Wheelchairs on two wheels are needed for disabled persons to perform some of the essential tasks in their living and work environments. In fact it offers great advantages and efficiency for the user. Besides allowing a disabled to lead independent life, it is expected not to take much space during mobility as compared to when it is on four wheels and thus a wheelchair on two wheels has associated design and development challenges. These include modelling and controller design for the system to perform comparably similar to normal four-wheeled wheelchair. In this paper physical model of a wheelchair on two wheels that mimics double inverted pendulum is designed and a novel fuzzy logic control mechanism is developed and tested with control of the two-wheeled wheelchair.