Fractional order derivatives

Detailed investigation of a simple nonlinear, active, adaptive approach of controlling the oscillation of a car proceeding on a bumpy road is presented. Its key idea is a frequency dependent control of the strictness of a traditional PID controller by applying fractional order derivatives in a simple kinematic design without any respect to the dynamic model of the system. The adaptive part of the controller relieves the designer of dealing with the system's dynamics within the frames of some linear control, and guarantees the implementation of this design. The operation of the approach is illustrated by the use of INRIA's scientific co-simulator Scicos for a rough model of a car. Well interpretable trends were revealed regarding the effect of the variation of the order of derivation, and that of the sampling time of the adaptive loop. These results seem to be promising for actively damping the vibration of systems having unmodeled, uncontrolled internal degrees of freedom.