Simplification of High-Order Mechanical Systems Using the Routh Approximation

[+] Author and Article Information
M. Hutton

Kearfott Division, The Singer Co., Little Falls, N. J.

M. J. Rabins

Operations Research and System Analysis Dept., Polytechnic Institute of New York, Brooklyn, N. Y.

J. Dyn. Sys., Meas., Control 97(4), 383-392 (Dec 01, 1975) (10 pages) doi:10.1115/1.3426954 History: Received July 28, 1975; Online July 13, 2010


In many recent applications, the control engineer is faced with the problem of controlling a linear system modeled by a transfer function of high or infinite order. In a majority of these cases it is possible and advantageous to approximate the original transfer function by a transfer function of lower order. The Routh approximation is a novel method for reducing the order based on the idea of truncating the well-known Routh table used to determine stability—hence the name given to the method. The Routh approximants can be computed by a finite recursive algorithm that is suited for programming on a digital computer. The algorithm, flow diagrams, and simple numerical examples are presented. A detailed description of the theoretical background and properties of the method are given in [1] and [2]. This paper focuses on the application of the Routh approximation method and the simplification of two mechanical systems are described. First, a low order transfer function for studying vibration is computed from a finite element model of the structure. Second, the Routh approximation is utilized in the design of a thermal control system where the heat conduction is modeled as a distributed parameter system whose transfer function has infinite order.

Copyright © 1975 by ASME
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