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Q3. (a) An automobile speed control system will be necessary for passenger cars travelling on the automatic highways of the future. As a design engineer, suggest a control system model for a standard automobile and concisely discuss the possible analysis and design procedure that you would recommend in order to achieve an effective speed control system. [7 marks) (b) The open-loop transfer function (OLTF) of a unity feedback servomechanism system is given by: G(s)H(s) = K(s + 10) 53 where K is the open-loop gain. ) investigate the condition(s) for the stability of the OLTF using the contour mapping technique and the Nyquist stability criterion. [7 marks] (ii) sketch the Nyquist diagram of the system in the GH(jw)-plane and investigate the system's behaviour for varying Kvalues. [6 marks) (iii) using the results from Part (i) show that the system is stable for K> 5.3 Validate your answer using the Routh-Hurwitz stability criterion. [4 marks) (iv) determine the gain margin and phase margin when K = 7.2 Comment on the relationship between the phase margin and the transient response of the servomechanism control system. (Take Wgc = 24 rad/s]. [6 marks) Q3 TOTAL = 30 MARKS END OF PAPER