This is a simple example of a first-principles model for simulation and control. This is a ONE state differential equation model. I've included the experimental results with the files.
We used this example as a teaching aide for Tom Edgar's control course at the University of Texas at Austin. We used a PID controller and nonlinear MPC (model predictive control) to show the difference in control performance and to review tuning correlations. The PID controller was difficult to tune because of the relatively long process time constant. Nonlinear MPC was outstanding because of the excellent predictive capability of the model.
The gravity drained water tank has a level that is controlled by a valve on the inlet stream. The tank is open to the atmosphere and continuously drains through a short outlet pipe.
More details on this example can be found at:
Download additional MATLAB nonlinear models and documentation from the Nonlinear Model Database: