Dynamical modeling and sliding mode control of inverted pendulum systems

Based on Lagrange equations, a brief way of the dynamical modeling method for n order inverted pendulum systems is proposed. For one order inverted pendulum systems in presence of uncertain length of pendulum and external disturbances, a novel sliding mode control strategy is presented. To simplify the controller design, the model of one order inverted pendulum systems is transformed to cascade normal forms by coordinate transformation. The sliding surface is designed to stabilize the indirectly controlled modes. A continued arithmetic of sign function is used to reduce chattering. The stability of the control system is proved by Lyapunov theory and perturbation theory. The simulation results are included to indicate the effectiveness and robustness of the proposed controller.