Method and apparatus for actively reducing multiple-source repetitive vibrations

• US 5,245,552 A
• Filed: 10/31/1990
• Issued: 09/14/1993
• Est. Priority Date: 10/31/1990
• Status: Expired due to Term

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Godo, Erik L., Andersson, Anders O.
• Primary Examiner(s): Cosimano, Edward R.
• Assistant Examiner(s): PIPALA, EDWARD J
• Application Number:
  US07/608,971
• Time in Patent Office: 1,049 Days
• Field of Search: 364/507, 364/508, 364/574, 364/551.02, 364/581, 381/71, 73/602, 73/625, 73/645-648, 416/34
• US Class Current: 700/280
• CPC Class Codes: G10K 11/17823 Reference signals, e.g. ambient acoustic environment
• CPC Class Codes: G10K 11/17857 Geometric disposition, e.g. placement of microphones
• CPC Class Codes: G10K 11/17883 the reference signal being derived from a machine operating condition, e.g. engine RPM or vehicle speed
• CPC Class Codes: G10K 2210/3011 Single acoustic input
• CPC Class Codes: G10K 2210/3025 Determination of spectrum characteristics, e.g. FFT
• CPC Class Codes: G10K 2210/3032 Harmonics or sub-harmonics
• CPC Class Codes: G10K 2210/3043 Phase locked loops [PLL]
• CPC Class Codes: G10K 2210/3044 Phase shift, e.g. complex envelope processing
• CPC Class Codes: G10K 2210/3046 Multiple acoustic inputs, multiple acoustic outputs
• CPC Class Codes: G10K 2210/3051 Sampling, e.g. variable rate, synchronous, decimated or interpolated
• CPC Class Codes: G10K 2210/3053 Speeding up computation or convergence, or decreasing the computational load

Abstract

A method and apparatus for reducing multiple-source repetitive vibrations in a region or structure (12) by applying control vibrations to the region or structure via actuators (18), frequently recalculating the control vibrations based on source elements to accommodate for varying phase differences between the sources of the repetitive vibrations (14) and (16), and cyclically updating the source elements of the control vibrations is disclosed. The repetitive vibrations are sensed (20) synchronously with the repetitive vibration source chosen as the reference source and decomposed into a number of frequency components corresponding to the reference source. The control vibrations are formed of the same frequency components and applied synchronously with the reference source. Each frequency component of the control vibrations is defined by source elements, one for cancelling vibrations produced by each of the repetitive vibration sources. A first estimate of the source elements of the frequency components, defining control vibrations that will reduce the sensed vibrations, is made. The source elements of the frequency components and the phase differences between the reference source and the other repetitive vibration sources are used to calculate control signals that drive the actuators ( 18) that produce the control vibrations. The control signals are frequently recalculated using the instantaneous phase differences. Cyclically, the source elements of the frequency components of the control vibrations are updated to improve the reduction of the sensed vibrations. The updated source elements are used to frequently recalculate the control signals driving the actuators based upon the instantaneous phase differences between the reference source and the other repetitive vibration sources.

Claims

1. A method of reducing vibrations in a region or structure, the vibrations being produced by multiple sources of repetitive vibrations, said method comprising the steps of:

(a) applying control vibrations at a plurality of first locations in a region or structure, said control vibrations created from sets of control-vibration frequency components so that each of said control vibrations is created from one of said sets of control-vibration frequency components, each of said control-vibration frequency components composed of source elements for cancelling vibrations produced by multiple sources of repetitive vibrations; and

(b) cyclically updating said control vibrations by;

(i) determining the phase difference between a reference signal and a source signal, said source signal being derived from a first source, said first source being one of said multiple sources of repetitive vibrations; and

(ii) updating said sets of control-vibration frequency components based on said phase difference and said source elements.

2. The method claimed in claim 1, wherein said step of updating said sets of control-vibration frequency components comprises the substeps of:

(a) weighting each of the source elements of each of the control-vibration frequency components with factors including said phase difference; and

(b) calculating an updated amplitude and phase pair for each of said control-vibration frequency components by forming a sum including the weighted source elements corresponding to the control-vibration frequency component whose amplitude and phase pair is being updated.

3. The method claimed in claim 2, wherein said phase difference represents the time integral of the difference between the frequency of said reference signal and said source signal.

