Abstract
We propose a flatness based approach for controlling the inverted pendulum cart system, under the assumption that the pendulum state is always located on a vicinity of its unstable equilibrium point. This is achieved by representing the original system, as a chain of integrators with an additive nonlinear state dependent perturbation. After discarding the small nonlinear perturbation, we may directly use design tools provided by the the flatness approach. The effectiveness and robustness of the obtained control law, which turned out to have a large domain of attraction, were numerically assessed in the context of stabilization and, also, for a reference oscillatory trajectory tracking task.
Highlights
The inverted pendulum on a cart IPC is a mechanical device that consists of a free vertical rotating pendulum with its pivot point mounted on a cart moved by a horizontal input force
We propose a flatness based approach for controlling the inverted pendulum cart system, under the assumption that the pendulum state is always located on a vicinity of its unstable equilibrium point
The IPC is locally controllable around the unstable equilibrium point; so that it can be stabilized by means of a direct pole placement procedure 6
Summary
The inverted pendulum on a cart IPC is a mechanical device that consists of a free vertical rotating pendulum with its pivot point mounted on a cart moved by a horizontal input force. Based on the approximate flatness property of the IPC system 21 , we introduce a linear control law, in transformed coordinates, for approximately solving both the stabilization and the reference trajectory tracking problems, under the assumption that the pendulum is located inside a vicinity around its unstable equilibrium point. To this end, we first rewrite the original IPC model as if it were an integrator chain affected by a nonlinear perturbation.
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