A special case of proportional control is the ON-OFF control. If the gain K, is made very high, the valve will move from one extreme position to the other if the pen deviates only slightly from the set point. This very sensitive action is called on-off action because the valve is either fully open (on) or fully closed (off); i.e., the valve acts like a switch.
The bandwidth of an on-off controller is approximately zero.
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