M.Phil. (Engineering Management) / Please refer to full text to view abstract

This thesis presents a robust nonlinear model predictive controller (RNMPC), nominal nonlinear model predictive controller (NMPC) and single-loop proportional-integral-derivative (PID) controllers that are applied to a nonlinear model of a run-of-mine (ROM) ore milling circuit. The model consists of nonlinear modules for the individual process units of the milling circuit (such as the mill, sump and cyclone), which allow arbitrary milling circuit configurations to be modelled easily. This study aims to cast a complex problem of a ROM ore milling circuit into an RNMPC framework without losing the flexibility of the modularised nonlinear model and implement the RNMPC using open-source software modules. The three controllers are compared in a simulations study to determine the performance of the controllers subject to severe disturbances and model parameter variations. The disturbances include changes to the feed ore hardness, changes in the feed ore size distributions and spillage water being added to the sump. The simulations show that the RNMPC and NMPC perform better than the PID controllers with regard to the economic objectives, assuming full-state feedback is available, especially when actuator constraints become active. The execution time of the RNMPC, however, is much too long for real-time implementation and would require further research to improve the efficiency of the implementation. / Thesis (PhD)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

A run-of-mine ore milling circuit is primarily used to grind incoming ore containing precious metals to a particle size smaller than a specification size. A traditional run-of-mine (ROM) ore single-stage closed milling circuit comprises of the operational units: mill, sump and cyclone. These circuits are difficult to control because of significant nonlinearities, large time delays, large unmeasured disturbances, process variables that are difficult to measure and modelling uncertainties. A nonlinear model predictive controller with state estimation could yield good control of the ROM ore milling circuit despite these difficulties. Additionally, the ROM ore milling circuit is an energy intensive unit and a controller or power optimizer could bring significant cost savings. A nonlinear model predictive controller requires good state estimates and therefore a neural network for state estimation as an alternative to the particle filter has been addressed. The neural network approach requires fewer process variables that need to be measured compared to the particle filter. A neural network is trained with three disturbance parameters and used to estimate the internal states of the mill, and the results are compared with those of the particle filter implementation. The neural network approach performed better than the particle filter approach when estimating the volume of steel balls and rocks within the mill. A novel combined neural network and particle filter state estimator is presented to improve the estimation of the neural network approach for the estimation of volume of fines, solids and water within the mill. The estimation performance of the combined approach is promising when the disturbance magnitude used is smaller than that used to train the neural network. After state estimation was addressed, this work targets the implementation of a nonlinear controller combined with full state estimation for a grinding mill circuit. The nonlinear controller consists of a suboptimal nonlinear model predictive controller coupled with a dynamic inversion controller. This allows for fast control that is asymptotically stable. The nonlinear controller aims to reconcile the opposing objectives of high throughput and high product quality. The state estimator comprises of a particle filter for five mill states as well as an additional estimator for three sump states. Simulation results show that control objectives can be achieved despite the presence of noise and significant disturbances. The cost of energy has increased significantly in recent years. This increase in price greatly affects the mineral processing industry because of the large energy demands. A run-of-mine ore milling circuit provides a suitable case study where the power consumed by a mill is in the order of 2 MW. An attempt has been made to reduce the energy consumed by the mill in the two ways: firstly, within the nonlinear model predictive control in a single-stage circuit configuration and secondly, running multiple mills in parallel and attempting to save energy while still maintaining an overall high quality and good quantity. A formulation for power optimization of multiple ROM ore milling circuits has been developed. A first base case consisted not taking power into account in a single ROM ore milling circuit and a second base case split the load and throughput equally between two parallel milling circuits. In both cases, energy can be saved using the NMPC compared to the base cases presented without significant sacrifice in product quality or quantity. The work presented covers three topics that has yet to be addressed within the literature: a neural network for mill state estimation, a nonlinear controller with state estimation integrated for a ROM ore milling circuit and power optimization of a single and multiple ROM ore milling circuit configuration. / Dissertation (MEng)--University of Pretoria, 2015. / Electrical, Electronic and Computer Engineering / Unrestricted

