Match the values of k_p to the root locus plots of the poles of G_{PI}(s) as k_i ranges from 0 to \infty.

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Which of the following plots shows the root locus plot of the poles of G_P(s) as k_p goes from 0 to \infty?

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A first-order plant P(s) = 1/(s+1) is connected in unity feedback configuration with a PI controller. If the controller gains are K_i =2 and K_p =1 then which of the following statements are true?

A The closed loop system has zero steady-state error for a step input.

B The closed loop system has complex conjugate poles at s = −1 \pm j

C The closed loop system is a first-order system

D The close loop system has a zero in the LHP

A controller P(s) and plant C(s) are connected as follows:

In the diagram below, the controller has transfer function C(s)=1+\frac{10}{s} and the plant has transfer function P(s) = \frac{1}{s+2}.

The root loci of three processes are shown below:

Which of the following statements is true when these processes are connected in negative feedback with a proportional gain controller?