Damping ratio from transfer function

In summary, the conversation discusses a transfer function for a system, specifically examining the coefficients in the numerator and denominator and how they relate to calculating the damping ratio. The possibility of dividing the coefficients by a constant to simplify the calculation is also mentioned.
  • #1
sgsawant
30
0
I have a transfer function for system.

23.23*s + 1.421
------------------------------------- = tf
s^2 + 25.88*s + 1.421


Since the numerator has a non-zero coefficient for "s" I am wary about equating

25.88 = 2 * zeta * omega [the stuff we usually do for calculating the damping ratio].


Can someone shed any light on this?

Regards,

-sgsawant

N.B.: I this question is a copy of the one I asked on the General Forum. I wanted to switch it from General to Classical but couldn't find a way. Please guide if you know.
 
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  • #2
Can you divide top and bottom on the left side of the equation by 23.23 to get rid of the unwanted coefficient??
 
  • #3
I believe that damping ratio is found in the same way. The numerator coefficients set the system zeros, but the denominator coefficients set the poles which control the character of the response (overdamped, underdamped or critically damped).
 

1. What is the damping ratio in a transfer function?

The damping ratio in a transfer function is a measure of the amount of damping in a system. It is represented by the Greek letter δ (pronounced as "zeta") and is defined as the ratio of the actual damping in a system to the critical damping (the minimum amount of damping required to prevent oscillations).

2. How is the damping ratio calculated from a transfer function?

The damping ratio can be calculated from a transfer function by using the formula δ = c/2√(km), where c is the damping coefficient, k is the spring constant, and m is the mass of the system. Alternatively, it can also be calculated using the natural frequency (ω) and the damped frequency (ωd) as δ = (ωd/ω) √(1-(ωd/ω)2).

3. What is the significance of the damping ratio in a transfer function?

The damping ratio is an important parameter in a transfer function as it determines the behavior of a system. A higher damping ratio indicates a greater amount of damping, leading to a slower response and less oscillations, while a lower damping ratio results in a faster response with more oscillations.

4. How does the damping ratio affect the stability of a system?

The damping ratio plays a crucial role in the stability of a system. A system with a damping ratio less than 1 (underdamped system) is stable, but may exhibit oscillatory behavior. On the other hand, a damping ratio greater than 1 (overdamped system) results in a stable system with no oscillations. A damping ratio equal to 1 (critically damped system) provides the fastest response without any oscillations, making it the most desirable for many engineering applications.

5. How can the damping ratio be adjusted in a system?

The damping ratio can be adjusted in a system by changing the damping coefficient or the mass of the system. Increasing the damping coefficient will result in a higher damping ratio, while decreasing the mass will also increase the damping ratio. Additionally, the use of damping devices, such as shock absorbers, can also be used to adjust the damping ratio in a system.

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