Motivation for Addition of Integral and Derivative Control Modes (Action and comparision of response of PI, PID controls on output signal)

Having introduced ideal transfer functions for integral and derivative modes of control, we now wish to indicate the practical motivation for use of these modes. The curves of Fig. show the behaviour of a typical, feedback control system using different kinds of control when it is subjected to a permanent disturbance.

With no control, this variable continues to rise to a new steady-state value. With control, after some time the control system begins to take action to try to maintain the controlled variable close to the value that existed before the disturbance occurred.

 

With proportional action only, the control system is able to arrest the rise of the controlled variable and ultimately bring it to rest at a new steady-state value. The difference between this new steady-state value and the original value is called offset. For the particular system shown, the offset is seen to be only 22 percent of the ultimate change that would have been realized for this disturbance in the absence of control.

 

With PI control:

As shown by the PI curve, the addition of integral action eliminates the offset the controlled variable ultimately returns to the original value. This advantage of integral action is balanced by the disadvantage of a more oscillatory behaviour.

With PID control:

The addition of derivative action to the PI action gives a definite improvement in the response. The rise of the controlled variable is arrested more quickly, and it is returned rapidly to the original value with little- or no oscillation.