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16 Cards in this Set
- Front
- Back
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1. What part of the output response is responsible for determining the stability of a linear system?
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1. Natural response
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2. What happens to the Natural response that creates instability?
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2. It grows without bound
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3. What would happen to a physical system that becomes unstable?
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3. It would destroy itself or hit limit stops
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4. Why are marginally stable systems considered unstable under the BIBO definition of stability?
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4. Sinusoidal inputs of the same frequency as the natural response yield unbounded responses even though
the sinusoidal input is bounded. |
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5. Where do system poles have to be to ensure that a system is not unstable?
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5. Poles must be in the left-half-plane or on the jω axis.
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6. What does the Routh-Hurwitz criterion tell us?
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6. The number of poles of the closed-loop transfer function that are in the left-half-plane, the right-halfplane,
and on the jω axis. |
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7. Under what conditions would the Routh-Hurwitz criterion easily tell us the actual location of the system's closed-loop poles?
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7. If there is an even polynomial of second order and the original polynomial is of fourth order, the original
polynomial can be easily factored. |
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8. What causes a zero to show up only in the first column of the Routh table?
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8. Just the way the arithmetic works out
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9. What causes an entire row of zeros to show up in the Routh table?
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9. The presence of an even polynomial that is a factor of the original polynomial
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10. Why do we sometimes multiply a row of a Routh table by a positive constant?
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10. For the ease of finding coefficients below that row
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11. Why do we not multiply a row of a Routh table by a negative constant?
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11. It would affect the number of sign changes
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12. If a Routh table has two sign changes above the even polynomial and five sign changes below the even polynomial, how many right-half-plane poles does the system have?
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12. Seven
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13. Does the presence of an entire row of zeros always mean that the system has jω poles?
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13. No; it could have quadrantal poles.
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14. If a seventh-order system has a row of zeros at the s3 row and two sign changes below the s4 row, how many jω poles does the system have?
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14. None; the even polynomial has 2 right-half-plane poles and two left-half-plane poles.
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15. Is it true that the eigenvalues of the system matrix are the same as the closed-loop poles?
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15. Yes
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16. How do we find the eigenvalues?
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16. Det (sI-A) = 0
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