## Introduction

In control theory, an on/off controller, also known as a hysteresis controller, is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a furnace that is either completely on or completely off.

For example, a thermostat is a simple negative-feedback control: when the temperature (the “process variable” or PV) goes below a set point (SP), the heater is switched on. Another example could be a pressure switch on an air compressor: when the pressure (PV) drops below the threshold (SP), the pump is powered. Refrigerators and vacuum pumps contain similar mechanisms

## Theory of on/off controller

Let us consider a level control system.

The valve in the inflow line to the system is an electrically operated solenoid valve. (Remember an electrically operated solenoid valve has only two operating positions . fully open or fully closed.) Assume that under initial conditions with a demand on the system the level will start to fall and V1 will have to be opened to provide an inflow. This can easily be achieved by mounting a differential pressure switch, P1 at the bottom of the tank to operate when the level falls to L1. When the level is at L1 the liquid will be height h1 above switch. The pressure at the switch will be P1 = ρgh1.

ρ. The mass density of the liquid

g. The acceleration due to gravity

h1. The height of the liquid

The resulting switch closure can energize the solenoid valve V1 causing an inflow to the tank. Assuming the valve is correctly sized, this will cause a rise in the level back towards the setpoint. In order to arrest the rise in level the built in differential feature of the switch can be employed to de-energize the solenoid valve when level L2 is reached. This system will achieve a mean level in the tank about the desired setpoint. This method is known as ON/OFF control. Clearly it is impossible to maintain the system at the setpoint since there must be a difference in the operating levels L1 and L2 as the valve can only be energized or de-energized. It is often counterproductive to try to reduce the differential between L1 and L2 to too small a value as this will result in excessive cycling, and hence wear, of the valve.

Summary

• On/off control – control signal is either 0% or 100%
• Control at setpoint not achievable, a dead band must be incorporated.
• Useful for large, sluggish systems particularly those incorporating electric heaters.

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