Trajectory tracking control with state restricted gains for a magnetic pendulum using electromagnetic actuators

Electromagnetic actuation results suitable for wireless driven motion, where the estimation of the force between magnetic elements is usually required. This force can lead to states where the magnetic-mechanical system remains fixed, requiring constraints to avoid the transgression of these states, and Barrier Lyapunov Functions (BLF) are useful for this purpose. This work presents an adaptive controller with BLF in a magnetic pendulum with state restrictions. It employs fixed electromagnets to induce motion on a pendulum with a permanent magnet as its bob. The force between the magnetic elements is obtained through approximation functions. A new implementation strategy for the control gains introduces the effect of state restrictions on the control action based on a control BLF. Results are analyzed in both simulations and experimental stages, which prove the advantages of employing BLF controllers in mechanical systems that require the avoidance of specific boundaries.