Systems and methods for robust vibration suppression in a motion control system

• US 6,294,891 B1
• Filed: 11/12/1998
• Issued: 09/25/2001
• Est. Priority Date: 08/15/1997
• Status: Expired due to Fees

• Current Assignee: Iowa State University Research Foundation Incorporated (Iowa State University)
• Original Assignee: Iowa State University Research Foundation Incorporated (Iowa State University)
• Inventors: Bouton, Chad E., McConnell, Kenneth G.
• Primary Examiner(s): Nappi, Robert E.
• Assistant Examiner(s): SMITH, TYRONE W
• Application Number:
  US09/190,874
• Time in Patent Office: 1,048 Days
• Field of Search: 700/188, 700/32, 700/38, 700/39, 700/69, 700/52, 700/97, 700/98, 700/182, 318/636, 318/105-110, 318/440-442, 318/629, 318/558, 318/560-569, 703/1, 703/14, 703/18, 702/75-78, 702/109-113, 702/115
• US Class Current: 318/619
• CPC Class Codes: G05B 5/01 electric

Abstract

Systems and methods for reducing unwanted vibration in motion system are provided using a Robust Vibration Suppression (RVS) methodology, in which acceleration frequency spectra are obtained for each of a number of command input functions developed for moving a load a specified distance within a specified move time interval using an actuator. The frequency spectra comprise peaks, with notches defined between adjacent peaks. A desirable command input function is one with a frequency spectra having either a notch with a maximum width or a peak with a minimum magnitude relative to frequency spectra associated with other command input functions, or, alternatively, a peak with a magnitude of less than or equal to a pre-established magnitude or a frequency notch having a width greater than or equal to a pre-established width. A suitable command input function may be characterized by a ramp function, a cosine function, a sine function, or a combination thereof. The period of a suitable command input function is related to a fundamental natural frequency of the motion control system. A bridge circuit may be employed to reduce motor ripple torque, and a control circuit may be employed to compensate for back EMF. A computer-based system may be used to design, test, and optimize a motion control system using RVS principles. Various system components may be graphically modeled. Command input functions may be applied to the system, modified, and optimized. Various graphical and character data may be displayed. RVS design software may be embodied in a computer-readable article of manufacture.

Claims

1. A method of controlling an actuator of a motion control system, comprising:

obtaining an acceleration frequency spectra for each of a plurality of command input functions developed for moving a load a specified distance within a specified move time interval using the actuator, the frequency spectra comprising a series of peaks and notches defined between adjacent peaks;

selecting from the plurality of command input functions a command input function having a frequency spectra with a notch having a maximum width relative to frequency spectra associated with other ones of the plurality of command input functions;

applying a selected command input function to the actuator so as to cause the actuator to move the load the specified distance within the specified move time interval.

2. The method according to claim 1, wherein the motion control system exhibits a fundamental natural period, T_n, the selected command input function has a period of between approximately 1.5T_n and approximately 3T_n.

3. The method according to claim 1, wherein the notch is one of the first five frequency notches in the respective frequency spectra.

4. The method according to claim 1, wherein the notch is the first frequency notch in the respective frequency spectra.

5. The method according to claim 1, wherein a period of the selected command input function is related to a fundamental natural frequency of the motion control system.

6. The method according to claim 1, wherein the selected command input function is characterized by a cosine function, a sine function, a parabolic function, or a cubic function.

7. The method according to claim 1, wherein the selected command input function has associated with it impulses in the third time derivative and a square wave in the second time derivative.

8. The method according to claim 1, wherein the selected command input function has associated with it impulses in the fourth time derivative and a square wave in the third time derivative.

9. The method according to claim 1, wherein an acceleration profile associated with the selected command input function is characterized by a cosine function, a sine function, a square function, or a linear function.

10. A method of developing a command input function for an actuator of a motion control system, comprising:

developing an acceleration profile for moving a load within predetermined displacement and move time limits using the actuator, a frequency spectra of the acceleration profile having a notch, defined between adjacent peaks, the notch having a width greater than or equal to a pre-established width;

obtaining a command input function using the acceleration profile; and

applying the command input function to the actuator so as to cause the actuator to move the load within the predetermined displacement and move time limits.

