Figure 16 illustrates a process system using a proportional temperature controller for providing hot water.

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Figure 16 Proportional Temperature Control System

Steam is admitted to the heat exchanger to raise the temperature of the cold water supply. The temperature detector monitors the hot water outlet and produces a 3 to 15 psi output signal that represents a controlled variable range of 100 to 300F. The controller 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-in control valve.

The controller has been set for a proportional band of 50%. Therefore, a 50% change in the 200F span, or a change of 100F, causes a 100% controller output change.

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

The combined action of the controller and control valve for different changes in the measured variable is shown in Figure 17.

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Figure 17 Combined Controller and Final Control Element Action

Initially, the measured variable value is equal to 100F. 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 t_l, the measured variable increases by 100F, or 50%, of the measured variable span. This 50% controller input change causes a 100% controller output change due to 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 50F, 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 purpose of this system is to provide hot water at a setpoint of 150F. The system must be capable of handling demand disturbances that can result in the outlet temperature increasing or decreasing from the setpoint. For that reason, the controller is set up such that the system functions as shown in Figure 18.

Figure 18 Controller Characteristic Curve

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 +50F error and a -50F error.

When the error equals zero, the controller provides a 50%, or 9 psi, signal to the control valve. As the error goes above and 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.

Summary

The important information in this chapter is summarized below.

Proportional Control Summary

in the proportional control mode, the final control element is throttled to various positions that are dependent on the process system conditions.

With proportional control, the output has a linear relationship with the input.

The proportional band is the change in input required to produce a full range of change in the output due to the proportional control action.

The controlled variable is maintained within a specified band of control points around a setpoint.