But I calculate a pulse width - how long the valve should be opened for in order to correct the error.
For a turbine deflector loop it might execute every 1s with a minimum pulse time of 50ms and a maximum pulse time of 1s.
For the weir control it might execute every 60s with a minimum pulse time of 300ms and a maximum pulse time of 20s, because the weir continues to move after the output is de-energized and the response of the water level over the weir depends on the area of the body of water behind the weir.
I set a gain that determines how long the output is energized (the pulse width) for a given magnitude error.
In my case the actuators are still discrete so the signal stays as a pulse train, it is not filtered up to be a continuous time signal.
[0]: https://www.google.ca/#tbm=isch&q=obermeyer+weir [1]: https://www.google.ca/#q=pelton+turbine+deflector&tbm=isch
They're everywhere - A/D are PWM, class D amps are PWM, power supplies...
[0] https://en.wikipedia.org/wiki/Pulse-width_modulation