Most physical processes sought to be controlled through modeling require a fast solution to a set of manipulated variables based upon a measured condition. The variables are frequently interdependent, and are subject to a constraint set that defines physical limitations of the physical actuators. Implementation of a desired control move therefore requires a fast solution that does not violate the constraints. Because of the complexities of the large number of constrained and potentially interdependent variables, typical optimal solutions to implement a control move are too computationally expensive.
These problems are encountered, for example, in the model predictive control of sheet and film processes. Sheet and film processes are prevalent in the chemical and pulp and paper industries, and include paper coating, polymer film extrusion, and papermaking. In this process, a sheet or film is moved via a web and is processed as it moves. The multivariable control of sheet and film processes is challenging due to their large dimensionality, model inaccuracies, and actuator limitations. On-line computation time for the control algorithm is limited by the scale and speed of the processes. This additional limitation has yet to be solved by the ever increasing processing speeds achieved by control hardware. Uncertainty is introduced into the model by low signal-to-noise ratios, sideways movement of the web, and imprecise actuator movements. An additional difficulty is the need to avoid excessive actuator movements that may compromise the integrity of the sheet/film and the actuating mechanism.
Conventional industrial control algorithms for sheet and film processes are kept relatively simple to handle the process dimensionality within the computational constraints. The simplicity is often achieved by choosing a sampling time for the control algorithm that is 100-1000 times longer than the time between individual sensor readings. An alternative or additional simplification strategy is the grouping of sensors into sensor blocks to reduce dimensionality. Model inaccuracies are addressed through excessive detuning. This simplicity results in reduced product quality and a loss of flexibility.
Some additional methods have been proposed for designing controllers for sheet and film processes which are robust to model inaccuracies but do not directly address actuator limitations. Other approaches have been proposed that directly address actuator limitations, but do not directly address model inaccuracies. Either of these approaches require significant computation for implementation on large scale machines rendering them inefficient or impractical to implement with much existing control hardware.
An improved control method was recently proposed by the inventors which: (i) directly addresses actuator limitations, (ii) has minimal on-line computational requirements, and (iii) has a controller structure proven to be robust to model inaccuracies. R. D. Braatz and J. G. VanAntwerp, "Model Predictive Control of Large Scale Processes", In AIChE Spring National Meeting, New Orleans, La., Feb. 27, 1996, Paper 81c; R. D. Braatz and J. G. VanAntwerp, "Advanced Cross-Directional Control", Control Systems '96Preprints, pp 15-18, Halifax, Nova Scotia, Canada, April 30-May 2, 1996. However, the method was only applicable to sheet and film processes in which all manipulated variable directions are controllable and the dynamics are adequately described by a pure time delay. These assumptions do not always hold in practice.
Thus, there is a need for an improved model predictive control process which addresses problems encountered in previous processes. It is an object of the invention to provide such an improved process. The improved process of the invention uses an ellipsoid constraint set approximation as part of an improved high speed control solution implementation.