4. The method claimed in claim 3, wherein said step of applying control vibrations comprises the substeps of:

(a) inverse-decomposing said sets of control-vibration frequency components to obtain control-vibration control signals; and

(b) using said control-vibration control signals to create the control vibrations in said region or structure.

5. The method claimed in claim 4, wherein each of said sets of control-vibration frequency components contains frequency components corresponding to the fundamental frequency of said reference signal and harmonics thereof.

6. The method claimed in claim 5, wherein said control vibrations are applied synchronously with said reference signal.

7. The method claimed in claim 6, wherein said source signal forms a first source signal and including the step of determining the phase difference between said reference signal and a second source signal, said second source signal being derived from a second source, said second source being one of said multiple sources of repetitive vibrations, and wherein each of said control-vibration frequency components is composed of two source elements according to the following equation:

space="preserve" listing-type="equation">a.sub. (n)=Q.sub.11 (n)e.sup.jnφ

1+R.sub. (n)e.sup.jnφ

2

where;

a.sub. (n) is a complex number representing the amplitude and phase of a frequency component of the set of control-vibration frequency components of the control-vibration applied at a particular first location identified by the subscript, .sub.

n is an integer equal to the harmonic number of said frequency component;

φ

₁ is the phase difference between said first source signal and said reference signal and φ

₂ is the phase difference between said second source signal and said reference signal; and

Q.sub. (n) and R.sub. (n) are complex numbers representing the source elements of said frequency component, wherein Q.sub. (n) is the source element corresponding to said first source and R.sub. (n) is the source element corresponding to said second source.

8. The method claimed in claim 7, wherein said source elements are periodically updated by:

(a) sensing vibrations at a plurality of second locations in said region or structure;

(b) determining representative values of said φ

₁ and φ

₂ phase differences based on the values of the φ

₁ and φ

₂ phase differences determined while said vibrations are being sensed at said plurality of second locations;

(c) decomposing said sensed vibrations into sets of sensed-vibration frequency components;

(d) calculating updates for the source elements of selected frequency components of said sets of control-vibration frequency components, said updates based on said sets of sensed-vibration frequency components and said representative values of said φ

₁ and φ

₂ phase differences; and

(e) updating the source elements by updating the source elements of said selected frequency components of said sets of control-vibration frequency components based on said calculated updates.

9. The method claimed in claim 8, wherein said step of calculating updates for the source elements of selected frequency components of said sets of control-vibration frequency components comprises:

(a) transforming frequency components of said sets of sensed-vibration frequency components into updates for said selected frequency components of said sets of control-vibration frequency components; and

(b) calculating source element updates based on said frequency component updates and said representative values of said φ

₁ and φ

₂ phase differences.

10. The method claimed in claim 9, wherein said source elements of the selected frequency components of said sets of control-vibration frequency components are updated by adding said source element updates to the present values of the corresponding source elements according to the following equations:

space="preserve" listing-type="equation">Δ

Q.sub. (n)+Q.sub. (n)→

Q.sub. (n)

space="preserve" listing-type="equation">Δ

R.sub. (n)+R.sub. (n)→

R.sub. (n)

where;

Q.sub. (n) and R.sub. (n) are the complex numbers representing the source elements of a frequency component of the set of control-vibration frequency components of the control-vibration applied at a particular first location identified by the subscript, , wherein Q.sub. (n) is the source element corresponding to said first source and R.sub. (n) is the source element corresponding to said second source; and

Δ

Q.sub. (n) and Δ

R.sub. (n) are complex numbers representing the updates for said source elements, wherein Δ

Q.sub. (n) is the update for said source element Q.sub. (n), and Δ

R.sub. (n) is the update for said source element R.sub. (n).

11. The method claimed in claim 10, wherein the source element updates are calculated by solving the following matrix equation in a weighted least-squares sense:

##EQU3## where;

γ

₁ and γ

₂ are scalars;

φ

₁ is said representative value of the phase difference between said first source signal and said reference signal;

φ

₂ is said representative value of the phase difference between said second source signal and said reference signal;

Δ

a.sub. (n) is a complex number representing the amplitude and phase update for a frequency component of the set of control-vibration frequency components of the control vibration applied at a particular first location identified by the subscript, ;

n is an integer equal to the harmonic number of said frequency component; and

Δ

Q.sub. (n) and Δ

R.sub. (n) are the updates for the source elements of said frequency component.

12. The method claimed in claim 11, wherein said second source signal forms said reference signal.

13. The method claimed in claim 11 or 12, wherein said step of decomposing said sensed vibrations comprises performing a Fast Fourier Transformation on each of said sensed vibrations.