11. The method according to claim 10, wherein the pre-established width is established as a maximum width of notches in frequency spectra associated with a plurality of acceleration profiles developed for moving the load within the predetermined displacement and move time limits.

12. The method according to claim 10, further comprising verifying that the width of the notch of the actual acceleration frequency spectra is greater than or equal to the pre-established width.

13. The method according to claim 10, wherein developing the acceleration profile further comprises selecting the predetermined displacement limit and the predetermined move time limit associated with relative movement between the load and the actuator.

14. The method according to claim 10, wherein a period of the command input function is related to a fundamental natural frequency of the motion control system.

15. The method according to claim 10, wherein the command input function is characterized by a cosine function, a sine function, a parabolic function, or a cubic function.

16. The method according to claim 10, wherein the acceleration profile for moving the load using the actuator is characterized by a cosine function, a sine function, a square function, or a linear function.

17. The method according to claim 10, wherein the command input function has associated with it impulses in the third time derivative and a square wave in the second time derivative.

18. The method according to claim 10, wherein the command input function has associated with it impulses in the fourth time derivative and a square wave in the third time derivative.

19. The method according to claim 10, wherein the motion control system exhibits a fundamental natural period, T_n, and the command input function has a period of between approximately 1.5T_n and approximately 3T_n.

20. A method of developing a command input function for controlling a motion control system using a computer system, comprising:

displaying a graphical representation of a base structure, a stator structure, and a rotor structure of an actuator, and a structure to be driven by the actuator;

characterizing one or more properties of the base structure, the stator structure, the rotor structure, and the driven structure;

obtaining an acceleration frequency spectra for each of a plurality of command input functions developed for moving the driven structure within specified displacement and move time limits using the actuator, the frequency spectra comprising a series of peaks and notches defined between adjacent peaks;

selecting a command input function with a frequency spectra having a notch with a maximum width relative to frequency spectra associated with other ones of the plurality of command input functions;

applying the selected command input function to the actuator; and

simulating movement of the driven structure relative to the actuator in response to the selected command input function.

21. The method according to claim 20, further comprising verifying that the selected command input function exhibits the notch with the maximum width.

22. The method according to claim 20, further comprising:

modifying the selected command input function;

applying the modified selected command input function to the actuator; and

simulating movement of the driven structure relative to the actuator in response to the modified selected command input function.

23. The method according to claim 20, wherein simulating movement of the driven structure relative to the actuator comprises simulating the movement graphically or in terms of data.

24. The method according to claim 20, further comprising modifying the displacement and move time limits.

25. The method according to claim 20, wherein characterizing one or more of the properties further comprises characterizing one or more dynamic and structural properties of the base structure, the stator structure, the rotor structure, and the driven structure.

26. The method according to claim 20, further comprising modifying one or more of the properties of the base structure, the stator structure, the rotor structure, or the driven structure.

27. The method according to claim 20, further comprising displaying a graphical representation of the frequency spectra associated with the selected command input function.

28. The method according to claim 20, further comprising displaying a graphical representation of the frequency spectra associated with one or more of the plurality of command input functions.

29. The method according to claim 20, further comprising displaying a graphical representation of position errors associated with one or more of the plurality of command input functions.

30. The method according to claim 20, further comprising displaying a graphical representation of velocity profiles associated with one or more of the plurality of command input functions.

31. The method according to claim 20, further comprising displaying a graphical representation of acceleration profiles associated with one or more of the plurality of command input functions.

32. The method according to claim 20, further comprising displaying a graphical representation of excitation time profiles associated with one or more of the plurality of command input functions.

33. A computer readable medium tangibly embodying a program executable for developing a command input function for an actuator of a motion control system, comprising:

displaying a graphical representation of a base structure, a stator structure, and a rotor structure of the actuator, and a structure to be driven by the actuator;

characterizing one or more properties of the base structure, the stator structure, the rotor structure, and the driven structure;

obtaining an acceleration frequency spectra for each of a plurality of command input functions developed for moving the driven structure within specified displacement and move time limits using the actuator, the frequency spectra comprising a series of peaks and notches defined between adjacent peaks;

selecting a command input function with a frequency spectra having a notch with a maximum width relative to frequency spectra associated with other ones of the plurality of command input functions;

applying the selected command input function to the actuator; and

simulating movement of the driven structure relative to the actuator in response to the selected command input function.

