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- State space systems
- State space systems
- I/o and i/s/o relationships in
(Blank Abstract)
I/o and i/s/o representation of siso linear systems
I/O |
I/S/O |
variables:
|
variables:
|
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Impulse Response |
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Poles -
characteristic roots - eigenfrequencies |
|
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Zeros |
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Matrix exponential |
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BIBO stability |
, requirement |
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Solution
in the time domain |
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Laplace
Transform: Solution in the frequency domain |
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Definition of state from i/o description
Let
,
. Define
so that
,
,
: degree of
.
Various responses
Zero-input or free response
- response due to initial conditions alone.
Zero-state or forced response
- response due to input (forcing function) alone (zero
initial condition).
Homogeneous solution
- general form of
free-response (arbitrary initial conditions).
Particular solution
- forced response.
Steady-state response
- response obtained
for large balues of time
.
Transient response
- full response minus steady
minus state response.
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Source:
OpenStax, State space systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10143/1.3
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