Simple mass balance controllers for continuous sedimentation

• We propose 3 different PI controllers for a clarifier–thickener Unit.
• Convergence and stability in two cases are proved.
• Numerical examples, using suitable method for solving PDE and ODE, illustrate the dynamic behavior of the controlled unit under changes in input disturbances and in the set point.

The rational use of water in the mineral processing industry has become an important issue due to the geographical location of many plants. The increase of capacity in many copper concentrators has lead to an increased effort for recovering the maximum amount of water in the solid–liquid separation process. Thickeners work continuously to produce a concentrated underflow and a water overflow free from particulate matter. The behavior of many processes can be represented by a set of intensive and extensive variables. In this case, practice has shown that standard feedback control based on intensive variables has not been very easy to tune and effective in providing consistent operations. In many plants, thickeners operate with poor standards, with high dosages of flocculants, overflows with high fine particles contents and highly variable underflows. This work presents a novel nonlinear PI controller which is able to stabilize thickener operation using a simple control structure. An internationally accepted model and calibration using plant data is used to illustrate the design methodology and the level of performance attained by the controllers. The analysis of the results points out the improved performance by using extensive variables. In addition some guidelines concerning controllers tuning are also provided.