Double Tank Level Control

A double tank is an example of a switching system where the input to the upper tank can be one of two flows. The upper tank drains to the lower tank and the lower tank drains to a reservoir. The flow to the upper tank is the manipulated variable to meet a lower tank target level. A higher upper tank level leads to a higher flowrate into the lower tank. The dynamics of the two levels are described by two differential equations.
The set point is 3. The two states x are the fluid levels in the upper and a lower tank. The flow into the upper tank is either 1 or 2, the upper tank flows into the lower tank, and the lower tank flow exits the system. The objective of the optimal control problem is for the lower tank to reach the setpoint during the optimization window of 10 minutes.
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