Research Papers

An Analytic Frequency-Response Solution for a Higher Order Servomechanism With a Nonlinear Control Element

[+] Author and Article Information
A. M. Hopkin

University of California, Berkeley, Calif.

K. Ogata

University of Minnesota, Minneapolis, Minn.

J. Basic Eng 81(1), 41-45 (Mar 01, 1959) (5 pages) doi:10.1115/1.4008356 History: Received November 01, 1957; Published March 01, 1959; Online February 20, 2019


On-off-type control systems designed on the basis of step-input response sometimes exhibit poor frequency-response characteristics. When subjected to periodic inputs, such systems may oscillate at subharmonics of the input frequencies under certain conditions. An example of subharmonic response of an on-off-type system is shown in Fig. 1(a). Fig. 1(b) shows the corresponding fundamental response.

When an on-off system is designed with a proportional band, the frequency response of the system must be carefully investigated for the possibility of “jump resonance” and subharmonic oscillations. This is particularly necessary when the system is known to be subjected to occasional periodic inputs.

This paper presents an effective method for evaluating the frequency response, both open-loop and closed-loop, for on-off-type feedback control systems with or without proportional bands. Fig. 2 shows one type of the system under discussion.

The essential material presented follows the Laplace-transform method suggested by D. Kahn [1]. It is an extension of the work already reported by K. Ogata [2, 3].

Copyright © 1959 by ASME
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