Adaptive vibration damping based on casual time-invariant green-functions and fractional order derivates

You are here: Homepage > Search

Adaptive vibration damping based on casual time-invariant green-functions and fractional order derivates

Free access

Tar, József K. / Rudas, Imre J. / Pátkai, Béla / Tenreiro Machado, J. A.

In this paper a simple nonlinear, adaptive control using causal time-invariant Green-functions and fractional order derivatives is applied for damping the vibration of a car forced during passing along a bumpy road. Its key idea is the replacement of the integer order derivates in a Green-functions-based nonlinear controller with a time-shift invariant, causal approximation of the Riemann-Liouville fractional derivative that also behaves like a Green-function. Since its physical essence is rather frequency filtering than providing inter order derivatives in limit cases, the approximation applied numerically is quite convinent. In this way simple kinematic design of the desired damping becomes possible. The adaptive part of the controller guarantees the realization of this kinematic design without making it necessary for the designer to have accurate and complete dynamic model of the system to be controlled or to design a sophisticated linear "CRONE" controller that has to take the responsability for the unknown dynamics of the system. The applicability of the approach is illustrated via simulations for a paradigm that is a rough model of a car. It was found that both adaptivity and the use of fractional order derivatives in the control are essential parts of the success of the method. ; info:eu-repo/semantics/publishedVersion