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What is a lead lag compensator? To get intution, we start with the simplest form of controllers: This shifts the root locus to the left, which enhances the responsiveness and stability of the system.

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It is a combination of both the lag and the lead.

Lead compensation introduces a zero, increasing system speed and reducing overshoot by improving the phase margin.

The lead compensator provides phase lead at high frequencies. Providing extra zeros eliminates annoying frequency. One solution is to use a notch filter.