A Novel Hierarchical Recursive Nonsingular Terminal Sliding Mode Control for Inverted Pendulum

This paper aims to develop a novel hierarchical recursive nonsingular terminal sliding mode controller (HRNTSMC), which is designed to stabilize the inverted pendulum (IP). In contrast to existing hierarchical sliding mode controllers (HSMC), the HRNTSMC significantly reduces the chattering problem in control input and improves the convergence speed of errors. In the HRNTSMC design, the IP system is first decoupled into pendulum and cart subsystems. Subsequently, a recursive nonsingular terminal sliding mode controller (RNTSMC) surface is devised for each subsystem to enhance the error convergence rate and attenuate chattering effects. Following this design, the HRNTSMC surface is constructed by the linear combination of the RNTSMC surfaces. Ultimately, the control law of the HRNTSMC is synthesized using the Lyapunov theorem to ensure that the system states converge to zero within a finite time. By invoking disturbances estimation, a linear extended state observer (LESO) is developed for the IP system. To validate the effectiveness, simulation results, including comparison with a conventional hierarchical sliding mode control (CHSMC) and a hierarchical nonsingular terminal sliding mode control (HNTSMC) are presented. These results clearly showcase the excellent performance of this approach, which is characterized by its strong robustness, fast convergence, high tracking accuracy, and reduced chattering in control input.