PI-controller for inverted pendulum

Version 1.0.0.0 (521 ko) par Maxim Vedenyov
animated, with derivation in jpg-image
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Mise à jour 26 nov. 2011

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http://simulations.narod.ru/
It is inverted pendulum. Down point is base can be controlled. It can be moved horizontally only. PI (not PID) controller used to set the pendulum in up direction. There are friction in base and frictiopn from air simulated. Random kick is applied periodically. The PI-controller for base velocityt is
dx/dt=p*phi+(q-g)*integral(phi*dt)
where phi is angle counted from vertical position. There was found theoretically that optimal p and q is defined by equation: p^2/R=-q, p<0,q<0. R is pendulum length.

See formula.jpg for derivation of equation of motion.

See formulas2_pd.jpg for derivation optimal gains. In this formulas phi=theta-pi is angle counted from vertical position. The PI-contoller:
d2x/dt2=p*dtheta/dt+(q-g)*(theta-pi)

See animation here:
http://www.youtube.com/watch?v=_2g8bzSk18I

Citation pour cette source

Maxim Vedenyov (2024). PI-controller for inverted pendulum (https://www.mathworks.com/matlabcentral/fileexchange/33942-pi-controller-for-inverted-pendulum), MATLAB Central File Exchange. Récupéré le .

Compatibilité avec les versions de MATLAB
Créé avec R2010b
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Version Publié le Notes de version
1.0.0.0