An adaptive control damping the forced vibration of a car while passing
along a bumpy road is investigated. It is based on a simple kinematic description
of the desired behavior of the damped system. A modified PID controller containing
an approximation of Caputo’s fractional derivative suppresses the high-frequency
components related to the bumps and dips, while the low frequency part of passing
hills/valleys are strictly traced. Neither a complete dynamic model of the car nor ’a
priori’ information on the surface of the road is needed. The adaptive control realizes
this kinematic design in spite of the existence of dynamically coupled, excitable
internal degrees of freedom. The method is investigated via Scicos-based simulation
in the case of a paradigm. It was found that both adaptivity and fractional order
derivatives are essential parts of the control that can keep the vibration of the load at
bay without directly controlling its motion
