In this paper a wheeled self-balancing robot is introduced as a benchmark mechanism to examine the performance of L1 adaptive control compared to the linear quadratic regulator. The paper focuses on the improvement of the reliability of the obtained results based on the benchmark system by introducing an ad-hoc technique to accurately simulate the wheeled mechanism. The aim of the paper is to reduce the level of approximation that inevitably exist in the analytical models. The deployed technique is verified via matching the developed linearized model and the analytical model. The grasped results show great proximity between the model of the proposed technique and the conventional mathematical models introduced in the literature. The overall benchmark mechanism accommodates the unmodeled dynamics, limitations and uncertainties of the system without mathematical hardships.