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1. What is a root locus?
(8) |
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Definition
| The plot of a system's closed-loop poles as a function of gain |
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2.
Do the zeros of a system change with a change in gain? Why or why not?
(8) |
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Definition
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3.
What are two ways to find where the root locus crosses the imaginary axis?
(8) |
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Definition
(1) Apply Routh-Hurwitz to the closed-loop transfer function's denominator. (2) Search along the
imaginary axis for 180 degrees. |
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4.
How can you tell from the root locus if a system is unstable?
(8) |
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Definition
| 7. If any branch of the root locus is in the rhp, the system is unstable. |
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5.
How can you tell from the root locus if the settling time does not change over a region of gain?
(8) |
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Definition
If the branch of the root locus is vertical, the settling time remains constant for that range of gain on the
vertical section. |
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6.
How can you tell from the root locus that the natural frequency does not change over a region of gain?
(8) |
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Definition
| If the root locus is circular with origin at the center |
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7.
How would you determine whether or not a root locus plot crossed the real axis?
(8) |
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Definition
| Determine if there are any break-in or breakaway points |
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8.
Briefly describe how the zeros of the open-loop system affect the root locus and the transient response.
(8) |
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Definition
The zeros of the open loop system help determine the root locus. The root locus ends at the zeros. Thus,
the zeros are the closed-loop poles for high gain. |
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Term
1.
Name two major advantages of the design techniques of Chapter 9 over the design techniques of Chapter 8.
(9) |
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Definition
A. Permits design for transient responses not on original root locus and unattainable through simple gain
adjustments. B. Transient response and steady-state error specifications can be met separately and
independently without the need for tradeoffs |
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2.
What kind of compensation improves the steady-state error?
(9) |
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Definition
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3.
What kind of compensation improves both steady-state error and transient response?
(9) |
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Definition
| PID or lag-lead compensation |
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4.
Cascade compensation to improve the steady-state error is based upon what pole- zero placement of the compensator? Also, state the reasons for this placement.
(9) |
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Definition
A pole is placed on or near the origin to increase or nearly increase the system type, and the zero is
placed near the pole in order not to change the transient response. |
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5.
What are the advantages and disadvantages of using a passive lead network instead of an active PD controller?
(9) |
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Definition
A PD controller yields a single zero, while a lead network yields a zero and a pole. The zero is closer to
the imaginary axis. |
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6.
In order to speed up a system without changing the percent overshoot, where must the compensated system's poles on the s-plane be located in comparison to the uncompensated system's poles?
(9) |
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Definition
| Further out along the same radial line drawn from the origin to the uncompensated poles |
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7.
Why is there more improvement in steady-state error if a PI controller is used instead of a lag network?
(9) |
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Definition
The PI controller places a pole right at the origin, thus increasing the system type and driving the error
to zero. A lag network places the pole only close to the origin yielding improvement but no zero error. |
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