Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms

Analysis of irrational and transcendental transfer functions

This thesis is an exposition of approximation techniques on irrational and transcendental functions. Continued fractions are used for approximating the irrational and transcendental functions. A new general matrix is then developed for the inversion of the continued fractions. Two digital computer programs for the expansion and the inversion are included.Electrical and Computer Engineering, Department o

An algebraic approach to system identification and compensator design

In modern design of Control Systems, the synthesis techniques originated by Letov, Kalman, Bass and Tyler start with a certain functional--the quadratic performance index. However, the quadratic performance index is not very suitable for using the industrial specifications. In other words, a link between the classical and modern methods is missing. We have to seek the missing link in the algebraic domain. This is mainly due to the digital computer consideration. This dissertation research attempts to consider the design of control systems into two problems: 1. the Identification Problem, 2. the Compensation Problem. Both problems are investigated from the algebraic viewpoint. As far as the identification problem is concerned, three methods are developed. If the specifications are given in the time domain completely, a z transform technique is developed which is an extension of the application of the powerful sensitivity matrix. If the specifications are given in the frequency domain completely, Chen-Phillip's and Chen, Knox and Shieh's methods are further studied. If the specifications are given in a hybrid form which means some index in the time domain, others in the frequency domain or in the complex domain, an original synthesis technique is established. The technique is by using the multidimensional Newton method to synthesize the transfer function from hybrid information. The compensation problem is investigated by establishing a new form which is similar to the Cauer second form in circuit theory. The judgment of the approximation and the error estimation are based on the Minimum Integral Square criterion. The general design philosophy is outlined as follows: To synthesize a desirable transfer function based on the hybrid specification. After finding the closed loop transfer function with an assigned compensator and simplifying the compensated overall transfer function, we equate it with the model we synthesized before and use the Newton multidimensional method to obtain the parameters.Electrical and Computer Engineering, Department o