Fuzzy Control of First-Level Inverted Pendulum Using Fusion Function Approach Based on Optimal Control

This study investigates fuzzy control for a first-level inverted pendulum by integrating fuzzy logic with optimal control principles through a fusion function approach. The research involves Simulink simulations to analyze how different parameters affect system response characteristics. The implementation typically includes designing membership functions for pendulum angle and angular velocity, establishing fuzzy rule bases using linguistic variables, and applying defuzzification methods like centroid calculation. For optimal control integration, algorithms such as LQR (Linear Quadratic Regulator) can optimize performance indices through Riccati equation solutions. Additional robustness analysis can be incorporated to enhance system stability and performance metrics. The fuzzy controller design employs fuzzy inference mechanisms (Mamdani or Takagi-Sugeno models) and fuzzy logic operations to refine control strategies. Optimization techniques from optimal control theory, including gradient-based algorithms or dynamic programming, can further tune system parameters against performance criteria. This comprehensive approach facilitates deep understanding of inverted pendulum control principles, improves control system stability and performance, and provides practical guidance for real-world engineering applications. Key implementation aspects involve Simulink blocks for fuzzy logic controllers, state-space representations for optimal control, and sensitivity analysis modules for robustness verification.