14. The method claimed in claim 13, wherein said step of inverse-decomposing said sets of control-vibration frequency components comprises performing an inverse Fast Fourier Transformation on each of said sets of control-vibration frequency components.

15. The method claimed in claim 14, wherein the frequency components of each of said sets of sensed-vibration frequency components are the same as the frequency components of each of said sets of control-vibration frequency components.

16. The method claimed in claim 15, wherein said sensed vibrations are sensed synchronously with said reference signal.

17. The method claimed in claim 16, wherein said selected frequency components of said sets of control-vibration frequency components are selected by:

(a) determining the magnitude of the frequency components of said sets of sensed-vibration frequency components based on selected criteria; and

(b) selecting those frequency components that have the greatest magnitude, the number of selected frequency components selected being less than the number of frequency components in said sets of control-vibration frequency components.

18. The method claimed in claim 1, wherein said source elements are periodically updated by:

(a) sensing vibrations at a plurality of second locations in said region or structure;

(b) determining a representative value of said phase difference between said reference signal and said source signal based on the values of said phase difference determined while said vibrations are being sensed at said plurality of second locations;

(c) decomposing said sensed vibrations into sets of sensed-vibration frequency components;

(d) calculating updates for the source elements of selected frequency components of said sets of control-vibration frequency components, said updates based on said sets of sensed-vibration frequency components and said representative value of said phase difference; and

(e) updating the source elements by updating the source elements of said selected frequency components of said sets of control-vibration frequency components based on said calculated updates.

19. The method claimed in 18, wherein said step of calculating updates for the source elements of selected frequency components of said sets of control-vibration frequency components comprises:

(a) transforming frequency components of said sets of sensed-vibration frequency components into updates for said selected frequency components of said sets of control-vibration frequency components; and

(b) calculating source element updates based on said frequency component updates and said representative value of said phase difference.

20. The method claimed in claim 19, wherein said source elements of the selected frequency components of said sets control-vibration frequency components are updated by summing said source element updates with the present values of the corresponding source elements.

21. The method claimed in claim 20, wherein said phase difference represents the time integral of the difference between the frequency of said reference signal and said source signal.

22. The method claimed in claim 21, wherein said source signal forms a first source signal and including the step of determining the phase difference between said reference signal and a second source signal, said second source signal being derived from a second source, said second source being one of said multiple sources of repetitive vibrations, and wherein each of said control-vibration frequency components is composed of two source elements, one for each of said first and second sources of repetitive vibrations.

23. The method claimed in claim 22, wherein said source element updates are calculated by solving the following matrix equation in a weighted least-squares sense:

##EQU4## where;

γ

₁ and γ

₂ are scalars;

φ

₁ is said representative value of the phase difference between said first source signal and said reference signal;

φ

₂ a representative value of the phase difference between said second source signal and said reference signal based on the values of the phase difference between said second source signal and said reference signal determined while said vibrations are being sensed at said plurality of second locations;

Δ

a.sub. (n) is a complex number representing the amplitude and phase update of a frequency component of the set of control-vibration frequency components of the control vibration applied at a particular first location identified by the subscript, .sub. ;

n is an integer equal to the harmonic number of said frequency component; and

Δ

Q.sub. (n) and Δ

R.sub. (n) are complex numbers representing the updates for the source elements of said frequency component, wherein Δ

Q.sub. (n) is the update for the source element Q.sub. (n) corresponding to said first source, and Δ

R.sub. (n) is the update for the source element R.sub. (n) corresponding to said second source.

24. The method claimed in claim 23, wherein said step updating said sets of control-vibration frequency components comprises the steps of:

(a) weighting each of the source elements of each of the control-vibration frequency components with factors including the corresponding phase differences; and

(b) calculating an updated amplitude and phase pair for each of said control-vibration frequency components by forming a sum including the weighted source elements corresponding to the control-vibration frequency component whose amplitude and phase pair is being updated.

25. The method claimed in claim 24, wherein said step of applying control vibrations comprises the steps of:

(a) inverse-decomposing said sets of control-vibration frequency components to obtain control-vibration control signals; and

(b) using said control-vibration control signals to create said control vibrations in said region or structure.

26. The method claimed in claim 25, wherein each of said sets of control-vibration frequency components contains frequency components corresponding to the fundamental frequency of said reference signal and harmonics thereof.

