Hybrid non-linear model predictive control of a run-of-mine ore grinding mill circuit

Abstract

A run-of-mine (ROM) ore milling circuit is primarily used to grind incoming ore containing precious metals to a powder fine enough to liberate the valuable minerals contained therein. The ground ore has a product particle size specification that is set by the downstream separation unit. A ROM ore milling circuit typically consists of a mill, sump and classifier (most commonly a hydrocyclone). These circuits are difficult to control because of unmeasurable process outputs, non-linearities, time delays, large unmeasured disturbances and complex models with modelling uncertainties. The ROM ore milling circuit should be controlled to meet the final product quality specification, but throughput should also be maximised. This further complicates ROM ore grinding mill circuit control, since an inverse non-linear relationship exists between the quality and throughput. ROM ore grinding mill circuit control is constantly evolving to find the best control method with peripheral tools to control the plant. Although many studies have been conducted, more are continually undertaken, since the controller designs are usually based on various assumptions and the required measurements in the grinding mill circuits are often unavailable.

To improve controller performance, many studies investigated the inclusion of additional manipulated variables (MVs) in the controller formulation to help control process disturbances, or to provide some form of functional control. Model predictive control (MPC) is considered one of the best advanced process control (APC) techniques and linear MPC controllers have been implemented on grinding mill circuits, while various other advanced controllers have been investigated and tested in simulation. Because of the complexity of grinding mill circuits non-linear MPC (NMPC) controllers have achieved better results in simulations where a wider operating region is required. In the search for additional MVs some researchers have considered including the discrete dynamics as part of the controller formulation instead of segregating them from the APC or base-layer controllers. The discrete dynamics are typically controlled using a layered approach. Discrete dynamics are on/off elements and in the case of a closed-loop grinding mill circuit the discrete elements can be on/off activation variables for feed conveyor belts to select which stockpile is used, selecting whether a secondary grinding stage should be active or not, and switching hydrocyclones in a hydrocyclone cluster. Discrete dynamics are added directly to the APC controllers by using hybrid model predictive control (HMPC). HMPC controllers have been designed for grinding mill circuits, but none of them has considered the switching of hydrocyclones as an additional MV and they only include linear dynamics for the continuous elements. This study addresses this gap by implementing a hybrid NMPC (HNMPC) controller that can switch the hydrocyclones in a cluster.

A commonly used continuous-time grinding mill circuit model with one hydrocyclone is adapted to contain a cluster of hydrocyclones, resulting in a hybrid model. The model parameters are refitted to ensure that the initial design steady-state conditions for the model are still valid with the cluster. The novel contribution of this research is the design of a HNMPC controller using a cluster of hydrocyclones as an additional MV. The HNMPC controller is formulated using the complete nonlinear hybrid model and a genetic algorithm (GA) as the solver. An NMPC controller is also designed and implemented as the base case controller in order to evaluate the HNMPC controller’s performance. To further illustrate the functional control benefits of including the hydrocyclone cluster as an MV, a linear optimisation objective was added to the HNMPC to increase the grinding circuit throughput, while maintaining the quality specification. The results show that the HNMPC controller outperforms the NMPC one in terms of setpoint tracking, disturbance rejection, and process optimisation objectives. The GA is shown to be a good solver for HNMPC, resulting in a robust controller that can still control the plant even when state noise is added to the simulation.