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 Engineering / unrestricted

In South Africa, where 75% of the worlds platinum is produced, electricity tariffs have increased significantly over recent years. This introduces challenges to the energy intensive mineral processing industry. Within the mineral processing chain, run-of-mine ore milling circuits are the most energy-intensive unit processes. Opportunities to reduce the operating costs associated with power consumption through process control are explored in this work. In order to reduce operating costs, demand side management was implemented on a milling circuit using load shifting. Time-of-use tariffs were exploited by shifting power consumption of the milling circuit from more expensive to cheaper tariff periods in order to reduce overall costs associated with electricity consumption. Reduced throughput during high tariff periods was recovered during low tariff periods in order to maintain milling circuit throughput over a week long horizon. In order to implement and evaluate demand side management through process control, a load shifting controller was developed for the non-linear Hulbert model. Implementation of the load shifting controller was achieved through a multi-layered control approach. A regulatory linear MPC controller was developed to address technical control requirements such as milling circuit stability. A supervisory real-time optimizer was developed to meet economic control requirements such as reducing electricity costs while maintaining throughput. Scenarios, designed to evaluate the sensitivities of the load shifting controller, showed interesting results. Mill power set-point optimization was found to be proportionally related to the mineral price. Set-points were not sensitive to absolute electricity costs but rather to the relationships between peak, standard, and off-peak electricity costs. The load shifting controller was most effective at controlling the milling circuit where weekly throughput was between approximately 90% and 100% of the maximum throughput capacity. From an economic point of view, it is shown that for milling circuits that are not throughput constrained, load shifting can reduce operating costs associated with electricity consumption. Simulations performed indicate that realizable cost savings are between R16.51 and R20.78 per gram of unrefined platinum processed by the milling circuit. This amounts to a potential annual cost saving of up to R1.89 m for a milling circuit that processes 90 t/h at a head grade of 3 g/t. / Dissertation (MEng)--University of Pretoria, 2015. / Electrical, Electronic and Computer Engineering / Unrestricted

Run-of-mine ore milling circuits are generally difficult to control owing to the presence of strong external disturbances, poor process models and the unavailability of important process variable measurements. These shortcomings are common for processes in the mineral-processing industry. For processes that fall into this class, the peripheral control tools in the control loop are considered to be as important as the controller itself. This work addresses the implementation of peripheral control tools on a run-of-mine ore milling circuit to help overcome the deteriorated control performance resulting from the aforementioned shortcomings. The effects of strong external disturbances are suppressed through the application of a disturbance observer. A fractional order disturbance observer is also implemented and a novel Bode ideal cutoff disturbance observer is introduced. The issue of poor process models is addressed through the detection of significant mismatch between the actual plant and the available model from process data. A closed-form expression is given for the case where the controller has a transfer function. If the controller does not have a transfer function, a partial correlation analysis is used to detect the transfer function elements in the model transfer function matrix that contain significant mismatch. The mill states and important mill parameters are estimated with the use of particle filters. Simultaneous state and parameter estimation is compared with a novel dual particle filtering scheme. A sensitivity analysis shows the class of systems for which dual estimation would provide superiorestimation accuracy over simultaneous estimation. The implemented peripheral control tools show promise for current milling circuits where proportional-integral-derivative (PID) control is prevalent, and also for advanced control strategies, such as model predictive control, which are expected to become more common in the future. AFRIKAANS : Maalkringe wat onbehandelde erts maal is oor die algemeen moeilik om te beheer as gevolg van die teenwoordigheid van sterk eksterne steurings, onakkurate aanlegmodelle en metings van belangrike prosesveranderlikes wat ontbreek. Hierdie probleme is algemeen vir aanlegte in die mineraalprosesseringsbedryf. Vir aanlegte in hierdie klas word die randbeheerinstrumente as net so belangrik as die beheerder beskou. Hierdie verhandeling beskryf die implementering van randbeheerinstrumente vir ’n maalkring wat onbehandelde erts maal, om die verswakte beheerverrigting teen te werk wat veroorsaak word deur bogenoemde probleme. Die impak van sterk eksterne steurings word teengewerk deur die implementering van ’n steuringsafskatter. ’n Breuk-orde-steuringsafskatter is ook geïmplementeer en ’n nuwe Bode ideale afsnysteuringsafskatter word voorgestel. Die kwessie van onakkurate aanlegmodelle word hanteer deur van die aanlegdata af vas te stel of daar ’n verskil is tussen die aanleg en die beskikbare model van die aanleg. ’n Uitdrukking word gegee vir hierdie verskil vir die geval waar die beheerder met ’n oordragsfunksie voorgestel kan word. Indien die beheerder nie ’n oordragsfunksie het nie, word van ‘n parsiële korrelasie-analise gebruik gemaak om die element, of elemente, in die aanleg se oordragsfunksiematriks te identifiseer wat van die werklike aanleg verskil. Die toestande en belangrike parameters in die meul word beraam deur van partikel-filters gebruikte maak. Gelyktydige toestand- en parameter-beraming word vergelyk met ’n nuwe dubbel-partikelfilter skema. ’n Sensitiwiteitsanalise wys die klas van stelsels waarvoor dubbel-afskatting meer akkurate waardes sal gee as gelyktydige afskatting. Die voorgestelde randbeheerinstrumente is toepaslik vir huidige maalkringe waar PID-beheer algemeen is, asook vir gevorderde beheerstrategieë, soos model-voorspellende beheer, wat na verwagting in die toekoms meer algemeen sal word. Copyright / Dissertation (MEng)--University of Pretoria, 2012. / Electrical, Electronic and Computer Engineering / unrestricted