these two problems. The sensitivity of the polynomial formulation is avoided by parameterizing the model in the poles and zeros, which are estimated on-line. With the plant expressed in this form it is possible to parameterize the controller such that the solution of the Diophantine equation corresponds to the solution of a triangular system of equations. The controller parameters can thus be computed recursively without extensive computations