Fractional order sliding mode control with pole-placement for non-linear systems with uncertain disturbances

in this paper a combination between fractional order sliding mode control (FOSMC) and pole-placement is introduced for non-linear systems with uncertain disturbances. A sliding surface with a fractional order PID form is given, in which the eigenvalues of the reduced state equation of the errors are forced to be negative via the pole-placement method. The control law is designed based on the Lyapunov stability condition and the fractional order calculus properties. In the simulation results, a comparison between our FOSMC controller and an integer order sliding mode control (IOSMC) for an inverted pendulum system demonstrates the better performance of our proposal.