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# Sample Question: Control Systems

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1. What is the phase margin and gain margin?

A system has a loop function:
A) P.M.= 32.5 degrees and G.M.=16.47 dB.
B) P.M.= 30.2 degrees and G.M.=15.67 dB.
C) P.M.= 31.8 degrees and G.M.=16.57 dB.
D) P.M.= 32.3 degrees and G.M.=16.67 dB.

2. The loop function of a unity feedback system is:

Using a Nyquist plot, determine P, N, Z, and the stability of the system.
A) 0, 0, 0, stable
B) 0, -1, -1, unstable
C) 0, 1, 1, unstable
D) 1, -1, 0, stable

3. The Bode plot for the loop function of a unity feedback system is shown below:

Determine the gain K which must be added to the system so that a phase margin of 45 degrees is achieved.
A) K=3.5
B) K=1.4
C) K=0.17
D) K=0.83

4. The loop function for a unity feedback system is:

Let K=1 so that Kv=2. Design a lag network using a Bode diagram so that the phase margin is 45 degrees. The compensator and the frequency used in the design are:
A)
B)
C)
D)

5. A feedback control system is shown below: The specification for the closed-loop system requires that the overshoot to a step input be less than 10%. Determine the corresponding specification Mpw and the resonant frequency in the frequency domain for the closed-loop system.

A) 1.05, 5.92 rad/sec B.
B) 18, 2.74 rad/sec C.
C) 05, 3.25 rad/sec D.
D) 18, 4.26 rad/sec

6. The figure below represents the response of a circuit. Find the output voltage of the circuit assuming the input voltage Vin = 1.0V at 0.1 radians/second.

A) -15V
B) 1.8
C) 0.18
D) 1.2
E) None of the above

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#### Solution Preview

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I have provided detailed solutions to all questions (1 through 6). Please see attached file ...

#### Solution Summary

The following posting provides detailed, step by step calculations and explanations, and answers to all of the problems, including MATLAB code and graphing when required.

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