An adaptive sliding mode observer for inverted pendulum under mass variation and disturbances with experimental...

Area of Science:

• Control Systems Engineering
• Robotics
• Nonlinear Dynamics

Background:

• Accurate state and parameter estimation is crucial for controlling complex systems like inverted pendulums.
• Traditional observers struggle with disturbances and nonlinearities, particularly estimating unknown parameters such as mass.
• The observer matching condition is often violated in the presence of disturbances, complicating estimation.

Purpose of the Study:

• To develop a robust adaptive estimation approach for the inverted pendulum system.
• To simultaneously estimate system states, the nonlinear pendulum mass parameter, and unknown disturbances.
• To address the limitations of existing observers concerning disturbance rejection and parameter identification.

Main Methods:

• A two-stage observer design: an auxiliary high-gain observer cascaded with an adaptive sliding-mode observer.
• The high-gain observer estimates auxiliary outputs to circumvent observer matching condition issues caused by disturbances.
• Lyapunov stability analysis is employed to rigorously prove the stability of the proposed estimation scheme.

Main Results:

• The proposed method successfully estimates the states, unknown pendulum mass, and disturbances concurrently.
• Numerical simulations validate the theoretical findings and demonstrate the observer's performance.
• Experimental tests on a real inverted pendulum setup confirm the practical applicability and effectiveness of the estimation approach.

Conclusions:

• The cascaded observer design provides a robust solution for state and parameter estimation in disturbed nonlinear systems.
• The method effectively handles nonlinear parameter uncertainties and external disturbances.
• The approach shows significant promise for real-world applications requiring precise system identification and control.