Frequency Response Testing and Low-Order Modelling by Relay Oscillation Method

Frequency response tests have been the most conventional method to control engineers for analysis and design of control systems. This paper presents a simple and quick way to obtain frequency response using relay with variable hysteresis width. Adding a relay in series with a system and forming a closed-loop unity negative feedback system, the system output will result with limit cycle oscillations. In adjusting the hysteresis width of the relay, the limit cycle oscillation will vary and different open-loop frequency response data for the system in second and third quadrants can then be obtained by measuring the amplitude of the output oscillation and the phase difference between the input and output signals. Low-order models con then be fitted to the frequency data obtained. Simulation studies are included to illustrate the proposed method.