Proportional-Integral-Derivative (PID) Control Systems

Proportional-Integral-Derivative

For processes that are able to operate with continuous cycling, the relatively inexpensive two position controller is sufficient. For processes that cannot tolerate continuous cycling, a proportional controller is used. For processes that tolerate neither cycling nor offset error, a proportional plus integral/reset controller can be used. For processes that require improved stability and can tolerate an offset error, a proportional plus derivative/rate controller is used.

Nevertheless, there are some processes that cannot tolerate offset error, yet need good stability. The rational solution is to use a control mode that combines the advantages of a proportional, integral and derivative (PID) action.

Proportional plus Integral plus Derivative Controller Actions

When an error is introduced to a PID controller, the controller’s response is a combination of the proportional, integral and derivative actions as illustrated in Figure (a).

Suppose the error is due to a slowly increasing measured variable. As the error increases, the proportional action of the PID controller produces an output that is proportional to the error signal. The integral action also called the reset action of the controller produces an output whose rate of change is determined by the magnitude of the error. In this case, as the error continues to increase at a steady rate, the integral output continues to increase its rate of change. The derivative action also called the rate action of the controller produces an output whose magnitude is determined by the rate of change of the error signal, and not the amplitude/magnitude of the error. When all these actions are combined, they produce an output illustrated in Figure (a).

Note that, these response curves are drawn presuming no corrective action is taken by the control action. In practice, as soon as the output controller begins to reposition the final control element, the magnitude of the error should begin to decrease. Ultimately, the controller will bring the error to zero and the controlled variable back to the setpoint.

Figure (b) below demonstrates the combined controller response to a demand disturbance.

The proportional action of the controller stabilizes the process. The integral action combined with the proportional action causes the measured variable to return to the setpoint. The derivative action combined with the proportional action reduces the initial overshoot and cyclic period.