Stabilization of an inverted pendulum-cart system by fractional PI-state feedback

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u ( t ) = K p x ( t ) + K I I α ( x ( t ) ) . The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n − 1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.