A simple model of a PID controller, controlling a valve refilling a leaky water tank.
In the scenario, at T=10 minutes, a faucet is opened for one minute, draining the tank. There's also a constant amount of leakage from the tank at all times.
The best way to play with the PID controller parameters is to click "Simulate", then click on the "map pin"-shaped icon on the simulation results, which will link the graphs to the model. Without closing the graphs, one can now drag the parameter sliders and see the graphs change.