27. The method claimed in claim 26, wherein said control vibrations are applied synchronously with said reference signal.

28. An apparatus for reducing vibrations in a region or structure, the vibrations being produced by multiple sources of repetitive vibrations, said apparatus comprising:

(a) phase differentiator means for determining the phase difference between a reference signal and a source signal, said source signal based on a first source, said first source being one of multiple sources of repetitive vibrations that produce vibrations in a region or structure;

(b) a plurality of actuators for applying control vibrations at a plurality of first locations in said region or structure; and

(c) output means coupled to said plurality of actuators and said phase differentiator means for;

(i) applying drive signals to said plurality of actuators, said drive signals created from sets of control-vibration frequency components so that each of said drive signals is created from one of said sets of control-vibration frequency components, each of said control-vibration frequency components composed of source elements for cancelling the vibrations produced by said multiple sources of repetitive vibrations; and

(ii) cyclically updating said control vibrations by;

(1) receiving said phase difference determined by said phase differentiator means; and

(2) updating said sets of control-vibration frequency components based on said phase difference and said source elements.

29. The apparatus claimed in claim 28, wherein said output means includes an inverse-decomposition means for producing control-vibration control signals by inverse-decomposing said sets of control-vibration frequency components, and wherein said output means synchronously creates said drive signals from said control-vibration control signals.

30. The apparatus claimed in claim 29, wherein said phase differentiator means includes:

(a) sensor means coupled to said first source for monitoring said first source and producing said source signal, the frequency of said source signal being based on the fundamental frequency of said first source;

(b) synchronized signal generating means coupled to said sensor means for;

(i) receiving said source signal produced by the sensor means; and

(ii) producing a synchronized signal having a frequency that is a multiple of the frequency of said source signal and is synchronized therewith; and

(c) a phase differentiator coupled to said synchronized signal generating means for;

(i) receiving said synchronized signal;

(ii) determining said phase difference between said reference signal and said source signal by analyzing the phase difference between said synchronized signal and said reference signal; and

(iii) applying said phase difference determined by analysis to said output means.

31. The apparatus claimed in claim 30, wherein said updated sets of control-vibration frequency components are formed by:

(a) weighting each of the source elements of each of the control-vibration frequency components with factors including said phase difference between said reference signal and said source signal; and

(b) calculating an updated amplitude and phase pair for each of said control-vibration frequency components by forming a sum including the weighted source elements corresponding to the control-vibration frequency component whose amplitude and phase pair is being updated.

32. The apparatus claimed in claim 31, wherein the phase difference determined by said phase differentiator represents the time integral of the difference between the frequency of said reference signal and the frequency of said source signal.

33. The apparatus claimed in claim 32, wherein each of said sets of control-vibration frequency components contains frequency components corresponding to the fundamental frequency of said reference signal and harmonics thereof.

34. The apparatus claimed in claim 33, wherein said drive signals are synchronized with said reference signal.

35. The apparatus claimed in claim 34, wherein said synchronized signal forms a first synchronized signal and said source signal forms a first source signal and wherein said sensor means includes means coupled to a second source, said second source being one of said multiple sources of repetitive vibrations, said means for monitoring said second source and producing a second source signal whose frequency is based on the fundamental frequency of said second source, and wherein said synchronized signal generating means includes means for receiving said second source signal and producing a second synchronized signal having a frequency that is a multiple of the frequency of said second source signal and is synchronized therewith, and wherein said phase differentiator receives said second synchronized signal and determines the phase difference between said second source signal and said reference signal by analyzing the phase difference between said second synchronized signal and said reference signal, and wherein each of said control-vibration frequency components is composed of two source elements according to the following equation:

space="preserve" listing-type="equation">a.sub. (n)=Q.sub. (n)e.sup.jnφ

1+R.sub. (n)e.sup.jnφ

2

where;

a.sub. (n) is a complex number representing the amplitude and phase of a frequency component of the set of control-vibration frequency components of the control-vibration applied by a particular actuator identified by the subscript, .sub. ,

n is an integer equal to the harmonic number of said frequency component;

φ

₁ is the phase difference between said first source signal and said reference signal;

φ

₂ is the phase difference between said second source signal and said reference signal; and

Q.sub. (n) and R.sub. (n) are complex numbers representing the source elements of said frequency component, Q.sub. (n) is the source element corresponding to said first source and R.sub. (n) is the source element corresponding to said second source.

