Robust multivariable dynamic surface control for position tracking of a bicycle

This paper considers position tracking control of a bicycle modeled as a four-state nonlinear dynamic system, with two inputs: the angular velocity of the handle bars and the forward velocity of the bicycle. The performance of a robust multivariable dynamic surface controller was compared to that of a multivariable controller using feedback linearization. In order to design both controllers, the matched four-state system was extended into a mismatched six-state system, with two inputs: the angular velocity of the handle bars and the jerk (second derivative of the forward velocity) of the bicycle. Integrating the jerk we approximate the necessary forward velocity input. We assume that the disturbances in the original channels are bounded, and we derive state-dependent disturbance bounds for the new channels. These bounds are used in the design of the dynamic surface controller. Both controllers perform well in the absence of disturbances. The dynamic surface controller is more robust when disturbances are introduced; however, a large control effort is required to reject the disturbances.