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2017 | OriginalPaper | Buchkapitel

15. Adaptive Feedforward Compensation of Disturbances

verfasst von : Ioan Doré Landau, Tudor-Bogdan Airimitoaie, Abraham Castellanos-Silva, Aurelian Constantinescu

Erschienen in: Adaptive and Robust Active Vibration Control

Verlag: Springer International Publishing

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Abstract

Adaptive feedforward compensation algorithms for the attenuation of broad-band disturbances are developed in this chapter. The proposed algorithms take into account the “positive” feedback coupling which appears in active vibration control systems using feedforward compensation. One considers also the case when a fixed feedback controller is present. The algorithms are evaluated in real time on the active flexible mechanical structure actuated by an inertial actuator which has been presented in Chap. 2.

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Fußnoten
1
Different solutions for reducing the effect of this internal positive feedback are reviewed in [8, 9].
 
2
Design of adaptive AVC does not require either the model of the disturbance or the model of the primary path.
 
3
The complex variable \(z^{-1}\) will be used for characterizing the system’s behaviour in the frequency domain and the delay operator \(q^{-1}\) will be used for describing the system’s behaviour in the time domain.
 
4
The following notation for polynomials is used: \(A(q^{-1})=a_0+\sum _{i=1}^{n_A}a_iq^{-i}=a_0\,+\,q^{-1}A^*(q^{-1})\).
 
5
\(\hat{y}(t+1)\) is available before adaptation of parameters starts at \(t+1\).
 
6
In many cases, the argument \(q^{-1}\) or \(z^{-1}\) will be dropped out.
 
7
In the field of adaptive feedforward compensation names are associated to various adaptation algorithms. Algorithm II uses the same filtering of the regressor as FULMS algorithm but with a matrix adaptation gain which lead to a structure called “pseudolinear regression” [14]. So Algorithm II can be termed FUPLR. Algorithm III is obtained from a stability point of view and it can be termed FUSBA (stability based algorithm).
 
8
See Appendix D, Sect. D.2 for further details.
 
9
The results are valid for the asymptotic behaviour obtained when using a decreasing adaptation gain.
 
10
The fact that the disturbance is a broad-band signal will imply that one has persistence of excitation.
 
11
The inertial actuator is driven by an external source.
 
12
An array implementation as in [17] can be also considered.
 
13
The scalar adaptation gain algorithms presented in this book can be denoted as NFULMS (normalized FULMS) for Algorithm II and SFUSBA (scalar FUSBA) for Algorithm III.
 
