Non‐linear optimal control for the hot‐steel rolling mill system

Abstract

Control of hot‐steel rolling mills aims at raising the levels of quality of the related industrial production and at minimising the cost of the electric energy consumed by such industrial units. This paper proposes a non‐linear optimal control approach for the hot‐steel rolling mill system. The non‐linear dynamic model of the hot‐steel rolling mill undergoes approximate linearisation around a temporary operating point which is recomputed at each iteration of the control method. The linearisation relies on Taylor series expansion and on the calculation of the system's Jacobian matrices. For the approximately linearised model of the hot‐steel rolling process, an H‐infinity feedback controller is designed. This controller provides the solution of the non‐linear optimal control problem for the system under model uncertainty and external perturbations. For the computation of the controller's feedback gain, an algebraic Riccati equation is iteratively solved at each time‐step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation‐based control for this system, the H‐infinity Kalman filter is proposed as a robust state estimator.