Self-Oscillation in a Control System with Dead Time and Saturation

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In this paper, the author analytically investigates a second order control system with dead time and saturation and he elucidates selective occurrence of self-oscillation in the system. The conclusions obtained are as follows: The system has several pairs of unstable characteristic roots in some intervals of dead time. Among a number of self-excited modes of oscillations which correspond to unstable roots, only one mode of oscillation develops and settles down to a steady state periodic oscillation under the effect of saturation (the oscillation is referred to as self-oscillation). Although occurrence of two or more modes of self-oscillations may be possible in some intervals of dead time, these modes of oscillations can never occur simultaneously, but only one mode of them can occur depending upon the initial condition. The condition of occurrence of self-oscillation is analytically expressed and also amplitudes and frequencies of self-oscillations are theoretically obtained. The theoretical results are in good agreement with the experimental results by analog computer.
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