H_∞ Preview Control for Discrete-Time Systems

A preview controller to be able to prepare a plant with the future information for external disturbances will guarantee better performance to suppress their effects. A design approach for the optimal $H∞$ preview controller in the discrete-time domain is given. The preview and feedback controller are simultaneously designed to minimize the worst case RMS value of the regulated variables when the bounded unknown disturbances and the previewable disturbances hit the dynamic plants. Thus, a state feedback controller and the related preview controller are derived in this design, even though problem formulation and solving an algebraic Riccati equation are based on the full-information $H∞$ controller design scheme. The performance of the proposed preview controller is simulated with a rolling stand of the tandem cold mill in the steel-making works. The objective of the control system for the rolling stand is to minimize thickness error of the exit strip and tension variation between stands simultaneously. The entry strip thickness to the stand and the roll gap variation are considered as previewable disturbances, since they can be measured and estimated. The future informations of these physical variables are utilized in the preview controller to suppress their effects on the exit strip thickness and the inter-stand tension. The simulation results shows that the $H∞$ preview controller is effective to satisfy the requirements for the thickness and the tension.