Design of minimum sensitivity systems

A method for the design of linear time-invariant multivariable minimum sensitivity systems is presented. The method utilizes a quadratic form in the parameter-induced output errors as a performance index to be minimized, with the constraint that a prescribed nominal transfer function matrix be obtained. An essential ingredient in the procedure is the use of a comparison sensitivity matrix. Two advantages that follow from the use of the sensitivity matrix are: 1) Physical realization constraints on the compensators may be included in the design. 2) The computational aspects of the problem are relatively simple and may be carried out routinely using any parameter optimization algorithm. A nontrivial multivariable example illustrates the procedure. The design method may be viewed as the second part in a two-part procedure, where the first part is the determination of a desired nominal transfer function. A two-degree-of-freedom feedback structure is used to realize an optimum or desired nominal closed-loop transfer matrix, as well as a minimum in a sensitivity index.