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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Fri, 7 Jan 2000 01:19:06 GMT
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Reply-To:
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<cgschaef@futurelinkinc.SPAMLESScom>
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Viewed:
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918 times
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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 I concur is
more desirable for controller design and analysis. I'm not sure why a fuzzy
logic approach is needed here, particularly since this is a fairly common
problem for optimal control and a number of solutions already exist, are
easily implemented, and are not computationally intensive. By their nature,
these optimal solutions can deal with the uncertainties associated with the
nonlinearities (to a degree).
My $0.02 ...
Carl
> -----Original Message-----
> From: news-gateway@lugnet.com [mailto:news-gateway@lugnet.com]On Behalf
> Of Jacob Schultz
> Sent: Thursday, January 06, 2000 6:39 PM
> To: lugnet.robotics@lugnet.com
> Subject: Re: Balancing Bots
>
>
> 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
>
> --
> /* Please notice another e-mail address change: Letters must be sent to
> eighter schertz@superbruger.dk (both of us), gandalf@superbruger (jacob)
> or galadriel@superbruger (anne). The @get2net.dk addresses will not work
> anymore (soon). *** Geek by nature - Linux by choice ***/
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Message is in Reply To:
 | | Re: Balancing Bots
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| (...) 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 (...) (25 years ago, 6-Jan-00, to lugnet.robotics)
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