Question 1 Figure Q1 shows the structure of a closed loop control system: d(s) e(s) u(s) sp(s)- K(s) ++ G(s) - y(s) Figu

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Question 1 Figure Q1 Shows The Structure Of A Closed Loop Control System D S E S U S Sp S K S G S Y S Figu 1 (150.85 KiB) Viewed 10 times

Question 1 Figure Q1 shows the structure of a closed loop control system: d(s) e(s) u(s) sp(s)- K(s) ++ G(s) - y(s) Figure Q1 a) Show that the transfer function for the above system is given by x(s) = ( _a(5)K(x)) JP(s)+ (1+G(s)K(s). 1+G(s)K(s) (5) 4²(6) b) One of the main requirements of a control system is to ensure that it rejects all 'disturbances' - which is shown in Figure Q1 as d(s). i) Determine the conditions the controller K(s) must satisfy, for any system G(s), so that this objective can be satisfied. ii) How does this choice of controller affect the response of the system to any set point, sp(s), changes it experiences? (7 Marks (3 Marks) (2 Marks)