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Design a PI compensator to yield a steady-state error equal to zero -Control System

Given the system of Figure 2, operating with a damping ratio of 0.174, show that the addition of the ideal integralcompensator shown in Figure 2 reduces the steady-state error to zero for a step input without appreciably affecting transient response. The compensating network is chosen with a pole at the origin to increase the system type and a zero at -0:1, close to the compensator pole, so that the angular contribution of the compensator evaluated at the original, dominant, second-order poles is approximately zero.Thus, the original, dominant, second-order  closed-loop poles are still approximately on the new root locus.

 

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