National Instruments 370753C-01 Manual De Usuario
© National Instruments Corporation
4-1
4
System Analysis
This chapter discusses time-domain solutions of the equations underlying
transfer functions and state-space system models, and what these solutions
tell us about the stability of the system. Xmath provides a number of
functions for performing this system analysis and computing the
time-domain system response to both general and specific “standard”
inputs.
transfer functions and state-space system models, and what these solutions
tell us about the stability of the system. Xmath provides a number of
functions for performing this system analysis and computing the
time-domain system response to both general and specific “standard”
inputs.
Time-Domain Solution of System Equations
Given the state-space equations:
you obtain:
letting x
0
denote any initial conditions on the system states. The integral
term in the preceding equation defines a convolution integral. Using
*
to
represent the convolution operator, the time-domain system output for all
time t
time t
≥ 0 is:
(4-1)
The response Y(s) of the system (with zero initial conditions) to a unit
impulse input
impulse input
δ(t) is H(s), the transfer function representation from the
section of Chapter 2,
. You accordingly term h(t), the inverse Laplace transform
of H(s), the impulse response.
x·
Ax Bu
+
=
y
Cx Du
+
=
x t
( )
e
At
x
0
e
A
τ
Bu t
τ
–
(
)dτ
0
t
∫
+
=
y t
( )
ce
At
x
0
h t
( )*u t()
(
)
+
=
h t
( )
Ce
At
B D
δ t
( )
+
=