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Example text
Finally, the differential flatness based GPI controller is obtained by replacing the actual time derivatives of the flat output in (19) by their structural estimates in (20) but using additional iterated integral error compensations as follows u¨ + ω 2 u = d4−1 v + d4−1 d1 y(4) + d2 y¨ + d3 y v = y∗(6) − α10 y(5) − y∗(5) − α9 y(4) − y∗(4) − α8 y(3) − y∗(3) − α7 y¨ − y¨∗ − α6 y˙ − y˙ ∗ − α5 [y − y∗ ] − α4 ξ 1 − α3 ξ 2 − α2 ξ 3 − α1 ξ 4 − α0 ξ 5 ξ˙1 ξ˙2 ξ˙3 ξ˙4 ξ˙5 = y − y∗ , = ξ1, = ξ2, = ξ3, = ξ4, ξ 1 (0) = 0 ξ 2 (0) = 0 ξ 3 (0) = 0 ξ 4 (0) = 0 ξ 5 (0) = 0 (21) This feedback and feedforward active vibration controller depends on the measurements of the flat output y and the excitation frequency ω, therefore, this dynamic controller can compensate simultaneously two harmonic components, corresponding to the tuned (passive) vibration absorber (ω2 ) and the actual excitation frequency (ω).
When its denominator D1 (t) is zero. 727s, which is too much time (more than 7 times) after the identification has been finished. 43 17 Design of Vibration ActiveAbsorbers Vibration Absorbers Using On-Line Design of Active Using On-line Estimation of Parameters and SignalsEstimation of Parameters and Signals Fig. 0109t) N. 1s to get a good estimation. 0108rad/s, it is activated the identifier for the amplitude F0 . 05 0 5 time [s] 10 15 -5 0 5 time [s] time [s] Fig. 7. 0109t) [N]. 75 t [s] Fig. 8.
Sira-Ramirez, H. (2003). Active Vibration Absorbers Using Generalized PI and Sliding-Mode Control Techniques, Proceedings of the American Control Conference 2003, pp. 791-796, Denver, CO, USA. , Silva-Navarro, G. & Sira-Ramirez, H. (2004). Application of On-line Algebraic Identification in Active Vibration Control, Proceedings of the International Conference on Noise & Vibration Engineering 2004, pp. 157-172, Leuven, Belgium, 2004. , Blanco-Ortega, A. (2010). Active Vibration Control Using On-line Algebraic Identification and Sliding Modes, Computación y Sistemas, Vol.