Modelling and control of a sedimentation column

In this experiment, we control the turbidity in a sedimentation column. To this end, we model the turbidity dynamic of a fixed point of the sedimentation column. We consider a nonlinear model that contains two different dynamics: the one given by the sedimentation phenomena and the one given by the actuator. We consider the inflow as an actuator and the outflow as a perturbation (and vice versa). The inflow is a mixture of water and calcium with an unknown calcium concentration. Similarly, the outflow is a mixture of water and calcium with a higher calcium concentration (because of sedimentation phenomena). The outflow calcium concentration is also not known. The only measurement is the turbidity (related to the calcium concentration) of a fixed point of the column. The sensor is located between the inflow and the top of the column.

We show the closed-loop stability between the nonlinear model and a Proportional Integral (PI) controller. In this process, one can keep a desired set point of turbidity while the water is recovery by an overflow of the sedimentation column. In the figures, we show three different levels of turbidity. The figure at the left shows a low level of turbidity, in which we are even able to see the inlet pipe. In the other two cases, we can obtain a bigger overflow (more water recovered), but with a higher level of turbidity. I let you attached the slides related to this project.

References

1. Toledo-Zucco, J.P., Sbarbaro, D., & Gomes da Silva Jr., J.M. (2024). Turbidity control in sedimentation columns by direction-dependent models. IEEE Transactions on Control Systems Technology. Link, arXiv.

2. Toledo-Zucco, J-P., & Sbarbaro, D. (2018). Tuning discrete PI controllers for direction-dependent systems with delay. IFAC Workshop on Linear Parameter Varying Systems (LPVS). Florianópolis, Brazil, September 2018. Link.