Recall that as the controller gain, K, increases, sometimes two closed loop poles on the real axis approach each other and then branch off from the real axis to form two complex conjugate poles. The point on the real axis at which two branches meet and break away is called a break-away point. Similarly, the point on the real axis where two complex conjugate branches meet is called a break-in point. Prove that the break-away and break-in points of the root locus can be found by solving the equation d/ds ( -1/L(s) ) = 0.
Hint: start from 1 + KL(s) = 0.
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Recall that as the controller gain, K, increases, sometimes two closed loop poles on the real...