ThreeP controller application laid down here is able to hold water level within say 1cm steady state regardless of the set point. The initial tuning are deliberately left deficient.
To achieve 1cm accuracy the deadband μ needs to be somewhere at around 1-2cm (0.01-0.02m). The hysteresis λ shoud be at a level of magnitude 1-2mm (0.001-0.002). The gain G should be at the same level of magnitude as the deadband. It is a good practice to leave it always a bit larger than the deadband. The time constant T that best fits this application is somewhere around 2 seconds.
The above tuning can be further refined by experimenting. ThreeP behavior can be easily followed through the trends below the kanta.
The following two videos are shot while I was tuning it myself.