State-dependent Riccati equation approach for optimal control of a tandem cold metal rolling process

The tandem cold rolling of metal strip is a large multiinput-multioutput process that presents a difficult challenge to the control designer because of the following factors: 1) the complex interactions between the process variables; 2) the nonlinearities; and 3) the interstand time delays that change significantly with the mill speed. Control systems using the present technology have produced an acceptable product but are limited in their capability for improvement in performance and robustness, and therefore, there is a need for a better approach. It is considered that the state-dependent algebraic Riccati equation technique for the control of nonlinear systems that has been quite successful in the aerospace industry might fulfil this need. This paper presents the results of an initial work performed to investigate the theoretical and applied aspects of this technique for the control of the tandem cold rolling mill. In this paper, nonlinear state space equations are derived from a mathematical model of the mill, and a controller using the state-dependent Riccati equation approach (with trims) is developed. By simulation of typical operating conditions, the controller, when coupled to the model, is shown to be effective in reducing the effects of disturbances in entry strip thickness and hardness.