Figure (4) shows a PID control system, where Gr(s) is: 1 G(s)= (s+1) The PID controller...

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Figure (4) shows a PID control system, where Gr(s) is: 1 G₁(s)= (s+1)² The PID controller (parallel form) is assumed to be of the form: K(s+a)² Gc(s) = S i. Using pole-zero cancellation (setting a = 1), find suitable values for K, such that the closed-loop system will have a dominant first order pole at -2. For the design of part (i), find the values of: ii. . • KP, Ti, and Ta iii. If a 3, find the new value of K such that the closed-loop system still has a first order pole at -2. Is this pole dominant, as in part (i)? Explain! [6, (3+3+3), and 10 marks) R(s) E(s) PID(s) →G,(s) Figure (4) U(s) C(s) Figure (4) shows a PID control system, where Gr(s) is: 1 G₁(s)= (s+1)² The PID controller (parallel form) is assumed to be of the form: K(s+a)² Gc(s) = S i. Using pole-zero cancellation (setting a = 1), find suitable values for K, such that the closed-loop system will have a dominant first order pole at -2. For the design of part (i), find the values of: ii. . • KP, Ti, and Ta iii. If a 3, find the new value of K such that the closed-loop system still has a first order pole at -2. Is this pole dominant, as in part (i)? Explain! [6, (3+3+3), and 10 marks) R(s) E(s) PID(s) →G,(s) Figure (4) U(s) C(s)