Nonlinear H-Infinity Control for Optimizing Cement Production

Abstract

Nonlinear H-infinity control is developed aiming at optimizing the functioning of cement mills. The dynamic model of a cement mill is difficult to control due to its high nonlinearity and its multivariable structure. For this reason several control methods have been proven to be little efficient (e.g. MPC or NMPC). The cement mill's dynamic model is subjected to approximate linearization around a temporary operating point which is recomputed at each iteration of the control algorithm. This operating point is defined by the present value of the system's state vector and by the last value of the control inputs vector that was applied on the cement's mill model. With the use of Taylor series expansion and the computation of the associated Jacobian matrices, linearization of the cement mill's model is accomplished. The robustness of the control method compensates for the modelling error which is due to the truncation of higherorder terms in this Taylor series expansion. Next, an H-infinity feedback controller is designed for the approximately linearized model of the cement mill. To compute the controller's feedback gain an algebraic Riccati equation is solved at each step of the control algorithm. Lyapunov analysis is used to prove the stability of the control scheme. First, it is demonstrated that the control loop satisfies the H-infinity tracking performance criterion which assures for robustness against model uncertainty and external perturbations. Additionally, conditions for the global asymptotic stability of this control scheme are provided. Finally, the H-infinity Kalman Filter is used as a robust state estimator thus allowing to implement sensorless control for the cement mill's model.