Modern Control Engineering

(Chris Devlin) #1

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Section 5–5 / Transient-Response Analysis with MATLAB 195

Impulse 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
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