This paper is devoted to the modelling and tracking control for a class of cart-pendulum systems which are driven by DC motor. First, the dynamic model for the cart-pendulum system is established by using dynamic and static method and the principle of relative motion, in which both the disturbance influence of the external environment on the mechanical system part and that of the heating for the resistor and other devices on the circuit part are considered. Remarkably, the disturbance is

more »

... c but does not necessarily have known period and upper bound which results in the ineffectiveness of the traditional method on this issue. Then, by combining the vectorial backstepping design method with disturbance learning and switching compensation mechanism, a state feedback controller is designed explicitly where certain pivotal controller parameters are included and adjusted online. It is proved that the switching mechanism will stop after some time, and then the proposed controller guarantees that all the states of the resulting closed-loop system are bounded while the system output asymptotically tracks the given reference signal. Finally, a simulation example is provided to verify the validity of the theoretical results. INDEX TERMS Cart-pendulum system, tracking control, switching control, disturbance.