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.

JO - Bulletin of the Polish Academy of Sciences: Technical Sciences L1 - http://journals.pan.pl/Content/111820/PDF/%2852-3%29153.pdf L2 - http://journals.pan.pl/Content/111820 IS - No 3 EP - 163 KW - pendulum control KW - state dependent Riccati equation KW - nonlinear control KW - artiļ¬cial gravity KW - fractal ER - A1 - Furuta, K. A1 - Iwase, M. VL - vol. 52 JF - Bulletin of the Polish Academy of Sciences: Technical Sciences SP - 153 T1 - Swing-up time analysis of pendulum UR - http://journals.pan.pl/dlibra/docmetadata?id=111820