Maximum amplitude of second order system

In summary, the conversation discusses solving a theoretical problem involving finding the appropriate expression for r to make the denominator a minimum in |H(jω)|. The solution involves setting the derivative of the denominator equal to 0 and solving for r, taking into consideration that there may be multiple values of r that result in a derivative of 0.
  • #1
MMCS
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See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
 

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  • #2
MMCS said:
See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
Okay, so far so good. :smile:

But you just sort of stopped. Is there a particular question that you had?

You've already found the derivative of the denominator. Set the derivative equal to 0 and solve for r. You'll find that there are two or three values of r that make the derivative go to 0, but not all of them are necessarily local minimums (there could be local maximums).

Once you find the appropriate expression for r that makes the denominator a minimum, plug that back into |H()| and simplify. :wink:
 

1. What is the maximum amplitude of a second order system?

The maximum amplitude of a second order system is the largest value that the system's output can reach. It is typically measured in units of the system's output, such as displacement or voltage.

2. How is the maximum amplitude of a second order system determined?

The maximum amplitude of a second order system is determined by analyzing the system's transfer function, which describes how the system responds to different input signals. It can also be determined experimentally by applying different input signals to the system and measuring the corresponding output amplitudes.

3. What factors affect the maximum amplitude of a second order system?

The maximum amplitude of a second order system is affected by several factors, including the system's natural frequency, damping ratio, and input amplitude. A higher natural frequency or lower damping ratio can result in a larger maximum amplitude, while a smaller input amplitude can also lead to a smaller maximum amplitude.

4. How does the maximum amplitude of a second order system relate to its stability?

The maximum amplitude of a second order system is closely related to its stability. In general, a larger maximum amplitude indicates a less stable system, as it means that the system's output can reach higher values and potentially become uncontrollable. On the other hand, a smaller maximum amplitude indicates a more stable system, as it means that the system's output is limited and can be easily controlled.

5. Can the maximum amplitude of a second order system be reduced?

Yes, the maximum amplitude of a second order system can be reduced by adjusting the system's parameters, such as its natural frequency and damping ratio. This can be achieved through design modifications or by using control strategies, such as feedback control, to actively regulate the system's response. It is important to keep the maximum amplitude within a safe range to ensure the stability and reliability of the system.

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