A Simple Fourier Analysis Technique for Measuring the Dynamic Response of Manual Control Systems

From a practical standpoint most dynamic response analysis techniques are complicated, expensive, and time consuming to mechanize and operate. These techniques usually require digital or special-purpose analog equipment, and the computations are often performed sometime after data are collected. Adaptive paramater tracking techniques partially overcome these faults: but they either have prescribed forms, which is an undesirable restriction for basic research, or in the case of free-form methods the computational requirements become excessive. To overcome these drawbacks, an on-line Fourier analysis technique has been developed which deals only with the input and error signals in a manual feedback control system. Several sine waves are used for the input, and the on-line data measurement includes the error variance and a simple means for obtaining the sine and cosine transforms of the error signal at each of the input frequencies. From this relatively small amount of data, we show simple ways to compute the open- and closed-loop dynamic response at input frequencies and the relative amount of linearly correlated power in the error signal. This paper describes the rationale and theory for the technique and discusses two methods for mechanizing it; one involving standard analog computer components and one based on conventional electromechanical components. Finally, a typical application of this method is presented.