Nonlinear controller for an inverted pendulum having restricted travel
Automatica (Journal of IFAC)
Linear controller for an inverted pendulum having restricted travel: a high-and-low gain approach
Automatica (Journal of IFAC)
Linear Optimal Control Systems
Linear Optimal Control Systems
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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 explicit expression of the region of attraction is also obtained. The analysis and design are performed based on the linearized 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 approaches the maximal one. These parameters are chosen to optimize the transient response of the closed-loop system considering the input constraint, observation noise, etc. The effectiveness of the control law is demonstrated by simulations and experiments.