A New Approach to Discrete and Continuous-Time Generalized Predictive Control

Abstract

The paper represents an alternative procedure for generalized predictive controller (GPC) design which is based on a state observer - Kalman filter and is applicable in discrete and continuous-time framework. It is shown that the described procedure yields the same controllers with the respect to feedback characteristics as standard GPC. Special form of Kalman filters for for processes disturbed by noise which is used at the GPC design (white noise filtered by a transfer function ) is developed and combined with state feedback controller which is the solution of a time variant Riccaty type equation. This equation is obtained if the standard optimal state controller cost function is made equal to the GPC cost function by introducing time variant costing coefficients. It is shown that using the proposed procedure GPC for any costing and control horizon can be designed and that with respect to feedback properties GPC is equivalent to the optimal state controller with a special representation of the Kalman filter. This extends previous results showing that the linear quadratic Gaussian (LQG) control is a special case of the GPC. The same procedure is then applied to continuous time systems yielding the continuous time GPC controller. Various possibilities leading to integral and proportional - integral type of controllers are reviewed. The described procedure can be combined with continuous time identification procedure in adaptive control systems. Simulation results illustrate the proposed controller design procedure.