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Section 5–5 / Transient-Response Analysis with MATLAB 195Impulse Response. The unit-impulse response of a control system may be
obtained by using any of the impulse commands such as
impulse(num,den)
impulse(A,B,C,D)
[y,x,t] = impulse(num,den)
[y,x,t] = impulse(num,den,t) (5–41)
[y,x,t] = impulse(A,B,C,D)
[y,x,t] = impulse(A,B,C,D,iu) (5–42)
[y,x,t] = impulse(A,B,C,D,iu,t) (5–43)
The command impulse(num,den)plots the unit-impulse response on the screen. The
commandimpulse(A,B,C,D)produces a series of unit-impulse-response plots, one for
each input and output combination of the system
Note that in Equations (5–42) and (5–43) the scalar iuis an index into the inputs of the
system and specifies which input to be used for the impulse response.
Note also that if the command used does not include “t” explicitly, the time vector
is automatically determined. If the command includes the user-supplied time vector “t”,
as do the commands given by Equations (5–41) and (5–43)], this vector specifies the
times at which the impulse response is to be computed.
If MATLAB is invoked with the left-hand argument [y,x,t], such as in the case of
[y,x,t] = impulse(A,B,C,D), the command returns the output and state responses of the
system and the time vector t. No plot is drawn on the screen. The matrices yandxcon-
tain the output and state responses of the system evaluated at the time points t.(yhas
as many columns as outputs and one row for each element in t.xhas as many columns
as state variables and one row for each element in t.) To plot the response curve, we
must include a plot command, such asplot(t,y).
y=Cx+Du
x
=Ax+Bu
EXAMPLE 5–5 Obtain the unit-impulse response of the following system:
C(s)
R(s)=G(s)=1
s^2 +0.2s+ 1