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A sinusoidal input was given to a process, Gp.= Gpz Gp and the resultant output was plotted as the Bode plot given below. Bode Diagram -20 -30 -40 Magnitude (dB) -50 -60 UL -70 0 Phase (deg) -45 -90 20 10-1 100 101 102 103 Frequency (rad/s) a. Estimate the transfer function of Gp and construct its Bode plot. Indicate in the Bode plot, the steps and measurement taken in estimating the transfer function of Gp. 18 marks) b. Given that the block diagram of the closed-loop system that contains the Gp as per below, derive the G and its appropriate PID settings. Ga Yap E K. GE G Gm ' where Gy asta Gm = 0.2s+1 Km = Ga = 1 You are required to list down the detail steps taken in deriving the G and finding its appropriate PID settings. (16 marks) C. The obtained PID settings in Question (b) are required to be tested via servo and regulator control and require fine tuning (if needed) to achieve acceptable control performances. Indicate your observation of the obtained PID settings towards process variations after a given reasonable magnitude of a step change and disturbance. Explain how you justify the fine-tuned PID settings (if there is any) is acceptable based on control performance criteria or characteristics. (16 marks) d. Suppose that a proportional controller is used and that a value of Kc is selected, by means of Routh stability method, determine the value or range of Ke that will make the system unstable. 10 marka