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14 Cards in this Set

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  • Back

Give two reasons for modeling systems in state space.

(1) Can model systems other than linear, constant coefficients; (2) Used for digital simulation
State an advantage of the transfer function approach over the state-space approach.
Yields qualitative insight
Define state variables.
That smallest set of variables that completely describe the system
Define state
The value of the state variables
Define state vector.
The vector whose components are the state variables
Define state space.
The n-dimensional space whose bases are the state variables
What is required to represent a system in state space?
State equations, an output equation, and an initial state vector (initial conditions)
An eighth-order system would be represented in state space with how many state equations?
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?
Forms linear combinations of the state variables and the input to form the desired output
What is meant by linear independence?
No variable in the set can be written as a linear sum of the other variables in the set.
What factors influence the choice of state variables in any system?
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.
What is a convenient choice of state variables for electrical networks?
The variables that are being differentiated in each of the linearly independent energy storage elements
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.
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.
What is meant by the phase-variable form of the state-equation?
The state variables are successive derivatives.