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Entry  Wed Nov 17 09:27:04 2021, Jiri Smetana, General, General, Lagrangian Model - Translation & Pitch plant_all_tfs.png
    Reply  Wed Dec 15 06:43:43 2021, Jiri Smetana, General, General, Lagrangian Model - Translation & Pitch 
Message ID: 50     Entry time: Wed Dec 15 06:43:43 2021     In reply to: 49
Author: Jiri Smetana 
Type: General 
Category: General 
Subject: Lagrangian Model - Translation & Pitch 

I've checked the validity of my state space model in a couple of ways so that we have confidence in the results that it gives. I've checked the DC gain of the transfer functions where it is non-zero. I did this by solving the static balance of forces problem in the extended body model by hand to get the DC CoM position as well as the pitch angle of both masses. In the previous ELOG entry I didn't quite do this for all transfer functions so here I completed the check. My values agree with the model's values to within 10% at the worst end and to within 0.1% at the best end. I performed a second check to see if the frequencies occur in the correct places by considering the case of very low coupling between the different resonant modes. It's difficult to check this in the case where the modes are strongly coupled (for example length-pitch is strong or the two pitch modes are close together) but if I sufficiently separate them, I get very good agreement between my analytic approximation and the state space model.

The model can easily be converted from one that gives motion in X and RY into one that gives motion in Y and RX. Running the model for both directions gives the following list of resonances (note pendulum modes in X and Y direction are identical):

Resonance Type Frequency [Hz]
Pendulum 1 0.85
Pendulum 2 2.10
Pitch 1 0.46
Pitch 2 2.37
Roll 1 17.13
Roll 2 46.09

Given that I think the model seems to give sensible values, I've pushed the updated model to the GitLab repository. It is now possible to quickly change the parameters of the suspension and very quickly see the corresponding shift in the resonances. To change the parameters, open the plain text file called 'params' and change the values to the new ones. Afterwards, run the file 'ss_extended.py', which will solve the state space model, save the resulting ABCD matrices to a folder and print out the values of the resonances to terminal.

Quote:

I've been having a look at the transfer functions for the translation and pitch of both masses. I'm attaching the plot of all input-to-output transfer functions of interest so far. Here I've identified the pitch resonances of the two masses (one each) as well as the two pendulum modes. I need to now investigate if they occur in the correct places. I have confirmed the DC response by directly solving the statics problem on paper.

 

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