Adaptive Control of a Gyroscopically Stabilized Pendulum and Its Application to a Single-Wheel Pendulum Robot

This paper presents an adaptive decoupling control strategy for a gyroscopically stabilized pendulum. In the proposed model, the gyro moment acts directly on the pivot of the pendulum, the magnitude of which is restricted by gyroscopic precession. A decoupling algorithm based on virtual control is proposed to regulate the upright posture of the pendulum through gyroscopic precession. Virtual control is considered a control torque that acts on the pivot of the pendulum; it forms nonlinear mapping along with the precession command. Consequently, gyroscopic precession matches the stability condition of the pendulum well. In the control design, an adaptive disturbance estimation method based on a smooth saturation function is proposed to avoid the adverse effects of parametric uncertainties, mechanical vibrations, and system nonlinearities. Accurate estimation of unstructured disturbances is easily achieved by adaptively tuning the weight coefficient of the saturation function. The results of stability analysis, simulations, and experiments show the validity of the proposed pendulum model and adaptive decoupling control scheme.