Subject:
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Re: Balancing Bots
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Newsgroups:
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lugnet.robotics
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Date:
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Thu, 6 Jan 2000 23:38:47 GMT
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Viewed:
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754 times
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Andy Gombos wrote:
>
> Not if you scale it up(alot).The higher the gear ratio, the higher the virtual
> accuracy.
> I hope I said that right, it sorta doesn't sound right.. If this is wrong the
> plaese correct me.
Of course you are right, but there are some problems:
It depends on the quality of the gearing. The problem here is backlash -
it doesn't help much to have 1/10 deg. resolution if you have 5 deg.
backlash in the gearing. Another problem is friction. If you do calculus
on inverted pendulums you will soon find out, that you end up with
unlinear differential equations if the friction is "dry" (don't know the
correct English word). Unlinearity is a bad thing, but fuzzy logic can
help a bit here.
By the way, the equations for a car mounted with a homogenous inverted
pendulum are:
4mL*sin(q)*q'^2 - 3mg*sin(q)*cos(q) + 4u
p'' = ------------------------------------------
4(M+m) - 3m*cos(q)^2
3g(M+m)*sin(q) - 3mL*sin(q)*cos(q)*q'^2 - 3*cos(q)*u
q'' = ------------------------------------------------------
L(4(M+m) -3m*cos(q)^2)
p is the cars position
q is the angle of the pendulum (0 is vertical)
m is the mass of the pendulum
L is half the length of the pendulum
g is the gravety (9.81 m/s^2)
M is the mass of the car
u is the force on the car
The force u can generaly be derived from the torque of a motor. This
implies a model of a motor.
The equations above can be changed into a state-space model, and the
optimal linear controller can be designed.
Just in case someone is interested
Jacob
--
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eighter schertz@superbruger.dk (both of us), gandalf@superbruger (jacob)
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Message has 1 Reply:
 | | RE: Balancing Bots
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| Jacob, Off-topic, I know, but .... I believe that the equations that you provided, although for a frictionless inverted pendulum, are nonlinear. You can linearize these equations about some reference point and convert them to state-space form, which (...) (25 years ago, 7-Jan-00, to lugnet.robotics)
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Message is in Reply To:
| | Re: Balancing Bots
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| Not if you scale it up(alot).The higher the gear ratio, the higher the virtual accuracy. I hope I said that right, it sorta doesn't sound right.. If this is wrong the plaese correct me. Andy (...) (25 years ago, 6-Jan-00, to lugnet.robotics)
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