36. The apparatus claimed in claim 35, further comprising:

(a) a plurality of sensors for sensing vibrations at a plurality of second locations in said region or structure;

(b) decomposition means coupled to said plurality of sensors for receiving and decomposing said sensed vibrations into sets of sensed-vibration frequency components; and

(c) controller means coupled to said decomposition means, said phase differentiator, and said output means for;

(i) receiving said sets of sensed-vibration frequency components from said decomposition means;

(ii) receiving from said phase differentiator means representative values of said φ

₁ and φ

₂ phase differences determined while said sensors are sensing the vibrations that are decomposed by said decomposition means;

(iii) calculating updates for the sources elements of selected frequency components of said sets of control-vibration frequency components, said updates based on said sets of sensed-vibration frequency components and said representative values of said φ

₁ and φ

₂ phase differences;

(iv) updating the source elements by updating the source elements of said selected frequency components of said sets of control-vibration frequency components based on said calculated updates; and

(v) supplying said updated source elements to said output means.

37. The apparatus claimed in claim 36, wherein said updates for the source elements of selected frequency components of said sets of control-vibration frequency components are calculated by:

(a) transforming frequency components of said sets of sensed-vibration frequency components into updates for said selected frequency components of said sets of control-vibration frequency components; and

(b) calculating source element updates based on said frequency component updates and said representative values of said φ

₁ and φ

₂ phase differences.

38. The apparatus claimed in claim 37, wherein said source elements of the selected frequency components of said sets of control-vibration frequency components are updated by adding said source element updates to the present values of the corresponding source elements according to the following equations:

space="preserve" listing-type="equation">Δ

Q.sub. (n)+Q.sub. (n)→

Q.sub. (n)

space="preserve" listing-type="equation">Δ

R.sub. (n)+R.sub. (n)→

R.sub. (n)

where;

Q.sub. (n) and R.sub. (n) are the complex numbers representing the source elements of a frequency component of the set of control-vibration frequency components of the control-vibration applied by a particular actuator identified by the subscript , wherein Q.sub. (n) is the source element corresponding to said first source and R.sub. (n) is the source element corresponding to said second source; and

Δ

Q.sub. (n) and Δ

R.sub. (n) are complex numbers representing the updates for said source elements, wherein Δ

Q.sub. (n) is the update for said source element Q.sub. (n), and Δ

R.sub. (n) is the update for said source element R.sub. (n).

39. The apparatus claimed in claim 38, wherein the source element updates are calculated by solving the following matrix equation in a weighted least-squares sense:

##EQU5## where;

γ

₁ and γ

₂ are scalars;

φ

₁ is the representative value of the phase difference between said first source signal and said reference signal;

φ

₂ is the representative value of the phase difference between said second source signal and said reference signal;

Δ

a.sub. (n) is a complex number representing the amplitude and phase update for a frequency component of the set of control-vibration frequency components of the control vibration applied by a particular actuator identified by the subscript, ;

n is an integer equal to the harmonic number of said frequency component; and

Δ

Q.sub. (n) and Δ

R.sub. (n) are the updates for the source elements of said frequency component.

40. The apparatus claimed in claim 39, wherein said second synchronized signal forms said reference signal.

41. The apparatus claimed in claim 39 or 40, wherein said decomposition means includes digital signal processor means programmed to perform Fast Fourier Transforms and said inverse-decomposition means includes digital signal processor means programmed to perform inverse Fast Fourier Transforms.

42. The apparatus claimed in claim 41, wherein the frequency components of each of said sets of sensed-vibration frequency components are the same as the frequency components of each of said sets of control-vibration frequency components.

43. The apparatus claimed in claim 42, wherein said selected frequency components of the sets of control-vibration frequency components are selected by:

(a) determining the magnitude of the frequency components of said sets of sensed-vibration frequency components based on selected criteria; and

(b) selecting those frequency components that have the greatest magnitude, the number of frequency components selected being less than the number of frequency components in said sets of control-vibration frequency components.

