Suppose a process operator has the task of holding the temperature, T, near the desired temperature, Td, while making sure the tank doesn’t overflow or the level get too low. The question is how the operator would cope with this task over a period of time. He or she would manually adjust the hot water inlet valve (HV-1) to maintain the temperature and occasionally adjust the outlet valve (HV-2) to maintain the correct level in the tank.
The operator would face several problems, however. Both indicators would have to be within the operator’s view, and the manual valves would have to be close to the operator and easy to adjust.
To make the operator’s work easier, suppose we installed electrically operated solenoid valves in place of the manual valves, as shown in the next figure. We can also install two hand switches (HS-1 and HS-2) so the solenoid valves can be operated from a common location. The valves can assume two states, either fully open (on) or fully closed (off). This type of control is called two-position or on/off control.
Assume for the moment that the level is holding steady and that the main concern is controlling temperature. The operator has been told to keep the temperature of the fluid in the tank at 100°F. He compares the reading of the temperature indicator with the selected set point of 100°F. The operator closes the hot water valve when the temperature of the fluid in the tank rises above the set point.
Because of process dead time and lags the temperature will continue to rise before reversing and moving toward the set point. When the temperature falls below 100°F, the operator opens the hot water valve. Again, dead time and lags in the process create a delay before the temperature begins to rise. As it crosses the set point, the operator again shuts off the hot water, and the cycle repeats.
This cycling is normal for a control system that uses on/off control. This limitation exists because it’s impossible for the operator to control the process exactly with only two options.
This on/off type of control can be expressed mathematically as follows:
e = PV – SP
In the on/off control mode, the valve is open valve when the error (e) is positive (+), and the valve is closed when e is negative (–).