Swing-up time analysis of pendulum

摘要

Swing-up control of a single pendulum from the pendant to the upright position is firstly surveyed.The control laws are comparatively studied based on swing-up time from a given initial state to the upright position.The State Dependent Riccati Equation is found effective for designing the swing-up control law under saturating control input.The control law is extended to a linear combination of sine function of the angle and the angular velocity,and a variable structure control with a sliding mode given by the linear combination.Making the swing-up time correspond to a colour,which is similar to the Fractal analysis,colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like figures.