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Question: 1 the transfer function of a plant is gs 1s1...

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1. The transfer function of a plant is G(s)- 1/(s1). Show that for proportional integral (PI) control, the steady state error for step input goes to zero. (10 pts.) 2. The plant G(s) given in Equation ??) will be controlled using proportional control. The frequency characteristics of the control system will be determined using a Bode diagram. G) (s 100) (s2 +4s +100) (a) Represent the system in Bode form. (3 pts.) (b) Draw the Bode diagram assuming control gain Kp-1. Draw two separate magnitude plots to ease our grading: On the first graph draw just the asymptotes, then on a new graph draw the complete magnitude response. Label the axes clearly, write the slopes of each asymptote clearly on each segment. Provide the phase graph below them. (10 pts.) (c) Approximately determine the phase margin and gain margin of this system (explain clearly why you (d) Can the control gain be increased to make the system unstable? Write the requirement for such a (e) Do we determine stability in Bode graph by looking at the open loop or closed loop transfer pick these values). (5 pts.) gain and if applicable and the critical gain value. (4 pts.) function? (3 pts.) 3. (a) Draw the Nyquist diagram of the open-loop transfer function shown in Equation?). Clearly show the real and imaginary axis intercept points and the high frequency asymptote. (10 pts.) (b) From the Nyquist diagram, can you determine if there a range of controller gains that will make this system stable? Explain and write the critical gain if available. (6 pts.) (c) Draw a generic Nyquist plot and show the gain margin and phase margin on the plot. (4 pts.) 4. Given the transfer function shown in Equation?), draw the block diagram representation in either of control canonical, observer canonical or modal canonical forms. (7 pts.) s2 +2s + 3)

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