Generalized polynomial H(infinity) predictive control utilizing minimax prediction.

摘要

Due to increased interest in the development and implementation of control schemes which are inherently robust, H{dollar}sbinfty{dollar} optimal control methods are the focus of a great deal of study in the current literature. Industry, however, has been slow in adopting these methods because of the difficulties often encountered in tuning the performance of many H{dollar}sbinfty{dollar} controllers. The new minimax predictive minimization which uses a minimax predictor incorporates several time-honored control concepts as integral components of the control algorithm, so that satisfaction of time and frequency domain design specifications by the control designer or plant operator can be accomplished in a more direct and intuitive manner. The resulting controller provides asymptotic reference tracking via an application of the internal model principle, minimax disturbance rejection using the embedding techniques of Kwakernaak, guaranteed stability resulting from a form of internal model control, and a simplified structure resulting from a derivation inspired by the solution of the H{dollar}sbinfty{dollar} model matching problem. The minimax predictor, when used as a component within the derivation of a predictive minimax control law, provides a tuning knob which can be used to provide a trade-off between performance and stability robustness by changing the length of the prediction horizon. This trade-off is not induced by the standard least squares predictor. The minimax predictor is unique in that it minimizes the cost function of the prediction error in a minimax sense, yielding minimization of the peaks of the prediction error spectrum, rather than its integral on the unit circle. Similarly, the control law minimizes the peaks of a generalized cost function in the frequency domain. The form of the equations which define the controller can be readily solved by the solution of a generalized eigen-value problem. The final algorithm offers an intuitive framework for tuning the controller performance in terms of a quantity that is conceptually clear to the designer.