Adaptive nonlinear vibration control based on causal time-invariant green functions and on a novel branch of soft computing

Tar, József K.; Rudas, Imre J.; Bitó, János F.; Tenreiro Machado, J. A.

http://hdl.handle.net/10400.22/13239

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Authors

Tar, József K.

Rudas, Imre J.

Bitó, János F.

Tenreiro Machado, J. A.

Abstract(s)

In this paper a simple nonlinear, adaptive approach inspired by the fractional derivatives based CRONE control is presented for vibration damping. Its key idea is replacement of the fractional derivatives with the mathematically less restricted concept of time-invariant Green functions. Instead of the traditional PID feedback terms it applies positive definite weighted moving average of the square of the error plus a nonlinear term making the error converge to zero. 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 to the designer to have an accurate and complete dynamic model of the system to be controlled or to design sophisticated linear controller. The applicability of the approach is illustrated via simulations for a paradigm consisting of a pair of coupled damper linear oscillators under external excitation. One of the oscillators is not modeled by the controller. The adaptive loop successively maps the observed system behavior to the desired one without exerting any effort to identify the reasons of the differences. The approach was found be useful for solving vibration damping problems with unmodeled and uncontrolled internal degrees of freedom.