This paper proposes an integrated modelling and control methodology for a two-wheeled foot-balanced robot, incorporating a simplified Virtual Model Control (VMC) approach and a Linear Quadratic Regulator (LQR). Initially, a simplified kinetic model is derived through the integration of VMC and classical mechanical analyses. Subsequently, a full-state feedback controller is designed utilizing LQR. The research further introduces customized jump control and model prediction compensation strategies tailored to the wheel-leg configuration. The simulation is conducted to validate the precision and stability of the proposed method. Finally, experimental tests were conducted on an actual two-wheeled foot-balanced robot, encompassing speed response, position step response, in-situ jumping, and slope traversal. The results indicate that the robot can reliably respond to step signals of 1.5 m, jump over a height of 18 cm, and traverse slopes with a maximum inclination of 19 degrees with stability.