Proportional Control Systems

The control mode

In the proportional control mode, the final control element is throttled to various positions that are dependent on the process systems conditions. The controller operates within a band that is between the 0 % output point and the 100 % output point and where the output of the controller is proportional to the input signal.

Proportional Band

Proportional band is the change in input required to produce a full range of change in the output due to the proportional control action or it can be defined in simple terms as the percentage change of the input signal required to change the output from 0 % to 100 %.

With proportional control, the final control element has a definite position for each value of the measured variable; that is to say, the output has a linear relationship with the input.

Related: Controller

The proportional band determines the range of output values from the controller that operate the final control element. The final control element acts on the manipulated variable to determine the value of the controlled variable. The controlled variable is maintained within a specified band of control points around a setpoint.

The proportional band is the input band over which the controller provides a proportional output and is defined as:

Example of an Industrial application of a Proportional Controller

The figure below shows a process system using a proportional temperature controller for providing hot water.

Steam is admitted to the heat exchanger to raise the temperature of the cold water supply. The temperature sensor (TT) monitors the hot water outlet and produces a 3 to 15 psi output signal that represents a controlled variable range of 100 °F to 300 °F. The controller (TC) compares the measured variable signal with the setpoint and sends a 3 to 15 psi output to the final control element, which is a 3 inch control valve (i.e. pneumatic control valve).

The controller has been set for a proportional band of 50%. Therefore a 50% change in the 200°F span, or a change of 100°F, causes a 100% controller output change (Recall, the proportional band is the change in input needed to produce a full range of change in the output due the Proportional control action).

The proportional controller is reverse-acting so that he control valve throttles down to reduce steam flow as the hot water outlet temperature increases and it will open further to increase steam flow as the water temperature decreases.

The combined action of the controller and the control valve for different changes in the measured variables is illustrated in the figure below:

Initially the measured variable value is equal to 100°F. The controller has been set so that this value of measured variable corresponds to a 100 % output; or 15 psi, which in turn corresponds to a ‘’full open’’ control valve position.

At time t₁, the measured variable increases by 100°F, or 50% of the measured variable span, this 50% controller input change causes a 100% controller output change due the controller’s proportional band of 50%. The direction of the controller output change is decreasing because the controller is reverse-acting. The 100% decrease corresponds to a decrease in output for 15 psi to 3 psi, which causes the control valve to go from fully open to fully shut.

At time t₂, the measured variable decreases by 50°F, or 25% of the measured variable span; the 25% controller input decrease causes a 50% controller output increase. This results in a controller output increase from 3 psi to 9 psi, and the control valve goes from fully shut to 50 % open.

The objective of this system is to provide hot water at a setpoint of 150 °F. The system must be capable of handling demand disturbances that can result in the outlet temperature increasing or decreasing from the setpoint. Hence, the controller is set up such that the system functions as illustrated below.

If the measured variable drops below the setpoint, a positive error is developed, and the control valve opens further. If the measured variable goes above the setpoint, a negative error is developed, and the control valve throttles down (opening is reduced). The 50% proportional band causes full stroke of the valve between a + 50 °F error and a +50 °F.

When the error equals zero, the controller provides a 50%, or 9 psi signal to the control valve. As the error goes above or below this point, the controller produces an output that is proportional to the magnitude of the error, determined by the value of the proportional band. The control valve is then capable of being positioned to compensate for the demand disturbances that can cause the process to deviate from the setpoint in either direction.

Related: Reset (Integral) Control Systems