To achieve accurate position tracking, there is need to develop high-fidelity robot arm models that are compliant and affordable. However, physics-based models are constrained by their stiffness and complexity. Reduced-order models developed from data through sub-space system identification is proposed as a solution to this problem. A high-fidelity simulation model of a two-link robot arm, developed in MATLAB and Simulink was used to generate synthetic data and the data acquired was used for estimation and validation of first- and second-order linear state-space models. Due to its effective tracking characteristics, model predictive control technique was used for trajectory tracking. The results of the simulations demonstrate that the first-order and second-order models can track the intended set-points accurately, but at the cost of larger joint torques required to counteract gravity. The results demonstrate that low-order and data-compliant models can be used to follow trajectories with high precision. MATLAB 2020a was used for all simulations.