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21 Cards in this Set
- Front
- Back
Name the performance specification for first-order systems.
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Time constant
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What does the performance specification for a first-order system tell us?
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The time for the step response to reach 67% of its final value
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In a system with an input and an output, what poles generate the steady-state response?
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The input pole
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In a system with an input and an output, what poles generate the transient response?
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The system poles
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The imaginary part of a pole generates what part of a response?
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The radian frequency of a sinusoidal response
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The real part of a pole generates what part of a response?
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The time constant of an exponential response
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What is the difference between the natural frequency and the damped frequency of oscillation?
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Natural frequency is the frequency of the system with all damping removed; the damped frequency of
oscillation is the frequency of oscillation with damping in the system. |
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If a pole is moved with a constant imaginary part, what will the responses have in common?
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Their damped frequency of oscillation will be the same.
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If a pole is moved with a constant real part, what will the responses have in common?
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They will all exist under the same exponential decay envelop.
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If a pole is moved along a radial line extending from the origin, what will the responses have in common?
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They will all have the same percent overshoot and the same shape although differently scaled in time.
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List five specifications for a second-order underdamped system.
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. ζ, ωn, TP, %OS, Ts
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For the list of specifications for a second-order underdamped system. how many specifications completely determine the response?
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Only two since a second-order system is completely defined by two component parameters
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What pole locations characterize (1) the underdamped system, (2) the overdamped system, and (3) the critically damped system?
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1) Complex, (2) Real, (3) Multiple real
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Name two conditions under which the response generated by a pole can be neglected.
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Pole's real part is large compared to the dominant poles, (2) Pole is near a zero
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How can you justify pole-zero cancellation?
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If the residue at that pole is much smaller than the residues at other poles
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Does the solution of the state equation yield the output response of the system? Explain.
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No; one must then use the output equation
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What is the relationship between (sI-A), which appeared during the Laplace transformation solution of the state equations, and the state-transition matrix, which appeared during the classical solution of the state equation?
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The Laplace transform of the state transition matrix is
(sI-A)-1 |
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Name a major advantage of using time domain techniques for the solution of the response.
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Computer simulation
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Name a major advantage of using frequency domain techniques for the solution of the response.
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Pole-zero concepts give one an intuitive feel for the problem.
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What three pieces of information must be given in order to solve for the output response of a system using state-space techniques?
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State equations, output equations, and initial value for the state-vector
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How can the poles for a system be found form the state equations?
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Det(sI-A) = 0
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