Consider the plant G(s) =s-0.5/s^2-2s+2 and a proportional controller G_c(s)=K i

Question

Consider the plant G(s) =s-0.5/s^2-2s+2 and a proportional controller G_c(s)=K in a unity gain feedback loop as shown below. Sketch the squareroot locus of the system as K varies from 0 to infinity. Determine the range of values of K where the system is stable. Determine the value of K where the system is stable and the damping ratio is 1 Squareroot 2. For the range of K where the system is stable, find an expression of the steady-state error to unit step reference input. Using the squareroot locus sketch in part (a) comment if an integral control G_c(s) = K/s can be used to achieve 0 steady-state error.

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