Fractional order PID control of an underactuated balancing system

A mobile inverted pendulum (MIP) is a best example of an underactuated system. It is a system which cannot be commanded to follow a given trajectory in the configuration space without a proper controller design. The condition occurs when there is less number of actuators than the degrees of freedom. In particular it has two degrees of freedom but only one of them is actuated. In this paper a fractional order PID (FOPID) controller is proposed that ensures accurate and precise trajectory tracking in the presence of exogenous disturbances. The numerical results of the proposed control scheme are compared with the conventional integer order PID (IOPID) controller. The results reveal that the fractional order PID out beats the performance of the conventional counterpart.