Newtonian Dynamics Approach for Single Inverted Pendulum System with Control Method Comparison

In this paper, we develop a mathematical model of the single inverted pendulum system using Newtonian dynamics principles. The modeling process involves deriving equations of motion through force-balance analysis and linearization around the unstable equilibrium point. Subsequently, we conduct comparative simulation studies analyzing three control approaches: PID control (implementing proportional, integral, and derivative gains), LQR control (utilizing state-weighting matrices Q and R for optimization), and fuzzy logic control (employing rule-based inference systems). The simulation architecture incorporates MATLAB/Simulink implementations with ode45 solver configuration for dynamic simulation. Through these analyses, we derive theoretically significant insights for directional research. Furthermore, we explore practical considerations including each method's robustness to disturbances, computational requirements, and parameter tuning complexities, along with potential enhancements such as gain scheduling for PID, integral action for LQR, and adaptive mechanisms for fuzzy controllers to improve system performance.