Stochastic modelling of computer-regulated linear plants in noisy environments †

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Abstract
The purpose is the discrete-time stochastic modelling of a linear plant in single-loop direct digital feedback control, particularly with a constant reference input. The system receives dynamic inputs by the intrinsic noise of the digital quantizers, and from environmental disturbances, which are assumed to have rational spectral densities. An equation is derived in the deviation from its mean of the random feedback variable, y(k), consisting in a linear difference expression in y(k), a so-called autoregrcssion, equated to a sum of linear difference expressions in white noise sequences, so-called moving averages. The sum of these also is a moving average. The conclusion is The stochastic process of a computer-regulated linear plant in a single feedback loop, whose dynamic inputs are all quantization noise sources and environmental disturbances with rational spectra, can be expressed as a stationary mixed auto-regressive, moving-average (ARMA) model, which also has a rational spectral density. Features of the model useful for identification purposes are discussed. In particular an algorithm for the computation of the autocovariance function is derived for use in a forthcoming paper.

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