8.7.2 Experiment 2—Response of Continuous Systems
Part 1. Consider a continuous-time linear system represented by its transfer function
(a) Find and plot the impulse response. Use the MATLAB function impulse.
(b) Find and plot the step response using the function step.
(c) Find the zero-state system output response due to an input given by
! #"
. Note that you must use the function lsim and specify input at
every time instant of interest. That can be obtained by t=0:0.1:5 (defines
at
"
"%$'&
"($ )
$'$'$
+*
$ ,
), f=exp(-3*t), and y=lsim(num,den,f,t). Check that
the results obtained agree with analytical results at
-.&
.
(d) Obtain the state space form for this system by using the function tf2ss. Repeat
parts (a), (b), and (c) for the corresponding state space representation. Use the
following MATLAB instructions
[y,x]=impulse(A,B,C,D)
[y,x]=step(A,B,C,D)
[y,x]=lsim(A,B,C,D,f,t)
respectively, with
and
as defined in (c). Compare the results obtained.
Part 2. Consider the continuous-time linear system represented by
/
10
/
*
/
0
+
/
*
0
/
/
324
+
5"
076
"
98
:)
;
096
"
78
<&
(a) Find the complete system state and output responses by using the MATLAB function
lsim. Compare the simulation results obtained with analytical results. (Hint:
Use [y,x]=lsim(A,B,C,D,f,t,x0) with
= 0:0.1:5.) Note that the initial
condition for the state vector, x0, must be found. This can be obtained by playing
algebra with the state and output equations and setting
-="
.
(b) Find the zeros and poles of this system using the function tf2zp.
(c) Find the system state and output responses due to initial conditions specified in Part
2(a) and the impulse delta function as an input. Since you are unable to specify
the system input in time (the delta function has no time structure), you cannot use
the lsim function. Instead use either the MATLAB function initial (zero-input
response) or the MATLAB program given at the end of this part. The required
response is obtained analytically as follows
>
?
1@
6
>
6
"
98
BA
8
Docsity.com
