Question 4 a) For a control system of the form shown in Figure 1, prove that the closed loop poles a

Question 4 a) For a control system of the form shown in Figure 1, prove that the closed loop poles at zero gain are the same as the open loop poles at any gain. 4 marks] b) Determine the closed loop poles at zero gain for the control system in Figure 1 with forward path transfer function a+2)G+2s+5) 14 marks c) Sketch the root locus for the system. What does it tell you about the system stability? 5 marks d) You may accept without proof that the steady state open loop response is 4 6-23-294 2+25 . Sketch the Nyquist diagram for the system. You will need to do some calculation to determine the general shape, but do not 16 marks attempt to plot it to scale. e) Discuss the implication of (d) in terms of closed loop stability and compare with your results in (c). 16 marks

 

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