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runway
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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 website 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.
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
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 website 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.
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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