Dear colleagues,(adsbygoogle = window.adsbygoogle || []).push({});

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 [Broken]

http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s7/s7invp2/s7invp2.html [Broken]

Equations (7.64) and (7.65) should give a complete state space

representation

of the nonlinear inverted pendulum.

Equations (7.55) and (7.57)

m*x''*cos(theta) + m*l*theta'' = m*g*sin(theta) (7.57)

(M+m)*x'' - m*l*sin(theta)*(theta')^2 + m*l*cos(theta)*theta'' = u (7.55)

define this system according to the figure.

I've managed to derive those equations but I don't know at all how to

use them to compute what force must I apply to the cart in order to keep the balance of the pendulum when theta != 0. (non zero - then the pendulim is not balanced).

Is there any method to solve those equations when initial conditions are given?

What force 'u' do I need to apply to the cart when the angle between the axis perpendicular to the cart and the rod of the pendulum is theta?

Thank you for any hints.

Tomas Selnekovic

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# Inverse pendulum on a cart

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