As a key type of mobile robot, the two-wheel mobile robot has been developed rapidly for varied domestic, health, and industrial applications due to human-like movement and balancing characteristics based on the inverted pendulum theory. This paper presents a developed Two-Wheel Self-Balanced Robot (TWSBR) model under road disturbance effects and simulated using MATLAB Simscape Multibody. The considered physical-mechanical structure of the proposed TWSBS is connected with a Simulink controller scheme by employing physical signal converters to describe the system dynamics efficiently. Through the Simscape environment, the TWSBR motion is visualized and effectively analyzed without the need for complicated analysis of the associated mathematical model. Besides, 3D visualization of real-time behavior for the implemented TWSBR plant model is displayed by Simulink Mechanics Explorer. Robot balancing and stability are achieved by utilizing Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) controllers' approaches considering specific control targets. A comparative study and evaluation of both controllers are conducted to verify the robustness and road disturbance rejection. The realized performance and robustness of developed controllers are observed by varying object-carrying loaded up on mechanical structure layers during robot motion. In particular, the objective weight is loaded on the robot layers (top, middle, and bottom) during disturbance situations. The achieved findings may have the potential to extend the deployment of using TWSBRs in the varied important application.