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I was reading about lead compensator from a website but i am not able to understand how they have extracted zero and pole from transfer function of lead compensator as shown in attached photo?

or they have extracted/calculated wrong values of zeros and poles?

enter image description here

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You're right, the given pole and zero are wrong. They should be

$$s_0=-\frac{1}{\tau}$$

and

$$s_{\infty}=-\frac{1}{\beta\tau}$$

because for $s=s_0$ the numerator becomes zero, and for $s=s_{\infty}$ the denominator becomes zero.

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