Question on input and output from linear state space system

[xxyao-95]

Hi
From the discussion #137, I understand that the aeroelastic model is in non-dimentional form. Hence if I extracted the state space matrices and I run a simulation in matlab with gust velocity as input, and tip deflection as output, I need to first scale my input to make it non-dimentional and the scale my output to get the deflection in meters, is this correct?

[ngoiz]

That is correct, when the system is scaled it includes inputs and outputs

[ACea15]

Dear xxyao,
Your definitions seem ok, have a look to the aeroelastic integration section in the following paper,
https://arc.aiaa.org/doi/abs/10.2514/1.J058153
and see if you can make sense of the theory and spot what you are missing in your MATLAB code.

[ngoiz]

Also, make sure that you are setting up your desired scaling factors through the setting in the LinearUvlm module (the setting ScalingDict) which is shown on the Goland Example

[xxyao-95]

Thanks for your reply! I will look into the paper.

For the ScalingDist Setting, just to double check that, I am assembleing state space at 50m/s
'ScalingDict': {'length': 0.5 * ws.c_ref,
'speed': u_inf,
'density': rho},
so my length used is half chord, speed is 50m/s and rho is the air density at the altitude where I am simulating.
Also can I double check that the 'dt' in my 'aero_settings' should be the dt at 50m/s which is dt = chord/M/U_inf?

[ngoiz]

Yes, the dt in your settings is your dimensional time step. The non-dimensionalisation is performed within SHARPy. If you are having trouble getting your scalings correct it might be worth going through the code seeing how the flutter analysis of the Goland wing is performed, for example.

Starting in the AsymptoticStability postproc, the system is rescaled for each velocity here. This updates the coupled aeroelastic system at this point which effectively means updating the structural equations with the new time scaling as done here.

[xxyao-95]

Hi, I finally got the correct output from the state space system in matlab. I found out that I forgot to transpose the matrix in matlab when reading it. Here is the result. The gust input is scaled by u_inf when it is input into the system. Thank you all for your help!