THE LEAST-SQUARES PADE METHOD FOR MODEL SIMPLIFICATION OF MULTIVARIABLE SYSTEMS

This paper is concerned with the simplification of multivariable systems in the frequency domain. Whereas the original model can be represented in either the time or frequency domains, the simplified model will be a transfer matrix. Dominant poles of the original system are retained in the simplified model and thereby the stablity of the latter is guaranteed. The matrices comprising the numerator of the simplified model are determined by imposing a number of constraints which is larger than the number of unknowns, and the resulting set of equations is solved in a least squares sense. This usually enables the determination of models which are more accurate over the range of midfrequencies. The contraints used are the approximate retention of Pade and Markov matrices. To apply least-squares techniques, a new formulation is suggested for the matrices of Pade and Markov parameters. By varying the total number of Pade and Markov constraints a family of simplified models is easily obtained, and performance criteria can be used to select the best model. The new algorithm is illustrated using the model of a real power system.