Dynamic equations of a Wheeled Inverted Pendulum with changing its center of gravity

In this research, dynamic equations a WIP (Wheeled Inverted Pendulum) changing center of gravity when some load or equipment on the WIP are changing. The WIP becomes a popular platform for mobile robots which should be equipping various load and apparatus on it. The WIP generally has two equilibrium points which are stable and unstable. The WIP should be stabilizing over the unstable equilibrium point. The unstable WIP is persistently controlled to stabilized its frame chassis. A proper controller needs controlled plant model which can be described by the dynamic equations.