Optimal Control of Tandem Cold Rolling Using A Pointwise Linear Quadratic Technique With Trims

The tandem cold rolling of metal strip is a complex multivariable process whose control presents a significant engineering challenge because of the complex interaction between the process variables, the nonlinearities (which change with operating conditions), and the interstand time delays (which change significantly with the mill speed). The present technology generally relies on a control structure that has been successful in producing an acceptable output, but has limited capability for improvement in performance. This paper describes a new strategy for control of the mill that overcomes many limitations of the present controllers. The new strategy is based on a pointwise linear quadratic technique wherein a state-dependent algebraic Riccati equation is solved pointwise to establish a control law for a multiinput–multioutput controller, with appropriate trimming functions. For this application, the features of this novel strategy compare favorably to those of other techniques for control of nonlinear systems in the areas of simplicity of implementation, provision for the use of physical intuition in the design process, and strong robustness to disturbances and uncertainties. During simulations using the new controller coupled to a nonlinear model of the process, the tolerance in mill exit thickness was ∼0.2% for several rolling schedules using mild steel during operations at steady speed and during speed changes, and in the presence of typical disturbances with uncertainties in modeling and measurement. This offers the potential for improvement over present industrial controllers, which typically hold the tolerance in mill exit thickness to within 0.5–0.8%. In addition, excursions in the individual mill stand output thicknesses and interstand tensions are reduced, which contributes to the stability of the rolling process.