05S-ME304-MT2-Solutions

# 05S-ME304-MT2-Solutions - Middle East Technical University...

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Middle East Technical University Mechanical Engineering Department 1956 ME 304 CONTROL SYSTEMS Spring 2005 Sections 02, 03, 04 Course Instructors: Dr. Bülent E. Platin, Dr. Tuna Balkan, Dr. Kemal Özgören MIDTERM EXAMINATION II SOLUTIONS May 04, 2005 Time Allowed: 120 minutes Open Notes and Books All questions are equally weighted List No. : ……. .……. .………… Student No. : ……. .…………… Name : ………………………… SURNAME : …………………. . Signature : ……………………. . 1 2 3 Σ

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ME304(Sections02,03,04)/05S/MT2-Solutions/Platin+Balkan+Özgören Page 1 PROBLEM 1: A plant is going to be controlled by a P-controller by using unity feedback. The transfer function of the plant is given as: p 2 2 G( s ) s4 s 5 = +− a) Determine the stability of the uncontrolled plant. b) Determine conditions on the proportional gain K>0 to have a stable closed-loop system. c) What is the maximum possible stability margin and corresponding minimum proportional gain for the closed-loop system? Solution: a) To determine the stability of the plant, apply Hurwitz test (necessary and sufficient condition for stability for second order systems) to the denominator polynomial of the plant transfer function.
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05S-ME304-MT2-Solutions - Middle East Technical University...

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