© 1984 by Institute of Mathematics and its Applications
Filtering Techniques in Self-Tuning
Department of Electrical & Electronic Engineering, University of Newcastle upon Tyne
Department of Electrical Engineering, Imperial College London
In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description.
This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case.
At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.