34. The medium according to claim 33, further comprising verifying that the selected command input function exhibits the notch with the maximum width.

35. The medium according to claim 33, further comprising modifying the selected command input function or the displacement and move time limits.

36. The medium according to claim 33, wherein characterizing one or more of properties further comprising characterizing one or more dynamic and structural properties of the base structure, the stator structure, the rotor structure, and the driven structure.

37. The medium according to claim 33, further comprising modifying one or more of the properties of the base structure, the stator structure, the rotor structure, or the driven structure.

38. The medium according to claim 33, further comprising displaying a graphical representation of the frequency spectra associated with the selected command input function.

39. The medium according to claim 33, further comprising displaying a graphical representation of the frequency spectra associated with one or more of the plurality of command input functions.

40. The medium according to claim 33, further comprising displaying a graphical representation of velocity profiles, acceleration profiles, or excitation time profiles associated with one or more of the plurality of command input functions.

41. A method of controlling an actuator of a motion control system, comprising:

obtaining an acceleration frequency spectra for each of a plurality of command input functions developed for moving a load a specified distance within a specified move time interval using the actuator, the frequency spectra comprising a series of peaks and notches defined between adjacent peaks;

selecting from the plurality of command input functions a command input function having a frequency spectra with a peak having a minimum magnitude relative to frequency spectra associated with other ones of the plurality of command input functions;

applying a selected command input function to the actuator so as to cause the actuator to move the load the specified distance within the specified move time interval.

42. The method according to claim 41, wherein the motion control system exhibits a fundamental natural period, T_n, and the selected command input function has a period of between approximately 1.5T_n and approximately 3T_n.

43. The method according to claim 41, wherein the peak with a minimum magnitude is either a first peak or a second peak in the respective frequency spectra.

44. The method according to claim 41, wherein a period of the selected command input function is related to a fundamental natural frequency of the motion control system.

45. The method according to claim 41, wherein the selected command input function is characterized by a cosine function, a sine function, a parabolic function, or a cubic function.

46. The method according to claim 41, wherein the selected command input function has associated with it impulses in the third time derivative and a square wave in the second time derivative.

47. The method according to claim 41, wherein the selected command input function has associated with it impulses in the fourth time derivative and a square wave in the third time derivative.

48. The method according to claim 41, wherein an acceleration profile associated with the selected command input function is characterized by a cosine function, a sine function, a square function, or a linear function.

49. A method of developing a command input function for an actuator of a motion control system, comprising:

developing an acceleration profile for moving a load within predetermined displacement and move time limits using the actuator, a frequency spectra of the acceleration profile having a peak with a magnitude of less than or equal to a pre-established magnitude;

obtaining a command input function using the acceleration profile; and

applying the command input function to the actuator so as to cause the actuator to move the load within the predetermined displacement and move time limits.

50. The method according to claim 49, wherein the pre-established magnitude is established as a minimum magnitude of frequency spectra associated with a plurality of acceleration profiles developed for moving the load within the predetermined displacement and move time limits.

51. The method according to claim 49, further comprising verifying that the magnitude of an actual acceleration frequency spectra associated with the command input function is less than or equal to the pre-established magnitude.

52. The method according to claim 49, wherein developing the acceleration profile further comprises selecting the predetermined displacement limit and the predetermined move time limit associated with relative movement between the load and the actuator.

53. The method according to claim 49, wherein a period of the command input function is related to a fundamental natural frequency of the motion control system.

54. The method according to claim 49, wherein the command input function is characterized by a cosine function, a sine function, a parabolic function, or a cubic function.

55. The method according to claim 49, wherein the acceleration profile for moving the load using the actuator is characterized by a cosine function, a sine function, a square function, or a linear function.

56. The method according to claim 49, wherein the command input function has associated with it impulses in the third time derivative and a square wave in the second time derivative.

57. The method according to claim 49, wherein the command input function has associated with it impulses in the fourth time derivative and a square wave in the third time derivative.

