Swinging-up and stabilization control based on natural frequency for pendulum systems

This paper proposes a swinging-up and stabilization method for inverted pendulums based on a pendulum oscillation model. A normalized oscillation model is derived by using only one model parameter, i.e., the natural frequency of a pendulum. As a control strategy, energy-based control with a normalized energy model is utilized for the swinging-up from the pendant position. For the stabilization of the pendulum at the upright position, variable structure system (VSS) type adaptive control is designed through the linearized oscillation model. Validity of the proposed method has been confirmed by simulation of an inverted pendulum on a cart. Swinging-up and stabilization control was realized by using only the natural frequency of the pendulum, and the proposed method was also confirmed to be robust against parameter perturbation for the natural frequency. Stability of the designed controller was proven for a given condition that angular velocity of the pendulum has an upper bound.