Self-Excited Oscillation of Relay-Type Sampled-Data Feedback Control System

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This paper presents a time domain investigation about the self-excited oscillation of relay-type feed back control systems with sampling and dead time. Because of the relay, dead time, sampler and holder involved in the system, there exists a self-excited oscillation whose amplitude and period vary within certain restricted ranges. The general method for calculating these ranges is studied at first by extending Hamel's method to the case of sampled-data control systems and then boundary values of these ranges are calculated about the second and third order feedback control system. Generally, the period of the self-excited oscilla tion is exactly obtained by applying this method, even though the system has higher-order dynamic elements. However, it is difficult to calculate the exact value of its amplitude especially in the case of higher-order systems. Describing function method utilizing the period obtained above can be used to avoid this difficulty for determining the amplitude.
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