4.6 MATLAB Laboratory Experiment
Purpose: This experiment presents the frequency domain analysis of continuous-time
linear systems using MATLAB. The impulse, step, sinusoidal, and exponential responses
of continuous-time systems will be examined using the transfer function method based
on the Laplace transform. In addition, MATLAB will be used to perform the partial
fraction expansion and to find the inverse Laplace transform.
Part 1. Consider the linear system represented by the transfer function
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Using MATLAB, find and plot:
(a) The system impulse response.
(b) The system step response.
(c) The system zero-state response due to the input signal
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.
(d) The system zero-state response due to the input signal
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.
Part 2. Consider the transfer function
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1
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3
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(a) Find the factored form of the transfer function by using the MATLAB function
[z,p,k]=tf2zp(num,den).
(b) The partial fraction expansion of rational functions can be performed using the
MATLAB function residue. Find the Laplace inverse of the given transfer function
using the MATLAB function residue; that is, find analytically the system impulse
response.
Part 3. Consider the system defined by
F<G
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F<G"I
H
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J๎;:
F
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and the input signal represented in Figure 4.13. Use MATLAB to plot the zero-state
response of this system. (Hint: See Example 4.24.)
t
f(t)
0321
-1
1
FIGURE 4.13: An input signal
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