This paper presents a comprehensive control study of an inverted pendulum on cart system enhanced with torsional spring-damper dynamics and cart damping. A Linear Quadratic Regulator (LQR) was designed using a linearized model, while Model Predictive Control (MPC) and Reinforcement Learning (RL) controllers were augmented with Monte Carlo simulations to evaluate robustness and sensitivity. Results demonstrated comparable performance among all methods in linear regimes, with stabilization times under 20 seconds and overshoot variation of 3%. To address nonlinear dynamics, a hybrid SMC-RL strategy was developed, reducing settling time and improving capability of maintaining stability under nonlinear behavior and large initial angles to 120-150°. The proposed SMC-RL framework achieved a success rate in stabilizing the system from diverse initial conditions, significantly outperforming standalone controllers in transient response and adaptability. System stability was formally verified through Lyapunov analysis and empirically confirmed by Monte Carlo simulations, which demonstrated consistent performance with minimal standard deviation across 80 randomized trials.