An algebraic approach to system identification and compensator design



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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.