Frequency Response of Controllers

In this section the frequency response of a PID controller will be discussed. The transfer function of a proportional integral derivative controller is  

The amplitude ratio and phase angle for the controller becomes then  

For the limit case, when co approaches zero, the amplitude ratio will approach infinity and the phase shift will approach -90°. For low frequency the integral action dominates, leading to a high gain. Consequently, the offset will approach zero. 

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