[Scilab-users] Bicycle Dynamics

[Gona]

Hello All,

First time poster here. Apologies in advance I am doing something in a wrong
way or not following the conventions. 

I have been using Scilab for few days now and I am trying to model a Bicycle
with it. The output of the system I modeled is not what i expected. 
As a first time user i am not so sure whether I have done the steps right or
modeled the system right in first place. If anyone with some modeling
experience can comment on whether what I have done is wrong or right it
would be much appreciated.

To start with I modeled the bicycle as an inverted pendulum. and I am trying
to control the bike with steering angle.
<http://mailinglists.scilab.org/file/n4030466/BikeLeanForces3.png> 

As we can see the horizontal force is a function of turning radius and it in
turn a function of steering angle.
Function between steering angle and turning radius is given by,
<http://mailinglists.scilab.org/file/n4030466/delta2r.png> 

After simple algebra I got the dynamic equation of the bike to be,
<http://mailinglists.scilab.org/file/n4030466/CodeCogsEqn.gif> 

1. Can anyone please comment up to this point what I have done is correct ?

Then I tried to model this equation in XCOS and this is the block diagram I
came up with.

<http://mailinglists.scilab.org/file/n4030466/bike-xcos.gif> 

2. Can anyone please comment up to this point what I have done is correct.
May be I have committed a stupid mistake like changing +-?

The output of the system came like this for a delta input in the steering
angle.
<http://mailinglists.scilab.org/file/n4030466/Output.gif> 

3. I guess the output should be diverging theta with exp like behavior. But
may be the output is linear because with theta change there is also the
turning radius changes and it compensate the m.g.sin\theta.l term. 

If anyone could confirm that the model seems to be realistic/ or correct I
would be so thankful. 

Thanks again
Gona.












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