Here we consider a P-only controller, since offset is less important than minimizing manipulated variable movement. The question is:
What value of the proportional gain should be used?
It seems reasonable to select a value for the proportional gain that will just assure that constraints will not be violated for the worst-case expected disturbance. Assume that level alarms are set at 20% and 80% of the volume of the vessel. Let ΔH represent the magnitude of the maximum allowable deviation of the tank height from setpoint, and let ΔL represent the maximum magnitude of a step disturbance.
Assuming that the flow rate out is proportional to the deviation from setpoint,
where kc is a negative ...