This paper describes two kinds of control method for parallel two-wheeled inverted pendulum. It is a method that is controlled by the torque input and is controlled by the velocity input. Generally, the equation of motion of this system is expressed by the torque input. From this equation of motion, equation of the velocity input was derived using back calculating equation of the torque input. Equation of the velocity input becomes hierarchical structure. To perform velocity input, we controlled the motor of second order system to first order system using discrete robust model matching control. In the both of control system, i.e, torque and input and velocity input, optimal regulator is employed. Robust stability was confirmed using sensitivity function. We compared performance of torque and velocity input with simulation and experiment using actual test vehicle.

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