Nonlinear H-infinity control for optimization of the functioning of mining products mills

Abstract

Control of the milling process of mining products (ore milling) is a non-trivial problem due to being related with a strongly nonlinear and multivariable state-space model. To provide an efficient solution to this problem, in this article a nonlinear optimal (H-infinity) control method is developed. In the considered nonlinear optimal control method, the dynamic model of the mining products' mill undergoes first approximate linearization with the use of Taylor series expansion and with the computation of the associated Jacobian matrices. The linearization point (temporary equilibrium) is recomputed at each time step of the control method and comprises the present value of the system's state vector and the last value of the control inputs' vector that was exerted on it. For the linearized description of the mill's functioning the optimal control problem is solved by applying an H-infinity controller. The feedback gain is computed again at each iteration of the control algorithm through the solution of an algebraic Riccati equation. The stability of the control scheme is confirmed through Lyapunov analysis. First, it is shown that the control method satisfies the H-infinity tracking performance, and this signifies elevated robustness against model uncertainty and external perturbations. Next, under moderate conditions, it is proven that the control loop is globally asymptotically stable.