# 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:

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 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.