Understanding Bode Plots for Second Order Systems with ς‚= 0

In summary, the conversation discusses a question about understanding the phase plot for a second order system with a specific value of ς‚. The speaker is struggling to understand why the initial phase is -360 degrees and how it changes to -180 degrees at the corner frequency. They are asking for an explanation and assistance in drawing the phase plot.
  • #1
ksurabhi
3
0
hey guys,

i have a question regarding bode plot

g(s)= 1/(s2+4)

i did get the magnitude plot correct but i am unable to understand the phase plot. by calculating on paper i got 0° but in MATLAB it changes from -360° to -180°

i haven't understood how the initial phase is -360 which changed to -180 at the corner frequency(2)

please explain. i would really appreciate if you could explain me how to draw the phase plot for second order system with ς‚= 0

thank you in advance
 
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  • #2
-360 degrees is equal to 0!

Typically each pole will add a 90 degrees phase shift that begins 1 decade before the pole and ends one decade after. Since there are two poles the phase shift will be 180 degrees
 
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1. What is a Bode plot for a second order system with ς = 0?

A Bode plot is a graphical representation of the frequency response of a system, showing the magnitude and phase of the system's output as a function of frequency. In a second order system with ς = 0, the system has no damping, resulting in a peak in the frequency response at the system's natural frequency.

2. How is the damping ratio, ς, related to the shape of a Bode plot for a second order system?

The damping ratio, ς, is a measure of the amount of damping present in a system. In a Bode plot for a second order system, the value of ς determines the shape of the plot. When ς = 0, the plot has a peak at the natural frequency, while higher values of ς result in a smoother, more gradual curve.

3. What information can be obtained from a Bode plot for a second order system with ς = 0?

A Bode plot for a second order system with ς = 0 can provide information about the system's frequency response, including the natural frequency and resonant frequency. It can also give insight into the stability and performance of the system.

4. How does increasing the damping ratio, ς, affect the behavior of a second order system?

Increasing the damping ratio, ς, results in a decrease in the amplitude of the system's response, making it less prone to resonance. However, too much damping can lead to slower response times and decreased performance.

5. How can Bode plots for second order systems with ς = 0 be useful in real-world applications?

Bode plots for second order systems with ς = 0 can be useful in designing and analyzing control systems, as they provide information about the system's response to different frequencies. This can help engineers optimize the system's performance and stability for a given application.

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