Adaptive simple pendulum swing-up controller based on the closed-loop fundamental dynamics

An adaptive energy-based swing-up controller for simple pendulums is presented. A state transformation from cartesian to polar phase space followed by approximation steps leads to the fundamental dynamics of the controlled simple pendulum. Based on the fundamental dynamics, the unknown natural frequency is estimated and a control gain is adjusted such that the system energy follows desired reference dynamics. We prove convergence of the natural frequency estimate to the true value as well as convergence of the system energy to the desired energy level under the fundamental dynamics assumption. The implications of the fundamental dynamics approximation are evaluated in simulation. Noise affected angle measurements simulate a realistic inverted pendulum experiment. The successful swing-up into the highly nonlinear regimes of the simple pendulum support the applicability of the fundamental dynamics.