A nonlinear control force is presented to stabilize the under-actuated inverted pendulum mounted on a cart. The control strategy is based on partial feedback linearization, in a first stage, to linearize only the actuated coordinate of the inverted pendulum, and then, a suitable Lyapunov function is formed to obtain a stabilizing feedback controller. The obtained closed-loop system is locally asymptotically stable around its unstable equilibrium point. Additionally, it has a very large attraction domain.
A nonlinear controller is presented for the stabilization of the underactuated inverted pendulum mounted on a cart. The fact that this system can be expressed as a chain of integrators, with an additionally nonlinear perturbation, allows us to use a nested saturation control technique to bring the pendulum to the top position, with zero displacement of the cart. The obtained closed-loop system is semiglobal, asymptotically stable, and locally exponentially stable, under the assumption that the position of the angle is initialized above the upper half plane.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.