NONLINEAR CONTROLLER FOR AN INVERTED PENDULUM HAVING RESTRICTED TRAVEL

The problem of balancing an inverted pendulum by moving the pivot hori zontally on a carriage is commonly used in control education to provid e a dramatic experiment and to illustrate the difficulties in controll ing a plant having unstable open-loop poles. This paper derives a lowe r bound on the horizontal travel required by the carriage in order to raise the pendulum to the vertical from an angle slightly different fr om its unstable equilibrium. A nonlinear controller is then described that, in principle, can achieve this lower bound. It is then shown tha t the pendulum can be driven from its stable, pendant, state arbitrari ly 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.