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20 Cards in this Set
- Front
- Back
Name the four components of a block diagram for a linear, time-invariant system.
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Signals, systems, summing junctions, pickoff points
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Name three basic forms for interconnecting subsystems.
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Cascade, parallel, feedback
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For each of the forms in Question 2, state (respectively) how the equivalent transfer function is found.
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Product of individual transfer functions, sum of individual transfer functions, forward gain divided by
one plus the product of the forward gain times the feedback gain |
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Besides knowing the basic forms as discussed in Questions 2 and 3, what other equivalents must you know in order to perform block diagram reduction?
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Equivalent forms for moving blocks across summing junctions and pickoff points
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For a simple, second-order feedback control system of the type shown in Figure 5-14, describe the effect that variations of forward-path gain, K, have on the transient response.
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As K is varied from 0 to ∞, the system goes from over damped to critically damped to under damped.
When the system is under damped, the settling time remains constant. |
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For a simple, second-order feedback control system of the type shown in Figure 5-14, describe the changes in damping ratio as the gain, K, is increased over the underdamped region.
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Since the real part remains constant and the imaginary part increases, the radial distance from the origin
is increasing. Thus the angle θ is increasing. Since ζ= cos θ the damping ratio is decreasing. |
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Name the two components of a signal-flow graph.
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Nodes (signals), branches (systems)
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How are summing junctions shown on a signal-flow graph?
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Signals flowing into a node are added together. Signals flowing out of a node are the sum of signals
flowing into a node. |
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If a forward path touched all closed loops, what would be the value of ?
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One
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Name five representations of systems in state space.
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Phase-variable form, cascaded form, parallel form, Jordan canonical form, observer canonical form
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Which two forms of the state-space representation are found using the same method?
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The Jordan canonical form and the parallel form result from a partial fraction expansion.
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Which form of the state-space representation leads to a diagonal matrix?
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Parallel form
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When the system matrix is diagonal, what quantities lie along the diagonal?
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The system poles, or eigenvalues
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What terms lie along the diagonal for a system represented in Jordan canonical form?
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The system poles including all repetitions of the repeated roots
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What is the advantage of having a system represented in a form that has a diagonal system matrix?
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Solution of the state variables are achieved through decoupled equations. i.e. the equations are solvable
Individually and not simultaneously. |
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Give two reasons for wanting to represent a system by alternative forms.
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State variables can be identified with physical parameters; ease of solution of some representations
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For what kind of system would you use the observer canonical form?
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Systems with zeros
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Describe state-vector transformations from the perspective of different bases.
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State-vector transformations are the transformation of the state vector from one basis system to another.
i.e. the same vector represented in another basis. |
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What is the definition of an eigenvector?
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A vector which under a matrix transformation is collinear with the original. In other words, the length
of the vector has changed, but not its angle. |
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Based upon your definition of an eigenvector, what is an eigenvalue?
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An eigenvalue is that multiple of the original vector that is the transformed vector.
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