Answer Happy

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: K(s + 10) G(s)H(s) = 53 where K is the open-loop gain. (i) 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 (ii) 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 = 7.7. Comment on the relationship between the phase margin and the transient response of the servomechanism control system. (Take Wgc = 12.08 rad/s]. [6 marks]