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 example in demonstrating and motivating various control design techniques. In this paper, we provide a linear state feedback design technique for balancing an inverted pendulum. The pivot of this pendulum is mounted on a carriage which has limited horizontal travel. For any given (arbitrarily small) allowable travel of the carriage, our design yields a linear state feedback controller which balances the pendulum with an infinite amount of gain margin in the sense that, if the feedback gain is perturbed by any multiplying factor greater than one, the controller will still balance the pendulum without requiring greater traveling distance than the maximum allowable.