Cascade direct adaptive fuzzy control design for a nonlinear two-axis inverted-pendulum servomechanism

Area of Science:

• Robotics and Control Systems
• Nonlinear System Control
• Adaptive Control Theory

Background:

• Two-axis inverted-pendulum servomechanisms represent complex nonlinear, unstable, nonminimum-phase, and underactuated systems.
• Designing effective control for simultaneous stabilization and tracking in such systems is challenging.
• Conventional methods like computed torque control are not directly applicable to these underactuated systems.

Purpose of the Study:

• To develop and analyze a cascade direct adaptive fuzzy control (DAFC) scheme for a two-axis inverted-pendulum servomechanism.
• To achieve real-time stabilization and accurate tracking control for the system.
• To guarantee overall system stability using Lyapunov stability analysis.

Main Methods:

• Implementation of a cascade DAFC scheme with distinct inner and outer control loops.
• Inner loop: DAFC law design for fitting the stick angle vector to a reference command.
• Outer loop: Adaptive path planner for the cart position vector to track a command signal.
• Lyapunov stability analysis to derive adaptive algorithms and ensure closed-loop stability.

Main Results:

• The cascade DAFC system successfully achieves simultaneous convergence of stick angle and cart position tracking errors to zero.
• Numerical simulations and experimental results validate the proposed control scheme.
• The system demonstrates favorable stabilizing and tracking performance.

Conclusions:

• The proposed cascade DAFC scheme effectively controls the two-axis inverted-pendulum servomechanism.
• The control strategy is robust to system uncertainties.
• This approach offers a viable solution for controlling complex underactuated nonlinear systems.