Optimal regulator for the inverted pendulum via Euler-Lagrange backward integration

Authors:
Thomas HolzhüTer
Affiliations:
Fachbereich Elektrotechnik und Informatik, Hochschule für angewandte Wissenschaften Hamburg, Berliner Tor 7, 20099 Hamburg, Germany
Venue:
Automatica (Journal of IFAC)
Year:
2004

Citing 4
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Abstract

We present a time invariant nonlinear controller for the inverted pendulum based on optimal control, which is defined for all pendulum angles. The paper provides a case study in the brute force method of calculating the extremal field by solving the Euler-Lagrange equations backward in time, thus exploring the stable manifold of the Hamiltonian flow. The controller is only given numerically on an interpolation grid. We use this controller for closed loop simulations corroborating considerable gain robustness.