Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the Cart-Pendulum...

Area of Science:

• Control Systems Engineering
• Robotics
• Nonlinear Control Theory

Background:

• Underactuated systems present significant control challenges due to fewer control inputs than degrees of freedom.
• Traditional control methods often struggle with uncertainties and robustness requirements in these systems.
• Backstepping and sliding mode control are established techniques for robust control design.

Purpose of the Study:

• To propose a novel integral backstepping sliding mode controller (IBSMC) for underactuated systems.
• To enhance robustness against matched and mismatched uncertainties.
• To achieve asymptotic stability with a chattering-free control law and reduced control effort.

Main Methods:

• Design of a feedback control law using the backstepping algorithm.
• Introduction of a sliding surface in the final stage of the backstepping design.
• Integration of integral action for improved disturbance rejection.
• Comparative analysis with a coupled sliding mode controller on the Cart-Pendulum System.

Main Results:

• The proposed IBSMC demonstrates immunity to matched and mismatched uncertainties.
• Asymptotic stability of the controlled system is guaranteed.
• The controller effectively performs swing-up and stabilization tasks on the Cart-Pendulum System.
• Simulation results show superior uncertainty rejection and reduced control effort compared to a conventional sliding mode controller.
• Chattering phenomenon in the control signal is significantly reduced.

Conclusions:

• The integral backstepping sliding mode controller offers a robust and effective solution for controlling underactuated systems.
• The controller provides enhanced performance in terms of uncertainty rejection and stability.
• The proposed method presents a viable alternative to existing control strategies for complex dynamic systems.