Geodesic
Rotary inverted pendulum: trajectory tracking via nonlinear control techniques
Kybernetika, Tome 38 (2002) no. 2, p. [217].

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The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is used here. As a specific feature, the approximate solution of the so-called regulator equation is used. The reason is that its exact analytic solution can not be, in general, expressed in the closed form. Though the approximate solution does not give asymptotically decaying tracking error, it provides reasonable bounded error. The performance of the designed feedback regulator is successfully tested via computer simulations.
Classification : 70Q05, 93B35, 93C10, 93D15
Keywords: rotary inverted pendulum; nonlinear control; trajectory tracking 
@article{KYB_2002__38_2_a6,
     author = {Ramos-Velasco, Luis E. and Ruiz-Le\'on, Jos\'e J. and \v{C}elikovsk\'y, Sergej},
     title = {Rotary inverted pendulum: trajectory tracking via nonlinear control techniques},
     journal = {Kybernetika},
     pages = {[217]},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2002},
     mrnumber = {1916453},
     zbl = {1265.93138},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2002__38_2_a6/}
}
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Ramos-Velasco, Luis E.; Ruiz-León, José J.; Čelikovský, Sergej. Rotary inverted pendulum: trajectory tracking via nonlinear control techniques. Kybernetika, Tome 38 (2002) no. 2, p. [217]. http://geodesic.mathdoc.fr/item/KYB_2002__38_2_a6/