A WIENER-HOPF APPROACH TO TRADE-OFFS BETWEEN STABILITY MARGIN AND PERFORMANCE IN 2-DEGREE-OF-FREEDOM AND 3-DEGREE-OF-FREEDOM MULTIVARIABLE CONTROL-SYSTEMS

Trade-offs between stability margin and performance are considered in two-and three-degree-of-freedom multivariable control systems using a Wiener-Hopf design approach. Maximum improvement in an approximate mea sure of stability margin is achieved at the expense of a prescribed in crease in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade-of f problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction de scription of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtai ned could serve as a very good initial one from which to search for be tter solutions iteratively.