The performance of the classical and adaptive backstepping control schemes for the angular position control of a nonlinear Propeller-Driven Pendulum System (PDPS) is investigated in this paper. A Particle Swarm Optimization (PSO) algorithm has been utilized to tune the design parameters of the proposed controllers. Based on the Lyapunov stability analysis the classical and the Adaptive Back-Stepping Controllers have been constructed in order to prove the convergence of the system's error with time. The Adaptive Backstepping Controller (ABSC) is designed to compensate for the variation in the system's mass magnitude. In terms of system transient response, a comparison study of the effectiveness of both controllers has been presented in this work. The simulation results have been obtained based on the MATLAB software. In addition, a comparison study between the proposed controllers and other controllers has been listed to demonstrate the effectiveness of the proposed controller. The simulation results show that the PSO based classical Backstepping Controller (BSC) has a better performance in terms of reducing the settling time, the steady-state error, and the Root Mean Square Error (𝑅𝑀𝑆𝐸) value in comparison with the STSMC and SMC. In addition, the simulation results reveal that the PSO based ABSC has a better performance in terms of reducing the steady state error and the maximum overshoot in comparison with the PSO based BSC and ASTSMC.