Nonlinear control design for stabilization and tracking of a rotary inverted pendulum

Area of Science:

• Robotics and Control Systems
• Nonlinear Dynamics
• Mechatronics

Background:

• Rotary inverted pendulum (RIP) systems are inherently unstable and underactuated, posing significant control challenges.
• Existing control methods often rely on linearized models, limiting performance to small operational regions.
• Advanced nonlinear control techniques are difficult to apply effectively to these underactuated systems.

Purpose of the Study:

• To develop a novel nonlinear controller framework for robust tracking and stabilization of RIP systems.
• To overcome the limitations of linearized models and address the underactuation challenge in RIP control.
• To enhance the operational region and stability of the pendulum using nonlinear dynamics.

Main Methods:

• A second-order sliding mode controller (SOSMC) was designed based on a proportional-integral-derivative (PID) sliding surface.
• The controller incorporates the nonlinear dynamic model of the RIP system for improved stabilization.
• Performance was evaluated against standard sliding mode control (SMC), reinforced PID-SMC, and linear quadratic regulator (LQR).

Main Results:

• The proposed SOSMC controller demonstrated superior tracking accuracy and faster response with reduced overshoot compared to other methods.
• Mean Square Error (MSE) for arm angle was minimized (0.2229), and pendulum angle MSE was reduced by up to 69.36%.
• The controller achieved significant reductions in control input RMS values (up to 41.99%) compared to benchmarks, indicating efficient energy consumption.

Conclusions:

• The developed SOSMC framework effectively stabilizes the RIP system in a larger region and achieves precise trajectory tracking.
• The controller offers significant improvements in speed, accuracy, and energy efficiency over conventional control strategies.
• This nonlinear approach provides a robust solution for controlling challenging underactuated systems like the RIP.