58. The method according to claim 49, wherein the motion control system exhibits a fundamental natural period, T_n, and the command input function has a period of between approximately 1.5T_n and approximately 3T_n.

59. A method of developing a command input function for controlling a motion control system using a computer system, comprising:

displaying a graphical representation of a base structure, a stator structure, and a rotor structure of an actuator, and a structure to be driven by the actuator;

characterizing one or more properties of the base structure, the stator structure, the rotor structure, and the driven structure;

obtaining an acceleration frequency spectra for each of a plurality of command input functions developed for moving the driven structure within specified displacement and move time limits using the actuator, the frequency spectra comprising a series of peaks and notches defined between adjacent peaks;

selecting a command input function with a frequency spectra having a peak with a minimum magnitude relative to frequency spectra associated with other ones of the plurality of command input functions;

applying the selected command input function to the actuator; and

simulating movement of the driven structure relative to the actuator in response to the selected command input function.

60. The method according to claim 59, further comprising verifying that the selected command input function exhibits the peak with the minimum magnitude.

61. The method according to claim 59, further comprising:

modifying the selected command input function;

applying the modified selected command input function to the actuator; and

simulating movement of the driven structure relative to the actuator in response to the modified selected command input function.

62. The method according to claim 59, wherein simulating movement of the driven structure relative to the actuator comprises simulating the movement graphically or in terms of data.

63. The method according to claim 59, further comprising modifying the displacement and move time limits.

64. The method according to claim 59, wherein characterizing one or more of the properties further comprises characterizing one or more dynamic and structural properties of the base structure, the stator structure, the rotor structure, and the driven structure.

65. The method according to claim 59, further comprising modifying one or more of the properties of the base structure, the stator structure, the rotor structure, or the driven structure.

66. The method according to claim 59, further comprising displaying a graphical representation of the frequency spectra associated with the selected command input function.

67. The method according to claim 59, further comprising displaying a graphical representation of the frequency spectra associated with one or more of the plurality of command input functions.

68. The method according to claim 59, further comprising displaying a graphical representation of position errors associated with one or more of the plurality of command input functions.

69. The method according to claim 59, further comprising displaying a graphical representation of velocity profiles associated with one or more of the plurality of command input functions.

70. The method according to claim 59, further comprising displaying a graphical representation of acceleration profiles associated with one or more of the plurality of command input functions.

71. The method according to claim 59, further comprising displaying a graphical representation of excitation time profiles associated with one or more of the plurality of command input functions.

73. The medium according to claim 71, further comprising verifying that the selected command input function exhibits the peak with the minimum magnitude.

74. The medium according to claim 71, further comprising modifying the selected command input function or the displacement and move time limits.

75. The medium according to claim 71, wherein characterizing one or more of properties further comprising characterizing one or more dynamic and structural properties of the base structure, the stator structure, the rotor structure, and the driven structure.

76. The medium according to claim 71, further comprising modifying one or more of the properties of the base structure, the stator structure, the rotor structure, or the driven structure.

77. The medium according to claim 71, further comprising displaying a graphical representation of the frequency spectra associated with the selected command input function.

78. The medium according to claim 71, further comprising displaying a graphical representation of the frequency spectra associated with one or more of the plurality of command input functions.

79. The medium according to claim 71, further comprising displaying a graphical representation of velocity profiles, acceleration profiles, or excitation time profiles associated with one or more of the plurality of command input functions.

72. A computer readable medium tangibly embodying a program executable for developing a command input function for an actuator of a motion control system, comprising:

displaying a graphical representation of a base structure, a stator structure, and a rotor structure of the actuator, and a structure to be driven by the actuator;

characterizing one or more properties of the base structure, the stator structure, the rotor structure, and the driven structure;

obtaining an acceleration frequency spectra for each of a plurality of command input functions developed for moving the driven structure within specified displacement and move time limits using the actuator, the frequency spectra comprising a series of peaks and notches defined between adjacent peaks;

selecting a command input function with a frequency spectra having a peak with a minimum magnitude relative to frequency spectra associated with other ones of the plurality of command input functions;

applying the selected command input function to the actuator; and

simulating movement of the driven structure relative to the actuator in response to the selected command input function.