Gaussian process based model predictive control to address uncertain milling circuit dynamics

Model predictive control performance rests heavily on the accuracy of the available plant model. To address (possibly) time-variant model uncertainty, a nominal nonlinear state-space model is combined with an additive residual model that takes the form of a Gaussian process. With sufficient operational data the Gaussian process model is able to effectively describe the residual model error and reduce the overall prediction error for effective model predictive control. The efficacy of the method is illustrated using a milling circuit simulator.https://www.journals.elsevier.com/ifac-papersonlineam2022Electrical, Electronic and Computer Engineerin

An EKF observer to estimate semi-autogenous grinding mill hold-ups

A non-linear observer model of a semi-autogenous grinding mill is developed. The observer model distinguishes between the volumetric hold-up of water, solids, and the grinding media in the mill. Solids refer to all ore small enough to discharge through the end-discharge grate, and grinding media refers to the rocks and steel balls. The rocks are all ore too large to discharge from the mill. The observer model uses the accumulation rate of solids and the mill’s discharge rate as parameters. It is shown that with mill discharge flow-rate, discharge density, and volumetric hold-up measurements, the model states and parameters are linearly observable. Although instrumentation at the mill discharge is not yet included in industrial circuits because of space restrictions, this study motivates the benefits to be gained from including such instrumentation. An extended Kalman filter is applied in simulation to estimate the model states and parameters from data generated by a semi-autogenous mill simulation model from literature. Results indicate that if sufficiently accurate measurements are available, especially at the discharge of the mill, it is possible to reliably estimate grinding media, solids and water hold-ups within the mill. Such an observer can be used as part of an advanced process control strategy.The first author gratefully appreciates support from the University of Pretoria postgraduate study abroad bursary programme. The second author gratefully acknowledges financial support provided by the Austrian Academy of Sciences in the form of an APART-fellowship at the Automation and Control Institute of Vienna University of Technology. The third author gratefully acknowledges financial support provided by the Austrian Federal Ministry of Science, Research and Economy, and the National Foundation for Research, Technology and Development. The fourth author would like to acknowledge the support of the National Research Foundation of South Africa (Grant No.90533).http://www.elsevier.com/locate/jprocont2018-03-31hb2017Electrical, Electronic and Computer Engineerin

Simplified grinding mill circuit models for use in process control

A grinding mill circuit forms a crucial part in the energy-intensive comminution process of extracting valuable metals and minerals from mined ore. The ability to control the grinding mill circuit is of primary importance to achieve the desired product specification with regards to quality and production rate. In order to achieve control objectives an accurate dynamic model of the milling circuit is required. Phenomenological models are preferred over linear-time-invariant models since the latter cannot describe the non-linear behaviour of the process. However, the available phenomenological models of grinding mill circuits are usually complex, use large parameter sets and are mostly aimed towards steady-state design of grinding mill circuits. This study investigates simplified non-linear dynamic models of grinding mill circuits suitable for process controller design. In the first part of this study, the number of size classes in a cumulative rates model of a grinding mill circuit is reduced to determine the minimum number required to provide a reasonably accurate model of the circuit for process control. Each reduced size class set is used to create a non-linear cumulative rates model which is linearized to design a linear model predictive controller. The accuracy of a model is determined by the ability of the corresponding model predictive controller to control important process variables in the grinding mill circuit as represented by the full non-linear cumulative rates model. The second part of the study validates a simple and novel non-linear model of a run-of-mine grinding mill circuit developed for process control and estimation purposes. This model is named the Hulbert-model and makes use of the minimum number of states and parameters necessary to produce responses that are qualitatively accurate. It consists of separate feeder, mill, sump and hydrocyclone modules that can be connected to model different circuit configurations. The model uses five states: rocks, solids, fines, water and steel balls. Rocks are defined as too large to be discharged from the mill, whereas solids, defined as particles small enough to leave the mill, consist of out-of-specification coarse ore and in-specification fine ore fractions. The model incorporates a unique prediction of the rheology of the slurry within the mill. A new hydrocyclone model is also presented. The Hulbert-model parameters are fitted to an existing plant’s sampling campaign data and a step-wise procedure is given to fit the model to steady-state data. Simulation test results of the model are compared to sampling campaign data of the same plant at different steady-state conditions.Dissertation (MEng)--University of Pretoria, 2012.Electrical, Electronic and Computer Engineeringunrestricte

Robust global state feedback stabilization of cement mills

peer reviewedPlugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust controller can be designed in order to fully prevent the mill from pluggin