Coating refers to the covering of a solid with a uniform layer of liquid. Of special industrial interest is the cross-directional control of coating processes, where the cross-direction refers to the direction perpendicular to the substrate movement. The objective of the controller is to maintain a uniform coating under unmeasured process disturbances.
Assumptions that are relevant to coating processes found in industry are used to develop a model for control design. We show how to identify the model from input-output data. This model is used to derive a model predictive controller to maintain flat profiles of coating across the substrate by varying the liquid flows along the cross direction.
The model predictive controller computes the control action which minimizes the predicted deviation in cross-directional uniformity. The predictor combines the estimate obtained from the model with the measurement of the cross-directional uniformity to obtain a prediction for the next time step. A filter is used to obtain robustness to model error and insensitivity to measurement noise. The tuning of the noise filter and different methods for handling actuator constraints are studied in detail. The three different constraint-handling methods studied are: the weighting of actuator movements in the objective function, explicitly adding constraints to the control algorithm, i.e. constrained model predictive control, and scaling infeasible control actions calculated from an unconstrained control law to be feasible.
Actuator constraints, measurement noise, model uncertainty, and the plant condition number are investigated to determine which of these limit the achievable closed loop performance. From knowledge of how these limitations affect the performance we find how the plant could be modified to improve the process uniformity. Also, because identification of model parameters is time-consuming and costly, we study how accurate the identification must be to achieve a given level of performance.
The theory developed throughout the paper is rigorously verified though simulations and experiments on a pilot plant. The effect of interactions on the closed loop performance is shown to be negligible for this pilot plant. The measurement noise and the actuator constraints are shown to have the largest effect on closed loop performance
