Stabilization of the cart pole system: by sliding mode control

This paper presents a control strategy designed as a combination of a PD controller and a twisting-like algorithm to stabilize the damped cart pole system, provided that the pendulum is initially placed within the upper-half plane. To develop the strategy, the original system is transformed into a four-order chain of integrator form, where the damping force is included through an additional nonlinear perturbation. The strategy consists of simultaneously bringing the position and velocity of the pendulum to within a compact region by applying the PD controller. Meanwhile, the system state variables are brought to the origin by the twisting-like algorithm. The corresponding convergence analysis is done using several Lyapunov functions. The control strategy is illustrated with numerical simulations.