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A non-linear first principle model of an industrial methane rich gas (MRG) network for a large petrochemical plant is developed in this paper. The model is validated against industrial plant data. The non-linearity of gas compressibility, which is sensitive to changes in pressure, composition and temperature, is a challenge for the control of such a network. This model addresses these non-linearities, and is validated with industrial plant data. Each subsystem in the network is modelled separately, and includes models for the pipe segments, gas compressibility, pipe friction factor and gas viscosity. A first principle non-linear model of the system will assist the design of supervisory and optimisation controllers which remain relevant over a large operating region.

The states and unknown parameters of a non-linear model of a grinding mill circuit are shown to be identifiable from manipulated, controlled and measurable variables. All the states in the mill and sump, the breakage rates in the mill, the mill and cyclone parameters and the mill power draw parameters can be algebraically expressed in terms of known variables. Theoretically, the tiered approach to estimate all states and parameters enables model-fitting without the need for unnecessary assumptions regarding model parameters. The analysis shows the necessity of accurate density and flow-rate measurements across the circuit, and especially the cyclone, to estimate all states and parameters. The aim is to enable non-linear model-based control through model characterisation using available real-time plant measurements.

A dynamic non-linear model was fitted to the grind curve data of an industrial semi-autogenous grinding (SAG) mill by means of a step-wise procedure. Grind curves give the steady-state values of the performance variables throughput, power draw, and grind in terms of the mill filling and critical mill speed. The grind curves indicate the operable region of the grinding mill. An analysis and dynamic simulation of the model show that the model captures the main dynamics of the grinding mill. Further simulations demonstrate that the model represents the full range of steady-state conditions defined by the grind curves. In other words, the dynamic model is quantitatively accurate as it settles at the correct steady-state for the operable region of the grinding mill. Therefore, the model is suitable as a simulator to test and develop optimizing control strategies for global operating conditions rather than only for local operating conditions.

A commonly used continuous grinding mill circuit model is expanded to a hybrid model which contains both continuous and discrete dynamics. The discrete dynamics in the grinding mill circuit are as a result of switching individual cyclones in a cluster of cyclones. With the additional discrete dynamics an investigation was conducted to establish whether the switching of cyclones can be used as an additional manipulated variable. A nonlinear model predictive controller was implemented using the hybrid grinding mill model. Through simulations it is shown that the switching of cyclones can be used to extend the range of control for the product particle size. When applying a substantial disturbance it was found that certain setpoints could not be reached by the NMPC controller, however by switching in an additional cyclone the particle size setpoint could be reached. Simulation results are given to show that the discrete switching of hydrocyclones can be considered as a manipulated variable for hybrid model based controllers to achieve additional controller benefits.

This paper presents the design and application of fractional single-input–single-output (SISO) controllers to a grinding mill circuit, which is a multiple-input–multiple-output (MIMO) process. Two kinds of controllers are presented: fractional order proportional-integral (FOPI) controllers, and a combination of FOPI and fractional order model reference adaptive controllers (FOMRAC). The parameters of the controller are tuned using off-line particle swarm optimization. In the presence of disturbances and process noise, the SISO fractional controllers achieve similar or better performance compared to linear model predictive control (LMPC).

A novel suboptimal control technique for output tracking was developed using model predictive static programming (MPSP). The control technique was applied to a nonlinear model of a single-stage closed grinding mill circuit in simulation. The control technique could determine a suboptimal input trajectory to maintain the output variables at their desired values within 7 iterations. The input trajectory determined after only 2 iterations was already close to the final solution. This technique shows promise to significantly reduce computational time to find a suboptimal input trajectory for output tracking in large industrial processes.

The states and unknown parameters of a simplified non-linear grinding mill circuit model for process control was estimated from real plant data by means of an Extended Kalman Filter. The output of the model as calculated from the states and parameters estimated by the Extended Kalman Filter closely follow the actual output of the plant. The continuous estimate of states and parameters from plant data allows for the continuous update of a process model used for process control. This limits model-plant mismatch which deteriorates controller performance.

A nonlinear phenomenological model of a grinding mill is used to determine five run-of-mine (ROM) grinding milling circuit parameters. The five parameters are fraction of fines and fraction of rocks in the ore fed to the mill, rock and steel abrasion factor and power needed for a ton of fines produced. The model is analyzed according to an identifiability procedure to identify the system data needed to calculate the parameter values. It is shown that a minimum of 18 measurements for a single-stage closed circuit and a minimum of 16 measurements for a single-stage open circuit are needed to determine the five milling circuit parameters. For the closed circuit, the time signals of 8 quantities in the mill will be sufficient to determine all five parameters since the other 10 measurements are time derivatives of these signals. The measurements require the holdup quantities of states within the mill. Since these measurements are not readily available in real-time at plants, it may be difficult to estimate the parameters on-line.