Abstract—This paper discusses an industrial case study related to the topics mathematical modeling, state-parameter-disturbance estimation, optimal control of large-scale complex control systems and technical computing. The case study involves the copper electrowinning process, which is a part of the copper leaching plant at Glencore Nikkelverk, Kristiansand, Norway. Improved control of chemical compositions within the electrowinning process through an optimal control strategy is one of our objectives. We present a way to solve this particular control problem, and in principal, the same procedure can be adapted to handle any large-scale complex control problem. State-parameter-disturbance estimation is a sub-problem, and two state estimators --- a modified version of the Extended Kalman Filter (EKF) and the Moving Horizon Estimate (MHE) --- are used to reconstruct the system state using simulated input-output data. It is shown that the EKF fails to estimate one of the parameters unless the algorithm is modified by adding an instability term. The MHE offers promising results in estimating parameters as compared to the classical EKF. Furthermore, the MHE explicitly handle constraints, which is an advantage. We use Modelica (as a systematic and efficient modeling approach for large-scale systems), Python (as a free and powerful tool for technical computing), structural analysis and graph-theory as main ingredients in the development and this combination significantly ease the analysis and synthesis of large-scale control systems. In the essence, our aim is twofold: (1) to demonstrate a simple, but a useful procedure of automating large-scale complex (optimal) controller design and synthesis and parameter estimation using available analytical and free computer-aided tools; and (2) to highlight the need of developing interfaces between Modelica/Simscape or similar modeling standards with a powerful programming language for technical computing, for example Python/MATLAB.
Index Terms—Controllability and observability, large-scale control systems, state and parameter estimation, technical computing.
M. Anushka S. Perera, Carlos Fernando Pfeiffer are with the University College of Southeast Norway (e-mail: anushka_mrt@yahoo.com, anushka.perera@hit.no,carlos.pfeiffer@hit.no).
Tor Anders Hauge is with Glencore Nikkelverk, Kristiansand, Norway (e-mail: tor.hauge@glencore.no).
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Cite: M. Anushka S. Perera, Tor Anders Hauge, and Carlos Fernando Pfeiffer, "A Case Study: State Estimation and Optimal Control of an Industrial Copper Electrowinning Process," International Journal of Modeling and Optimization vol. 6, no. 5, pp. 277-288, 2016.