14
This algorithm can be termed FUeSBA since both the input and the error are filtered.
 
15
For the adaptive schemes, the PSD is evaluated after the adaptation transient has settled.
 
Literatur
1.
Zurück zum Zitat Burgess J (1981) Active adaptive sound control in a duct: a computer simulation. J Acoust Soc Am 70:715–726CrossRef Burgess J (1981) Active adaptive sound control in a duct: a computer simulation. J Acoust Soc Am 70:715–726CrossRef
2.
Zurück zum Zitat Widrow B, Shur D, Shaffer S (1981) On adaptive inverse control. In: Proceedings of the 15th asilomar conference circuits, systems and computers. Pacific Grove, CA, USA Widrow B, Shur D, Shaffer S (1981) On adaptive inverse control. In: Proceedings of the 15th asilomar conference circuits, systems and computers. Pacific Grove, CA, USA
3.
Zurück zum Zitat Widrow B, Stearns S (1985) Adaptive signal processing. Prentice-Hall, Englewood Cliffs, New JerseyMATH Widrow B, Stearns S (1985) Adaptive signal processing. Prentice-Hall, Englewood Cliffs, New JerseyMATH
4.
Zurück zum Zitat Elliott S, Nelson P (1994) Active noise control. Noise/news international, pp 75–98 Elliott S, Nelson P (1994) Active noise control. Noise/news international, pp 75–98
5.
6.
Zurück zum Zitat Jacobson CA, Johnson CR, Jr, McCormick DC, Sethares WA (2001) Stability of active noise control algorithms. IEEE Signal Process Lett 8(3):74–76. doi:10.1109/97.905944 Jacobson CA, Johnson CR, Jr, McCormick DC, Sethares WA (2001) Stability of active noise control algorithms. IEEE Signal Process Lett 8(3):74–76. doi:10.​1109/​97.​905944
8.
Zurück zum Zitat Kuo M, Morgan D (1996) Active noise control systems-algorithms and DSP implementation. Wiley, New York Kuo M, Morgan D (1996) Active noise control systems-algorithms and DSP implementation. Wiley, New York
10.
Zurück zum Zitat Hu J, Linn J (2000) Feedforward active noise controller design in ducts without independent noise source measurements. IEEE Trans Control Syst Technol 8(3):443–455CrossRef Hu J, Linn J (2000) Feedforward active noise controller design in ducts without independent noise source measurements. IEEE Trans Control Syst Technol 8(3):443–455CrossRef
11.
Zurück zum Zitat Landau I, Karimi A, Constantinescu A (2001) Direct controller order reduction by identification in closed loop. Automatica 37:1689–1702MathSciNetCrossRefMATH Landau I, Karimi A, Constantinescu A (2001) Direct controller order reduction by identification in closed loop. Automatica 37:1689–1702MathSciNetCrossRefMATH
13.
Zurück zum Zitat Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, LondonCrossRefMATH Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, LondonCrossRefMATH
14.
Zurück zum Zitat Ljung L, Söderström T (1983) Theory and practice of recursive identification. MIT Press, CambridgeMATH Ljung L, Söderström T (1983) Theory and practice of recursive identification. MIT Press, CambridgeMATH
15.
Zurück zum Zitat Anderson B, Bitmead R, Johnson C, Kokotovic P, Kosut R, Mareels I, Praly L, Riedle B (1986) Stability of adaptive systems. MIT Press, CambridgeMATH Anderson B, Bitmead R, Johnson C, Kokotovic P, Kosut R, Mareels I, Praly L, Riedle B (1986) Stability of adaptive systems. MIT Press, CambridgeMATH
16.
Zurück zum Zitat Landau I, Zito G (2005) Digital control systems—design, identification and implementation. Springer, London Landau I, Zito G (2005) Digital control systems—design, identification and implementation. Springer, London
17.
Zurück zum Zitat Montazeri P, Poshtan J (2010) A computationally efficient adaptive IIR solution to active noise and vibration control systems. IEEE Trans Autom Control AC-55:2671–2676 Montazeri P, Poshtan J (2010) A computationally efficient adaptive IIR solution to active noise and vibration control systems. IEEE Trans Autom Control AC-55:2671–2676
18.
Zurück zum Zitat Alma M, Martinez J, Landau I, Buche G (2012) Design and tuning of reduced order H\(_\infty \) feedforward compensators for active vibration control. IEEE Trans Control Syst Technol 20(2):554–561. doi:10.1109/TCST.2011.2119485 CrossRef Alma M, Martinez J, Landau I, Buche G (2012) Design and tuning of reduced order H\(_\infty \) feedforward compensators for active vibration control. IEEE Trans Control Syst Technol 20(2):554–561. doi:10.​1109/​TCST.​2011.​2119485 CrossRef
19.
