This paper presents the model of the heating furnace in continuous annealing processes for use in design of self-tuning control systems. A simplified mathematical model is derived from first principles. The model parameters are recursively estimated with an algorithm called recursive parameter estimation with a vector-type variable forgetting factor (REVVF). The REVVF algorithm was developed for such cases where some knowledge on parameter variability can be obtained beforehand. The control system of strip temperature presented here is hierarchical. The upper level is called "optimal preview control," which performs preset control. It previews the approaching setup change, which is the change of strip size or reference temperature, and optimizes the line speed and the strip temperature trajectory. Next, the lower level is called "temperature tracking control," which performs closed-loop control using the above trajectory as the control target. At this level, the generalized pole-placement self-tuning control was first employed; and later, the generalized predictive self-tuning control was introduced. These control methods were applied with some practical modifications and with the above mentioned REVVF. The control has been working successfully in several real plants.

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