Synthesis and Stability Analysis of Self-tuning Controllers

Abstract

<p>The problem of self-tuning reference signal tracking is considered for systems represented by autoregressive moving average (ARMA) as well as state-space models. By self-tuning control, it is meant to be a combination of recursive parameter estimation and control algorithm. A new strategy of controller design is proposed, which is pole/zero placement in the 'error transfer function' (ETF) in contrast with the usual closed-loop pole-placement. Sufficient conditions for arbitrary simultaneous assignment of ETF poles and zeros are derived. For ARMA models, a recursive extended least squares type algorithm with a general nonlinear criterion function, which can be defined by the user, is suggested and the strong consistency of the algorithm is proved. Reference signal model identification is introduced for the first time into the context of adaptive control, which provides great flexibility to track any unknown external reference trajectory. The global convergence of the adaptive ETF pole/zero placement is theoretically established for deterministic systems. New stochastic optimal control algorithms are derived for the case where the control objective is reference signal tracking. The novelty of the proposed algorithms is that the performance indices are determined by the prespecified locations of ETF poles as well as zeros. State-space approach to self-tuning control has been studied also. The recursive prediction error method is used for joint state and parameter estimation, of state-space innovations model. Adaptive reference signal tracking control laws are derived for system output as well as an immeasurable physical state.</p> <p>To demonstrate practical applications, the derived self-tuning algorithms were applied to surface accuracy control in turning and end milling process. The results of simulations indicate considerable improvements in geometric accuracy of finished workpieces over conventional numerical control in the presence of significant tool workpiece deflection.</p>