Reduction of the parameter estimation time for an adaptive control system

The following work is concerned with the use of the Method of Least Squares in the parameter estimation of a discrete-time model of a system. In particular, the emphasis is upon both the initial convergence and accuracy of the estimates. The investigation is therefore pertinent to both the "cold-starting" of least squares estimators, and to systems in which "jump" changes in parameters occur, requiring resetting of the estimator. The work was approached from an engineering viewpoint, with the requirement that the theory be applied to a real system. The real system selected was a positional servosystem, using a DC motor. A number of least squares algorithms were compared for their suitability to such an application. The algorithms examined were: 1) A standard, non-recursive solution of the least squares equations by Lower-Upper Factorisation of the information matrix. 2) A standard, recursive solution, i.e. Recursive Least Squares, RLS. 3) Two reduced order solutions using a priori knowledge of the type number of the servosystem (LU Factorisation and RLS). 4) An Extended Least Squares Solution, using a recursive algorithm. 5) Several non-recursive solutions using instrumental variables. The methods were initially examined using a software simulation of the servosystem. This simulation was based on a linear, second-order model. It was concluded that the preferred methods were the reduced-order solutions using a priori knowledge. The following hypothesis was examined: By raising the rate at which the signals are sampled, more information is provided to the estimator in any given period of time. Increasing the sampling rate should therefore result in a superior, real-time parameter estimator