A Simulation Study of Singular Value Decomposition for Controlled Plant Identification

A methodology is presented for the adaptive control of a single-input single-output system using the numerically stable method of singular value decomposition (SVD) for identification. This methodology is suitable for industrial applications where the plant parameters change slowly compared to the plant dynamics. A procedure is included for automatically identifying situations where the results of the identification are questionable. This procedure is based on three indices which are used to evaluate the identification. Expressions for computing these indices from the output of the SVD are derived. The identification procedure is numerically stable but computationally expensive. The computation time for identification may exceed the largest suitable sampling interval for some applications. To accommodate the long computation time, a parallel processing structure is used. In this structure, the identification is done as a background task in parallel with the controller function being performed by the processor. This structure permits use of the SVD method at low hardware cost for applications where the plant parameters are expected to change slowly. The feasibility of using an 8-b microprocessor to implement this methodology for adaptive control is demonstrated for a simulated plant of known structure and measurement noise characteristics. The identification time required is tabulated as a function of a) the number of parameters to be estimated, and b) the number of equations that are formed from the observed data.