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14 Cards in this Set
- Front
- Back
Give two reasons for modeling systems in state space. |
(1) Can model systems other than linear, constant coefficients; (2) Used for digital simulation
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State an advantage of the transfer function approach over the state-space approach.
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Yields qualitative insight
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Define state variables.
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That smallest set of variables that completely describe the system
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Define state
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The value of the state variables
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Define state vector.
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The vector whose components are the state variables
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Define state space.
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The n-dimensional space whose bases are the state variables
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What is required to represent a system in state space?
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State equations, an output equation, and an initial state vector (initial conditions)
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An eighth-order system would be represented in state space with how many state equations?
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Eight
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If the state equations are a system of first-order differential equations whose solution yields the state variables, then the output equation performs what function?
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Forms linear combinations of the state variables and the input to form the desired output
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What is meant by linear independence?
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No variable in the set can be written as a linear sum of the other variables in the set.
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What factors influence the choice of state variables in any system?
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1) They must be linearly independent; (2) The number of state variables must agree with the order of
the differential equation describing the system; (3) The degree of difficulty in obtaining the state equations for a given set of state variables. |
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What is a convenient choice of state variables for electrical networks?
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The variables that are being differentiated in each of the linearly independent energy storage elements
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If an electrical network has three energy-storage elements, is it possible to have a state-space representation with more than three state variables? Explain.
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Yes, depending upon the choice of circuit variables and technique used to write the system equations.
For example, a three -loop problem with three energy storage elements could yield three simultaneous second-order differential equations which would then be described by six, first-order differential equations. This exact situation arose when we wrote the differential equations for mechanical systems and then proceeded to find the state equations. |
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What is meant by the phase-variable form of the state-equation?
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The state variables are successive derivatives.
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