LINEAR CONTROLLER FOR AN INVERTED PENDULUM HAVING RESTRICTED TRAVEL -A HIGH-AND-LOW GAIN APPROACH

The problem of balancing an inverted pendulum has been a benchmark exa mple in demonstrating and motivating various control design techniques . In this paper, we provide a linear state feedback design technique f or balancing an inverted pendulum. The pivot of this pendulum is mount ed on a carriage that has limited horizontal travel. For any given (ar bitrarily small) allowable travel of the carriage, our design yields a linear state feedback controller that balances the pendulum with an i nfinite amount of gain margin in the sense that, if the feedback gain is perturbed by any multiplying factor greater than one, the controlle r will still balance the pendulum without requiring greater traveling distance than the maximum allowable. Copyright (C) 1996 Elsevier Scien ce Ltd.