An analog computer study of multivariable model simplification



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There are several methods of simplifying a high order system with lower order one. These methods are discussed briefly and a technique developed by Chen and Shieh is chosen as the most versatile one. The Chen-Shieh technique involves performing a Second Cauer continued fraction expansion of a system's transfer function and then discarding the higher frequency terms. The higher frequency terms are those last determined by the dividing procedures of the continued fraction. General techniques are developed for single input-single output systems and two examples were modeled and then simplified. Next, the Chen-Shieh method is extended to multi input/output systems. The basic matrix form of the second Cauer continued fraction expansion is developed. A general analog program block is also developed. An example of a two input-two output system is presented and the techniques that were derived are used to simplify the system. The results of all of the systems simplified by the Chen-Shieh method and the extension of their method to multi input-output system were excellent.