Stability control of a double inverted pendulum using a decoupled backstepping sliding mode strategy

Abstract

The double inverted pendulum on a cart (DIPC) is a classical benchmark in nonlinear control due to its high instability, underactuated structure, and complex dynamic behavior. Traditional control approaches, such as Linear Quadratic Regulators (LQR) or conventional Sliding Mode Control (SMC), often face limitations in robustness and dynamic decoupling when applied to such systems. In response to these challenges, this study presents a Decoupled Backstepping Sliding Mode Control (DB-SMC) strategy that integrates the systematic design framework of backstepping with the robustness properties of sliding mode control. By introducing intermediate virtual control surfaces, the DB-SMC method effectively decouples the dynamics of the cart and the two pendulums, simplifying controller design and improving system stability. The control law is derived using Lyapunov stability theory to ensure convergence and robustness in the presence of uncertainties. Simulation results demonstrate that the proposed method achieves fast convergence, reduced overshoot, and strong disturbance rejection compared to traditional methods. The effectiveness of the DB-SMC controller highlights its potential for broader applications in nonlinear and underactuated systems.