| Topic: |
Science > Physics |
| User: |
"Tomas Selnekovic" |
| Date: |
28 Dec 2005 06:45:24 PM |
| Object: |
Inverse pendulum on a cart problem |
Dear colleagues,
I am trying to program a java application which should demonstrate
the control of the inverse pendulum on a cart using a complex of two
neural
networks using two-stage learning process. The problem is keeping the
balance
of the rod of the pendulum.
I have found this web site which thorougly describes the problem of the
inverse
pendulum on a cart:
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp1/s7invp1.html
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp2/s7invp2.html
Equations (7.64) and (7.65) should give a complete state space
representation
of the nonlinear inverted pendulum.
I've managed to derive those equations but I don't know at all how to
use them.
I need to get about 100-200 discrete values of the dependency/function
f(angle of the rod)=x,
where x is the position of the cart on the x-axis in order to keep the
balance of the inverse pendulum.
for example when the angle is 0.3rad, then the cart should be at the
position 0.7 at the x axis.
or 0.7 rad then the cart should be at the position 0.4 on the x-axis.
or 0.3rad, then dx=0.03 (delta-shift of the cart)
-0.7rad then dx=0.08
Thanks for any hints.
Tomas Selnekovic
.
|
|
| User: "Dastardly Fiend" |
|
| Title: Re: Inverse pendulum on a cart problem |
29 Dec 2005 04:20:11 AM |
|
|
"Tomas Selnekovic" <tomas@rainwest.net> wrote in message
news:1135817124.002475.188720@f14g2000cwb.googlegroups.com...
Dear colleagues,
I am trying to program a java application which should demonstrate
the control of the inverse pendulum on a cart using a complex of two
neural
networks using two-stage learning process. The problem is keeping the
balance
of the rod of the pendulum.
I have found this web site which thorougly describes the problem of the
inverse
pendulum on a cart:
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp1/s7invp1.html
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp2/s7invp2.html
Equations (7.64) and (7.65) should give a complete state space
representation
of the nonlinear inverted pendulum.
I've managed to derive those equations but I don't know at all how to
use them.
I need to get about 100-200 discrete values of the dependency/function
f(angle of the rod)=x,
where x is the position of the cart on the x-axis in order to keep the
balance of the inverse pendulum.
for example when the angle is 0.3rad, then the cart should be at the
position 0.7 at the x axis.
or 0.7 rad then the cart should be at the position 0.4 on the x-axis.
or 0.3rad, then dx=0.03 (delta-shift of the cart)
-0.7rad then dx=0.08
Thanks for any hints.
Tomas Selnekovic
Have the neural network solve it.
Dastardly Fiend.
.
|
|
|
|
| User: "tadchem" |
|
| Title: Re: Inverse pendulum on a cart problem |
29 Dec 2005 04:50:05 AM |
|
|
Tomas Selnekovic wrote:
Dear colleagues,
I am trying to program a java application which should demonstrate
the control of the inverse pendulum on a cart using a complex of two
neural
networks using two-stage learning process. The problem is keeping the
balance
of the rod of the pendulum.
I have found this web site which thorougly describes the problem of the
inverse
pendulum on a cart:
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp1/s7invp1.html
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp2/s7invp2.html
Equations (7.64) and (7.65) should give a complete state space
representation
of the nonlinear inverted pendulum.
I've managed to derive those equations but I don't know at all how to
use them.
Good. At least you know a little calculus.
I need to get about 100-200 discrete values of the dependency/function
f(angle of the rod)=x,
where x is the position of the cart on the x-axis in order to keep the
balance of the inverse pendulum.
When the inverse pendulum is balanced, theta = 0, no matter what x is.
If theta is not equal to zero, then the pendulum is not in balance.
for example when the angle is 0.3rad, then the cart should be at the
position 0.7 at the x axis.
or 0.7 rad then the cart should be at the position 0.4 on the x-axis.
or 0.3rad, then dx=0.03 (delta-shift of the cart)
-0.7rad then dx=0.08
If you are anywhere *near* the balance point, then theta is
approximately zero, cos(theta) ~1, and sin(theta)~0, and Equation 7.57
simplifies to:
m*(x") + m*l*(theta") = 0
X itself is arbitrary, since if the mechanism is working the pendulum
will remain balanced wherever the cart is. The scalar value of x is
simply a 'constant of integration.'
HTH
Tom Davidson
Richmond, VA
.
|
|
|
| User: "Tomas Selnekovic" |
|
| Title: Re: Inverse pendulum on a cart problem |
29 Dec 2005 10:33:22 AM |
|
|
tadchem wrote:
Tomas Selnekovic wrote:
Dear colleagues,
I am trying to program a java application which should demonstrate
the control of the inverse pendulum on a cart using a complex of two
neural
networks using two-stage learning process. The problem is keeping the
balance
of the rod of the pendulum.
I have found this web site which thorougly describes the problem of the
inverse
pendulum on a cart:
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp1/s7invp1.html
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp2/s7invp2.html
Equations (7.64) and (7.65) should give a complete state space
representation
of the nonlinear inverted pendulum.
I've managed to derive those equations but I don't know at all how to
use them.
Good. At least you know a little calculus.
I need to get about 100-200 discrete values of the dependency/function
f(angle of the rod)=x,
where x is the position of the cart on the x-axis in order to keep the
balance of the inverse pendulum.
When the inverse pendulum is balanced, theta = 0, no matter what x is.
If theta is not equal to zero, then the pendulum is not in balance.
for example when the angle is 0.3rad, then the cart should be at the
position 0.7 at the x axis.
or 0.7 rad then the cart should be at the position 0.4 on the x-axis.
or 0.3rad, then dx=0.03 (delta-shift of the cart)
-0.7rad then dx=0.08
If you are anywhere *near* the balance point, then theta is
approximately zero, cos(theta) ~1, and sin(theta)~0, and Equation 7.57
simplifies to:
m*(x") + m*l*(theta") = 0
X itself is arbitrary, since if the mechanism is working the pendulum
will remain balanced wherever the cart is. The scalar value of x is
simply a 'constant of integration.'
HTH
Tom Davidson
Richmond, VA
Tom,
thanks for your answer.
cos(theta) ~1, and sin(theta)~0
I didn't realize this .., now it's clear :)
Tomas
.
|
|
|
|
|
|
Related Articles |
|
|
