Robust optimal receding horizon control

• Main Author: Bell, Margaret
• Published: Imperial College London 1997
• Subjects: 629.8
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505917

Receding horizon optimal control has a long history and provides the basis for several of the currently popular techniques for model predictive control of chemical processes. Based on a prediction of the current state of the process, derived from plant measurements, and predictions of the likely input conditions over a certain period ahead (the time horizon), optimal controls are computed to maximise a given "performance function", which can be either an economic or technical measure of performance. The state predictions are regularly updated as new measurements are made and the controls are re-computed if either the current state or the predicted input conditions change significantly. An important advantage of computing optimal controls is that this can take direct account of process operating constraints. However, general inequality constraints have always posed a difficult problem in numerical optimal control algorithms and we propose a new algorithm for dealing with this problem for systems described by DAEs of any index. Due to both the excessive time required for model development and the excessive computational time required for a full model, the on-line model is generally of a much lower complexity than the true system and although parameters in the model may be re-estimated using plant measurements, there is inevitably some uncertainty in the model predictions as well as in the input predictions. The controls must therefore be robust, giving reasonable performance in the face of variations of actual conditions from the predictions. To obtain a sufficiently simple controller, the H∞ approach has been to design a controller to perform optimally if the worst possible set of inputs and model predictions actually occur, and this can also be applied within the receding horizon optimal control framework. The result is a game, with the controls playing against the uncertain inputs and model parameters. However, this does not guarantee robustness in the presence of inequality constraints and here we propose a new simple technique for dealing with this problem, which exploits the sampling interval of the receding horizon formulation of the problem.