Stochastic identification of computer-regulated linear plants in noisy environments

Abstract

The object of study is a computer-regulated linear plant in a D.D.C arrangement. The plant is a representation in discrete form of a continuous process and its associated equipment, subject to computer quantization noise and environmental disturbances, all describable by rational transfer functions. It was shown in a previous paper (indberger 1972) that the discrete-time model of the system is a linear, stationary, mixed autoregressive, moving-average (RMA) process in the feedback variable deviation from its mean. After obtaining a large sample of this variable and computing its covariance function, a parameter estimation is performed by fitting the model autocovariance to the sample covariance in a maximum likelihood (L) sense. For a correct model assumption the procedure converges in probability and the estimates have typical ML properties such as consistency and normal distribution. The ML estimate is equivalent to a weighted least squares estimate, obtained by the minimization of certain quadratic forms with respect to the process parameters. The convergence in probability of the latter procedure and the ML properties of the estimates were shown by this author (indberger 1970). The method of identification is by repeated hypothesis trial and test using models of different configurations, under guidance of the results of previous trials. An example is given of a second-order plant subject to two different types of noise sources. Under the restrictions given, and at least for simple configurations of plant and noise sources, a computer-regulated plant can, therefore, be identified without using the standard method of injecting noise of a known spectral density.