May 26, 2019, 12:59 AM
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Discussion

# How to Plot Transient Response

Hi everyone, I am researching a RC model, I had the result of some below derivatives. I want to ask: How to plot transient response over time like that graph?

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 May 26, 2019, 09:48 AM Registered User Those derivatives come from linearizing and decoupling the aircraft’s equations of motion. To get the transient response you just advance the resulting equations of motion in time. You start with the aircraft at some initial state. Based on that state, and the forces and moments associated with it, you calculate the rate of change of the state variables. With the rates of change, you can calculate the aircraft’s state after some time step. Once you have the “new” state, you again calculate the rate of change of the state variables. With this information, you can advance by another time step. You continue this process for as long as you’re interested in the transient response. Typically you’d use a higher order time integration method (like Runge Kutta), but that’s not really necessary if you can afford to take very small time steps. Last edited by ShoeDLG; May 26, 2019 at 09:58 AM.
 May 26, 2019, 07:09 PM Closed Account You should be able to solve for the eigenvalues (as you evidently did in the thread you started on dynamic stability ) The eigenvalues give you the characteristic modes of motion. For the lateral-directional case, these usually are: - roll mode (a rapid convergence to a roll rate) - spiral mode (slow convergence or slow divergence, mostly yaw with some roll) - Dutch roll mode (moderately damped stable oscillation in yaw and roll) Sometimes the Dutch roll is replaced with a "coupled roll-spiral" mode. Once you have the eigenvalues, characteristics like frequency, damping ratio, rise time, and settling time are easily found. You can sketch the results by hand, or use many different computer codes to plot them. If you are using some sort of code for your analysis already it probably has a plot routine included. Are you doing this for course work or your own benefit? Do you have a faculty or student advisor to help you?
 May 26, 2019, 08:13 PM Registered User Term to google is "State space control" https://en.wikipedia.org/wiki/State-...representation https://in.mathworks.com/help/control/ref/initial.html
May 28, 2019, 02:21 AM
Registered User
Quote:
 Originally Posted by NC14310 You should be able to solve for the eigenvalues (as you evidently did in the thread you started on dynamic stability ) The eigenvalues give you the characteristic modes of motion. For the lateral-directional case, these usually are: - roll mode (a rapid convergence to a roll rate)
Thank you for your help! I love your way to explain about roll mode, spiral mode,... It's very easy to understand.
I have also calculated eigenvalues for corresponding modes. But I want to use matlab to plot transient response but I don't know how to do.

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May 28, 2019, 02:29 AM
Registered User
Quote:
 Originally Posted by Buwa Term to google is "State space control" https://en.wikipedia.org/wiki/State-...representation https://in.mathworks.com/help/control/ref/initial.html
Wow. You helped me so much!
Thank you!
May 28, 2019, 02:34 AM
Registered User
Quote:
 Originally Posted by ShoeDLG Those derivatives come from linearizing and decoupling the aircraft’s equations of motion. To get the transient response you just advance the resulting equations of motion in time. You start with the aircraft at some initial state. Based on that state, and the forces and moments associated with it, you calculate the rate of change of the state variables. With the rates of change, you can calculate the aircraft’s state after some time step. Once you have the “new” state, you again calculate the rate of change of the state variables. With this information, you can advance by another time step. You continue this process for as long as you’re interested in the transient response. Typically you’d use a higher order time integration method (like Runge Kutta), but that’s not really necessary if you can afford to take very small time steps.
I have tried with time range from 0s to 30 with 0.2s in time step, but It's fail. the result of new state is a huge number up to 10e20 and I don't know why.
May 28, 2019, 07:53 AM
Closed Account
Quote:
 Originally Posted by phantrieuphu97 I have tried with time range from 0s to 30 with 0.2s in time step, but It's fail. the result of new state is a huge number up to 10e20 and I don't know why.
Your spiral mode is divergent, so a huge value might build up in 30 sec. Try 0 to 1 sec with a time step of 0.01

Roll mode also converges to a roll rate, so depending on what you are calculating the airplane might be rolling ang rolling and rolling, like an electric drill

You will also need a different time period for each mode. The roll mode converges much faster than the spiral diverges, and the Dutch roll is in between.

Do you know how to calculate frequency and damping ratio from the eigenvalues? Spend some time with this paper:

http://web.mit.edu/2.151/www/Handout...econdOrder.pdf
Last edited by NC14310; May 28, 2019 at 06:23 PM.