Transient uniformity model predictive control in dealing with non-uniformity of multivariable systems

In this article, the model predictive control scheme is studied for a class of multiple-input multiple-output linear systems with different transient trajectories among the outputs. To eliminate the transient errors among the outputs, a modified model predictive control scheme is designed making one output track following the reference while the other outputs track following this output instead of the reference. Utilizing the specified output as the alternative reference for all the other outputs, a constructive model predictive control scheme is developed to diminish the differences of the transient-state trajectories among each output such that both the uniformity of the transient-state trajectories and the optimal steady-state trajectories are achieved. The effectiveness of the proposed transient uniformity model predictive control scheme is demonstrated in the experiment of the semiconductor wafer manufacturing baking process. The experimental results show that the transient uniformity model predictive control scheme has successfully reduced the integral square error of transient-state uniformity between any two outputs by 90% as compared to the conventional model predictive control scheme. The robustness of the proposed scheme has also been experimentally evaluated in the presence of external disturbance and plant modeling inaccuracy.