Abstract
Adaptive feedforward broadband vibration (or noise) compensation is currently used when an image (a correlated measurement) of the disturbance is available. However, in most of the systems there is a “positive” feedback coupling, between the compensator system and the measurement of the image of the disturbances, which cannot be ignored. The feedforward filter should compensate for the effect of the disturbance while assuring the stability of the internal “positive” feedback loop. Algorithms for adaptive feedforward compensation in the context of this internal positive feedback will be presented and analyzed. The algorithms are evaluated in real time on an active vibration control (AVC) system using an inertial actuator.
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Notes
- 1.
- 2.
The complex variable z −1 will be used for characterizing the system’s behavior in the frequency domain and the delay operator q −1 will be used for describing the system’s behavior in the time domain.
- 3.
\(\hat{u}(t+1)\) is available before adaptation of parameters starts at t+1.
- 4.
In many cases, the argument q −1 or z −1 will be dropped out.
- 5.
The fact that the disturbance is a broadband signal will imply that one has persistence of excitation.
- 6.
The inertial actuator is driven by an external source.
- 7.
These experiments have been carried out by M. Alma (GIPSA-LAB).
- 8.
The filter used in Algorithm III has been computed using the estimated values of N obtained with Algorithm II after 40 s.
- 9.
The filter used in simulation has been also used in real time.
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© 2011 Springer-Verlag London Limited
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Landau, I.D., Lozano, R., M’Saad, M., Karimi, A. (2011). Adaptive Feedforward Compensation of Disturbances. In: Adaptive Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-664-1_15
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DOI: https://doi.org/10.1007/978-0-85729-664-1_15
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