Digital-computer analysis of relay feedback systems

The paper describes several ways in which an accurate analysis may be made of relay feedback systems. Methods are described which enable the signals at any part of the loop to be determined when the loop input is a d.c. signal. If the loop transfer function is simple, a solution may be possible using a desk calculator, but when the loop becomes more complex a digital computer becomes necessary. In cases where the loop input is a sinusoidal signal of frequency well removed from the oscillation frequency, it is shown how the analysis used for the d.c.-input case may be extended to enable the components at any part of the system to be determined. A method is also described which shows how the frequency spectrum, of the loop output may be determined. When the input of the loop is a sine wave, the output spectrum will in general consist of a series of sidebands displaced about the oscillating frequency of the loop and its harmonics. It is shown how the amplitude of all these components may be determined for any size and frequency of input sinusoid if a digital computer is available. Examples of solutions obtained for various feedback systems are given, and comment is made on the way in which system design is influenced by the results of the analysis.