Why Does the Bode Plot of a Type 1 System Show a Damped Slope Initially?

In summary, the conversation discusses finding the initial magnitude in dB for a transfer function with a denominator of higher order. The initial magnitude is found by taking the amplitude of the transfer function, which can be approximated at low frequencies as 100/(5Ѡ), and converting it to dB. This results in a decrease of 20 dB per decade for a type 0 system and 40 dB per decade for a type 1 system. However, in some cases, the bode plot may show a slightly damped slope until it reaches 0 dB before decreasing at a steady rate of 40 dB.
  • #1
CognitiveNet
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1
For a transfer function of G(s) = 100 / (s(s+5)), I'm having trouble finding the initial magnitude in dB. It's a type 1 system. If it was a type 0 system with only (s+5) in the denominator, the initial magnitude would be 20log(nominator/denominator) where s is an element of 0, and would decrease by 20 dB per decade. For the system 1, the magnitude should decrease by 40 dB each decade. However, most transfer functions which I've bode plotted in wolfram alpha, appear to have a slightly damped slope until it reaches 0 db, before decreasing at a steady rate of 40dB.

Care to explain how I find the initial magnitude?

[This is NOT homework, but research of (art of) bode plotting transfer functions with denominator of higher order]
 
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  • #2
G(s) = 100/(s² + 5s)
Let s ← jѠ

G(s) = 100/(-Ѡ² + j5Ѡ)

amplitude = 100/ √(25Ѡ² + Ѡ⁴)
      = 100/(5Ѡ √(1 + Ѡ²/25)) 

At low frequencies where Ѡ « 5, amplitude ≈ [PLAIN]https://www.physicsforums.com/images/icons/icon5.gif [PLAIN]https://www.physicsforums.com/images/icons/icon5.gif

How many dB/decade will the slope of this be in the region Ѡ « 5?
 
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FAQ: Why Does the Bode Plot of a Type 1 System Show a Damped Slope Initially?

1. What is a Bode plot of type 1 system?

A Bode plot of type 1 system is a graphical representation of the frequency response of a system, which shows how the output of the system changes in response to different input frequencies. It is commonly used in control systems analysis to study the stability and performance of a system.

2. How is a Bode plot of type 1 system different from other types of Bode plots?

A Bode plot of type 1 system is characterized by a single pole at the origin in its transfer function. This means that it has a -20dB/decade slope for the magnitude plot and a -90 degree/decade slope for the phase plot. Other types of Bode plots, such as type 2 and type 3, have multiple poles and zeros in their transfer functions, resulting in different slopes in the Bode plot.

3. What information can be obtained from a Bode plot of type 1 system?

A Bode plot of type 1 system provides information about the gain and phase margin, which are important indicators of stability in control systems. It also shows the frequency at which the system's gain is maximum (called the resonant frequency) and the frequency at which the phase is -180 degrees (called the phase crossover frequency).

4. How is a Bode plot of type 1 system used in control systems design?

A Bode plot of type 1 system can be used to design controllers and filters for a system. By analyzing the plot, the designer can determine the necessary parameters for the controller or filter to achieve a desired performance, such as stability, disturbance rejection, or tracking of a specific input frequency.

5. Can a Bode plot of type 1 system be used for non-linear systems?

No, a Bode plot of type 1 system is only applicable for linear time-invariant systems. Non-linear systems have varying transfer functions and do not follow the -20dB/decade and -90 degree/decade slopes of a Bode plot of type 1 system. Therefore, different techniques must be used to analyze and design control systems for non-linear systems.

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