# The study of control systems by correlation methods

Falconer, J (1962) The study of control systems by correlation methods. MSc(R) thesis, University of Glasgow.

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## Abstract

In the testing of control systems, particularly the smaller types, it has long been the practice to apply to them test signals of a simple mathematical nature, for ease in evaluating test results. The principal signals used for this purpose are the step functions, ramp function, and the sinusoid. As the scale of systems has grown, so the complexity has increased also, and with that the severity of the effect of such disturbances until the stage is reached when dangerous conditions may be induced thereby. an alternative, means have been sought to obtain information of the system characteristics from data collected during normal operation; by this means, unduly severe disturbances are avoided. This work describes one such method of system analysis. In it, certain statistical properties of the data produced by the normal running of a control system are calculated. These statistical features are used to determine in the end the frequency response of the system, both in amplitude and in phase. mince in laboratory tests the scale of the apparatus used is restricted, use is made of an analogue computer to simulate the control systems, and also to assist in the statistical computations. source of random signals of the type encountered in practical systems is required to drive such a simulator, and an account of the development of such a device is included. device giving fixed time delay, needed for the statistical work is also described. The process is based on the use of the correlation functions of the time time signals produced by the system; the auto-correlation function of the input or output signal, and the cross-correlation function between these two signals, form Fourier transform pairs vdth the power spectral densities of in-out and output signals, and the cross-spectral density between them, respectively. Numerical methods of iburier transformation are used to obtain these power spectra; once they are known for both input and output of a control system, its frequency transfer function is readily determined. This direct approach to the mathematical manipulations represents a departure from most previous methods used, in that they have frequently involved the preparation and adjustment of a model to have the same performance as the original system, followed by a response analysis of the model. esults of tests on two types of systems are given, and probable sources of error indicated. It is conceded that the system as up:lied here is tedious to operate, and has several inherent sources of error. Lines of further development are indicated which could dispose of these, and would produce an attractive and versatile nethod of system analysis.

Item Type: Thesis (MSc(R)) Masters Adviser: F M Bruce Systems science 1962 Enlighten Team glathesis:1962-73439 Copyright of this thesis is held by the author. 14 Jun 2019 08:56 14 Jun 2019 08:56 https://theses.gla.ac.uk/id/eprint/73439