Self-tuning controller

Abstract
A strategy for the design of self-tuning controllers of systems with constant but unknown parameters is presented. A cost function which incorporates system input, output and set-point variations is selected, and a control law for a known system is derived. This control law is shown to comprise a least-squares predictor of a function related to the cost function, and the control input is chosen to make the prediction zero. The parameters of the control law for the unknown system are estimated using a recursive-least-squares algorithm, and the optimal parameters are shown to be a fixed point of the algorithm. Whilst retaining their computational simplicity, the proposed method has several advantages over self-tuning-regulator strategies which attempt to minimise the output variance alone: weighting of control is allowed for; set-point variation may be optimally followed; there is no requirement to choose a system-related parameter to ensure convergence; and, for stable but nonminimum phase systems, there is no need to employ time-consuming methods, such as the solution of a Riccati equation. Several simulated examples are used to demonstrate the potential of the method.

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