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Sample Question: Control Systems

See the attachment.

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:

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


Solution Preview


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.