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# ps7 - 2.14/2.140 Problem Set 7 Assigned Fri April 6 2007...

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2.14/2.140 Problem Set 7 Assigned: Fri. April 6, 2007 Due: Thurs. April 12, 2007, in class Reading: Nise sections 10.3–10.10; Notes Chapters 4,5,6 The following problems are assigned to both 2.14 and 2.140 students. In all of this prob- lem set, you are free to use Matlab or any other computational tools to aid your solutions. There are no additional problems for 2.140 students. Problem 1 A unity-gain feedback loop is shown below; note that the plant has a pair of poles located on the imaginary axis. a) Sketch a root locus plot for K > 0. b) Use a Bode plot of the return ratio L ( s ) to choose the controller gain K such that the loop crossover frequency is 100 rad/sec. What gain K is required? What is the resulting phase margin φ m ? c) Make a Nyquist plot for this loop, which is accurately drawn in the region where φ m is defined. Be sure to label the corresponding points on the diagram. Note that your Nyquist analysis will require detours around the poles at ± j 10. Please clearly show the portion of the Nyquist contour corresponding to these detours.

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