Solving system characteristics with GNU Octave

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Solving system characteristics with GNU Octave [Copy link]

 

In the field of electronics, linear time-invariant systems have broad representative significance.

The impulse response h(t) and system function H(s) of the system characterize two aspects of the same system from the time domain and transform domain. H(s) is the system function expressed in the s domain, which is not just a concept in the frequency domain.

Using GNU Octave's impulse() function, we can find the impulse response h(t) from the system function H(s).

For example, for the system function H1(s), the impulse response and step response can be found using the following procedure.

num=[1 -2];den=[1 1 0];

sys=tf(num,den);

figure(1)

subplot(221);

pzmap(sys);

axis([-2.5 2.5 -1.5 1.5]);

t=0:0.02:15;

subplot(222);

y=impulse(sys,t);

plot(t,y);

subplot(223);

z=step(sys,t);

plot(t,z);

Figure 1 is the impulse response: the waveform of y=-2+3exp(-t)

Figure 1

Figure 2 shows the step response: y=-2t+3-3exp(-t) waveform

Figure II

However, when encountering the following system function, problems will occur when solving it according to the above procedure.

The problem is displayed as follows:

The reason is: the system function in this example, both the numerator and the denominator are of order 2. According to the definition of s-transform, when transformed into the impulse response in the time domain, there is a δ(t) function. The complete impulse response is: h(t) = δ(t)-2exp(-t)*cost. However, when solving with a symbolic function, h(t) is directly written as: -2exp(-t)*cost.

Therefore, in order to use the above procedure to find the impulse response function of this system, it is necessary to first subtract 1 from the s function, that is, eliminate δ(t), and become as follows:

Figure 3

The program outputs the zero poles, impulse response h(t), and frequency response H(jw), as shown in Figure 4.

Figure 4

Summarize:

This paper uses the impulse function of GNU Octave software to solve the impulse response and frequency response curves corresponding to the system function.

When the order of the numerator of the system function is greater than or equal to the order of the denominator, an unsolvable problem will occur.

Analyze the causes and solve them.