Zurück zum Zitat Eriksson L (1991) Development of the filtered-U LMS algorithm for active noise control. J Acoust Soc Am 89(1):257–261CrossRef Eriksson L (1991) Development of the filtered-U LMS algorithm for active noise control. J Acoust Soc Am 89(1):257–261CrossRef
20.
24.
Zurück zum Zitat Alma M, Landau ID, Airimitoaie TB (2012) Adaptive feedforward compensation algorithms for AVC systems in the presence of a feedback controller. Automatica 48(10):982–985MathSciNetCrossRefMATH Alma M, Landau ID, Airimitoaie TB (2012) Adaptive feedforward compensation algorithms for AVC systems in the presence of a feedback controller. Automatica 48(10):982–985MathSciNetCrossRefMATH
26.
Zurück zum Zitat Widrow B, Hoff M (1960) Adaptive swithching circuits. Oric IRE WESCON Convention Record 4(Session 16):96–104 Widrow B, Hoff M (1960) Adaptive swithching circuits. Oric IRE WESCON Convention Record 4(Session 16):96–104
27.
Zurück zum Zitat Widrow B (1971) Adaptive filters. In: Kalman R, DeClaris H (eds) Aspects of network and system theory. Holt, Rinehart and Winston Widrow B (1971) Adaptive filters. In: Kalman R, DeClaris H (eds) Aspects of network and system theory. Holt, Rinehart and Winston
28.
Zurück zum Zitat Billoud DG (2001) LL-6508 active control at lord corporation—A reality Billoud DG (2001) LL-6508 active control at lord corporation—A reality
29.
Zurück zum Zitat Tang Y, Zhu ZC, Shen G, Li X (2015) Improved feedforward inverse control with adaptive refinement for acceleration tracking of electro-hydraulic shake table. J Vib Control. doi:10.1177/1077546314567725 Tang Y, Zhu ZC, Shen G, Li X (2015) Improved feedforward inverse control with adaptive refinement for acceleration tracking of electro-hydraulic shake table. J Vib Control. doi:10.​1177/​1077546314567725​
33.
Zurück zum Zitat Erdogan G, Alexander L, Rajamani R (2010) Adaptive vibration cancellation for tire-road friction coefficient estimation on winter maintenance vehicles. IEEE Trans Control Syst Technol 18(5):1023–1032. doi:10.1109/TCST.2009.2031326 CrossRef Erdogan G, Alexander L, Rajamani R (2010) Adaptive vibration cancellation for tire-road friction coefficient estimation on winter maintenance vehicles. IEEE Trans Control Syst Technol 18(5):1023–1032. doi:10.​1109/​TCST.​2009.​2031326 CrossRef
35.
Zurück zum Zitat Sayyarrodsari B, How J, Hassibi B, Carrier A (2001) Estimation-based synthesis of H\(_\infty \)-optimal adaptive FIR filters for filtered-LMS problems. IEEE Trans Signal Process 49(1):164–178. doi:10.1109/78.890358 CrossRef Sayyarrodsari B, How J, Hassibi B, Carrier A (2001) Estimation-based synthesis of H\(_\infty \)-optimal adaptive FIR filters for filtered-LMS problems. IEEE Trans Signal Process 49(1):164–178. doi:10.​1109/​78.​890358 CrossRef
36.
Zurück zum Zitat Fraanje R (2004) Robust and fast schemes in broadband active noise and vibration control. PhD thesis, University of Twente, Twente, The Netherlands Fraanje R (2004) Robust and fast schemes in broadband active noise and vibration control. PhD thesis, University of Twente, Twente, The Netherlands
37.
Zurück zum Zitat Popov V (1960) Criterii de stabilitate pentru sistemele automate conţinând elemente neunivoce, probleme de automatizare. Publishing House of the Romanian Academy, pp 143–151 Popov V (1960) Criterii de stabilitate pentru sistemele automate conţinând elemente neunivoce, probleme de automatizare. Publishing House of the Romanian Academy, pp 143–151
38.
Zurück zum Zitat Popov V (1966) Hiperstabilitatea Sistemelor Automate. Editura Academiei Republicii Socialiste România Popov V (1966) Hiperstabilitatea Sistemelor Automate. Editura Academiei Republicii Socialiste România
39.
Zurück zum Zitat Popov V (1963) Solution of a new stability problem for controlled systems. Autom Remote Control 24(1):1–23MathSciNetMATH Popov V (1963) Solution of a new stability problem for controlled systems. Autom Remote Control 24(1):1–23MathSciNetMATH
40.
Zurück zum Zitat Popov V (1973) Hyperstability of control systems, trans. edn. Springer, Heidelberg Popov V (1973) Hyperstability of control systems, trans. edn. Springer, Heidelberg
42.
Zurück zum Zitat Landau I (1979) Adaptive control: the model reference approach. Marcel Dekker, New YorkMATH Landau I (1979) Adaptive control: the model reference approach. Marcel Dekker, New YorkMATH
45.
Zurück zum Zitat Landau ID, Airimitoaie TB, Alma M (2013) IIR Youla-Kučera parameterized adaptive feedforward compensators for active vibration control with mechanical coupling. IEEE Trans Control Syst Technol 21(3):765–779CrossRef Landau ID, Airimitoaie TB, Alma M (2013) IIR Youla-Kučera parameterized adaptive feedforward compensators for active vibration control with mechanical coupling. IEEE Trans Control Syst Technol 21(3):765–779CrossRef
