Abstract
For the problem of stabilizing an inverted pendulum with restricted travel, a saturating control law is developed that satisfies the amplitude constraint on the cart and has a large region of attraction. The analysis and design is performed based on the linearlized model of the system, as in the study of Lin et al. The control law has two design parameters: T and k, which are both positive. As T approaches 0, the region of attraction becomes to close to the maximal one. These parameters are chosen to optimize the transient response of the system considering the input constraint, the bandwidth of the actuator, observation noise, etc. The performance of the control system, the size of the region of attraction, and the robustness for measurement and modeling errors are evaluated, via simulation and experiment, by comparing them with the ones of the control system designed by Lin et al.'s method.
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