PIαDβ controller design for underactuated mechanical systems

Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. In this paper, we propose a Fractional Order Controller for an underactuated mechanical system named Double Inverted Pendulum on a Cart system (DIPOAC). The proposed system has three degrees-of-freedom and one control input. The mathematical model is derived using Lagrangian method and the stabilization is achieved with constraints using Fractional Order Controller. Simulation are performed to validate the control law and compared with Integer Order Controller.