46.
Zurück zum Zitat Treichler J, Larimore M, Johnson C, Jr (1978) Simple adaptive IIR filtering. In: IEEE international conference on acoustics, speech, and signal processing, ICASSP ’78, vol 3, pp 118–122. doi:10.1109/ICASSP.1978.1170389 Treichler J, Larimore M, Johnson C, Jr (1978) Simple adaptive IIR filtering. In: IEEE international conference on acoustics, speech, and signal processing, ICASSP ’78, vol 3, pp 118–122. doi:10.​1109/​ICASSP.​1978.​1170389
47.
Zurück zum Zitat Mosquera C, Gomez J, Perez F, Sobreira M (1999) Adaptive IIR filters for active noise control. In: Sixth international congress on sound and vibration, ICSV ’99, pp 1571–1582 Mosquera C, Gomez J, Perez F, Sobreira M (1999) Adaptive IIR filters for active noise control. In: Sixth international congress on sound and vibration, ICSV ’99, pp 1571–1582
48.
Zurück zum Zitat Snyder S (1994) Active control using IIR filters—a second look. In: 1994 IEEE international conference on acoustics, speech, and signal processing, 1994, ICASSP-94, vol 2, pp II/241 –II/244. doi:10.1109/ICASSP.1994.389675 Snyder S (1994) Active control using IIR filters—a second look. In: 1994 IEEE international conference on acoustics, speech, and signal processing, 1994, ICASSP-94, vol 2, pp II/241 –II/244. doi:10.​1109/​ICASSP.​1994.​389675
52.
Zurück zum Zitat Moheimani SR, Fleming AJ (2006) Piezoelectric transducers for vibration control and damping. Springer, LondonMATH Moheimani SR, Fleming AJ (2006) Piezoelectric transducers for vibration control and damping. Springer, LondonMATH
54.
Zurück zum Zitat Reza Moheimani S, Pota H, Petersen I (1997) Broadband disturbance attenuation over an entire beam. In: Control Conference (ECC), 1997 European, pp 3896–3901 Reza Moheimani S, Pota H, Petersen I (1997) Broadband disturbance attenuation over an entire beam. In: Control Conference (ECC), 1997 European, pp 3896–3901
55.
Zurück zum Zitat Lin CY, Huang YH (2014) Enhancing vibration suppression in a periodically excited flexible beam by using a repetitive model predictive control strategy. J Vib Control. doi:10.1177/1077546314564451 Lin CY, Huang YH (2014) Enhancing vibration suppression in a periodically excited flexible beam by using a repetitive model predictive control strategy. J Vib Control. doi:10.​1177/​1077546314564451​
56.
Zurück zum Zitat Lee Y, Halim D (2004) Vibration control experiments on a piezoelectric laminate plate using spatial feedforward control approach. In: 43rd IEEE conference on decision and control, 2004. CDC, vol 3, pp 2403–2408. doi:10.1109/CDC.2004.1428764 Lee Y, Halim D (2004) Vibration control experiments on a piezoelectric laminate plate using spatial feedforward control approach. In: 43rd IEEE conference on decision and control, 2004. CDC, vol 3, pp 2403–2408. doi:10.​1109/​CDC.​2004.​1428764
57.
Zurück zum Zitat Kuhnen K, Krejci P (2009) Compensation of complex hysteresis and creep effects in piezoelectrically actuated systems. A new Preisach modeling approach. IEEE Trans Autom Control, 54(3), 537–550. doi:10.1109/TAC.2009.2012984 Kuhnen K, Krejci P (2009) Compensation of complex hysteresis and creep effects in piezoelectrically actuated systems. A new Preisach modeling approach. IEEE Trans Autom Control, 54(3), 537–550. doi:10.​1109/​TAC.​2009.​2012984
66.
Zurück zum Zitat Hansen C, Snyder S, Qiu X, Brooks L, Moreau D (2012) Active Control of Noise and Vibration. CRC Press, Taylor and Francis Group, Milton Park Hansen C, Snyder S, Qiu X, Brooks L, Moreau D (2012) Active Control of Noise and Vibration. CRC Press, Taylor and Francis Group, Milton Park
67.
Zurück zum Zitat Hoagg J, Lacy S, Bernstein D (2005) Broadband adaptive disturbance rejection for a deployable optical telescope testbed. In: Proceedings of the American control conference, 2005, pp 4953–4958, vol 7. doi:10.1109/ACC.2005.1470791 Hoagg J, Lacy S, Bernstein D (2005) Broadband adaptive disturbance rejection for a deployable optical telescope testbed. In: Proceedings of the American control conference, 2005, pp 4953–4958, vol 7. doi:10.​1109/​ACC.​2005.​1470791
Metadaten
Titel
Adaptive Feedforward Compensation of Disturbances
verfasst von
Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-41450-8_15