Abstract
the problem of balancing an inverted pendulum by moving the pivot horizontally on a carriage is commonly used in control education to provide a dramatic experiment and to illustrate the difficulties in controlling a plant having unstable open-loop poles. This paper derives a lower bound on the horizontal travel required by the carriage in order to raise the pendulum to the vertical from an angle slightly different from its unstable equilibrium. A nonlinear controller is then described that, in principle, can achieve this lower bound. It is then shown that the pendulum can be driven from its stable, pendant, state arbitrarily close to its unstable equilibrium by a controller with arbitrarily small horizontal travel. Finally, an output feedback version of this controller has been built. The experimental results are reported.
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