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Engineering · Mechanical Engineering
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1. The transfer function of a plant is G(s) 1/(s+1). Show that for proportional integral (PI) control the steady state error for step input goee to zero. (10 pts) 2. The plant G(s) given in Equation (??) will be controlled using proportional control. The frequency characteristice of the control system will be determined using a Bode diagram (s +100) +4s+100) (a) Represent the system in Bcde form. (3 pts.) (b) Draw the Bode diagram assuming control gain K 1. Draw two separate magnitude plots to ense our grading: On thc first graph draw just the asymptotes, then on a cw 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 e open loop or closed loop trausfer pick these vales) (5 pts.) gain and if applicable and the critical gain value. (4 pts.) function? (3 pts.)

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