44. The apparatus claimed in claim 28, further comprising:

(a) a plurality of sensors for sensing vibrations at a plurality of second locations in said region or structure;

(b) decomposition means coupled to said plurality of sensors for receiving and decomposing said sensed vibrations into sets of sensed-vibration frequency components; and

(c) controller means coupled to said decomposition means, said phase differentiator means, and said output means for;

(i) receiving said sets of sensed-vibration frequency components from said decomposition means;

(ii) receiving from said phase differentiator means a representative value of said phase difference between said reference signal and said source signal based on the values of the phase difference between said reference signal and said source signal while said sensors are sensing the vibrations that are decomposed by said decomposition means;

(iii) calculating updates for the source elements of selected frequency components of said sets of control-vibration frequency components, said updates based on said sets of sensed-vibration frequency components and said representative value of said phase difference;

(iv) updating the source elements by updating the source elements of said selected frequency components of said sets of control-vibration frequency components based on said calculated updates; and

(v) supplying said updated source elements to said output means.

45. The apparatus claimed in claim 44, wherein said updates for the source elements of selected frequency components of said sets of control-vibration frequency components are calculated by:

(a) transforming frequency components of said sets of sensed-vibration frequency components into updates for said selected frequency components of said sets of control-vibration frequency components; and

(b) calculating source element updates based on said frequency component updates and said representative value of said phase difference.

46. The apparatus claimed in claim 45, wherein said source elements of the selected frequency components of said sets of control-vibration frequency components are updated by summing said source element updates with the present values of the corresponding source elements.

47. The apparatus claimed in claim 46, wherein said phase difference represents the time integral of the difference between the frequency of said reference signal and the frequency of said source signal.

48. The apparatus claimed in claim 47, wherein said source signal forms a first source signal and wherein said phase differentiator means determines the phase difference between said reference signal and a second source signal, said second source signal based on a second one of said multiple sources of repetitive vibrations, further wherein said control-vibrations frequency components are composed of two source elements, one for each of said first and second source of repetitive vibrations.

49. The apparatus claimed in claim 48, wherein said source element updates are calculated by solving the following matrix equation in a weighted least-squares sense:

##EQU6## where;

γ

₁ and γ

₂ are scalars;

φ

₁ is said representative value of the phase difference between said first source signal and said reference signal;

φ

₂ is a representative value of the phase difference between said second source signal and said reference signal, said φ

₂ representative value based on the values of the phase difference between said second source signal and said reference signal while said sensors are sensing the vibrations that are decomposed by said decomposition means;

Δ

a.sub. (n) is a complex number representing the amplitude and phase update of a frequency component of the set of control-vibration frequency components of the control vibration applied by a particular actuator identified by the subscript, ;

n is an integer equal to the harmonic number of said frequency component; and

Δ

Q.sub. (n) and Δ

R.sub. (n) are complex numbers representing the updates for the source elements of said frequency component, wherein Δ

Q.sub. (n) is the update for the source element corresponding to said first source, and Δ

R.sub. (n) is the update for the source element corresponding to said second source.

50. The apparatus claimed in claim 49, wherein said output means includes an inverse-decomposition means for producing control-vibration control signals by inverse-decomposing said sets of control-vibration frequency components, and wherein said output means synchronously creates said drive signals from said control-vibration control signals.

51. The apparatus claimed in claim 50, wherein said phase differentiator means includes:

(a) sensor means coupled to said first and second sources of repetitive vibrations for monitoring said first and second sources and producing said first and second source signals each of whose frequency is based on the fundamental frequency generated by the related source;

(b) synchronized signal generating means coupled to said sensor means for producing synchronized signals, said synchronized signal generating means;

(i) receiving the first and second source signals produced by the sensor means; and

(ii) producing for said first and second source signals, related first and second synchronized signals each having a frequency that is a multiple of the frequency of the related source signal and is synchronized therewith; and

(c) a phase differentiator coupled to said synchronized signal generating means for;

(i) receiving said first and second synchronized signals;

(ii) determining said phase differences between said reference signal and said first and second source signals by analyzing the phase differences between said reference signal and said first and second synchronized signals; and

(iii) applying said phase differences determined by analysis to said output means and said controller means.

52. The apparatus claimed in claim 51, wherein said updated sets of control-vibration frequency components are formed by:

(a) weighting each of the source elements of each of the control-vibration frequency components with factors including the corresponding phase differences between said reference signal and said first and second source signals; and

(b) calculating an updated amplitude and phase pair for each of said control-vibration frequency components by forming a sum including the weighted source elements corresponding to the control-vibration frequency component whose amplitude and phase is being updated.

53. The apparatus claimed in claim 52, wherein each of said sets of control-vibration frequency components contains frequency components corresponding to the fundamental frequency of said reference signal and harmonics thereof.

54. The apparatus claimed in claim 53, wherein said drive signals are synchronized with said reference signal.