Vibration Control of a System having Non-Linearly Coupled Unmodeled Internal Degree of Freedom

J.K. Tar, I.J. Rudas, and P. Kerepesi (Hungary)


Adaptive control, fractional order derivatives, vibration damping


A nonlinear, adaptive control using fractional order derivatives is applied for evading the forced vibration of a car while passing along a bumpy road. Its key idea is the partial replacement of the integer order derivatives in a traditional PID controller with time-shift invariant, causal fractional derivatives behaving as frequency filters. Simple kinematic design of the desired damping is satisfactory. The adaptive controller guarantees its realization without needing accurate and complete dynamic model of the system to be controlled or to design a sophisticated linear controller taking the responsibility for the unknown dynamics of the system. The applicability of the approach is illustrated via Scicos based simulations for a car consisting of a wheel, a passive elastic and viscous damping system, a chassis, and the carried payload modeled by a weight fixed on a spring. It can vibrate between stiff elastic bumpers representing the ceiling and the floor of the travellers’ cabin. The active force provided by the controller acts between the wheel and the chassis only. 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.

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