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14 Cards in this Set
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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 statespace 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 ndimensional 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 eighthorder system would be represented in state space with how many state equations?

Eight


If the state equations are a system of firstorder 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 energystorage elements, is it possible to have a statespace 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 secondorder differential equations which would then be described by six, firstorder 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 phasevariable form of the stateequation?

The state variables are successive derivatives.
