Method and apparatus for robust vibration suppression

• US 20070032890A1
• Filed: 03/21/2006
• Published: 02/08/2007
• Est. Priority Date: 03/21/2005
• Status: Abandoned Application

• Current Assignee: Board of Regents of Oklahoma State University
• Original Assignee: Board of Regents of Oklahoma State University
• Inventors: Zhou, Li, Misawa, Eduardo
• Application Number:
  US11/385,065
• Publication Number:
  US 20070032890A1
• Time in Patent Office: Days
• US Class Current: 700/63
• CPC Class Codes: G05B 19/416 characterised by control of velocity, acceleration or deceleration G05B19/19 takes precedence
• CPC Class Codes: G05B 2219/41144 Element used such as low pass filter to cut resonance at non needed regions
• CPC Class Codes: G05B 2219/41337 Linear drive motor, voice coil
• CPC Class Codes: G11B 19/042 due to external shock or vibration
• CPC Class Codes: G11B 5/5582 system adaptation for working during or after external perturbation, e.g. in the presence of a mechanical oscillation caused by a shock
• CPC Class Codes: G11B 5/596 for track following on disks G11B5/5526, G11B5/5552, G11B5/5565, G11B5/5582 take precedence

Abstract

According to a preferred aspect of the instant invention, there is provided a system and method of robust vibration suppression which might be used in many subject matters, but which is preferably used in connection with computer controlled electromechanical devices such as disk drive arms. In a first preferred embodiment, a Gaussian waveform is selected as a velocity profile, with its integral and derivatives providing position and acceleration/jerk profiles respectively. According to another preferred embodiment, the movement velocity profile will be selected to be a member of the prolate spheroid family of waveforms. This family of functions has certain optimal properties with respect to the frequency domain concentration of energy for a given time-domain length time series. The movement of a flexible arm that is performed according to the invention will be one that has minimal or reduced residual vibration after it has reached its destination.

Claims

1. A method of moving a flexible dynamic system from an initial position to a final position, comprising the steps of:

(a) determining at least one resonance frequency of the system;

(b) determining a smallest of said at least one resonance frequencies;

(c) selecting a move time;

(d) selecting a velocity profile function, wherein said velocity profile function has at least one parameter associated therewith;

(e) using at least said selected move time to determine a value for each of said at least one parameters such that a near maximum spectral energy in said velocity profile function is contained within frequencies less than said smallest resonance frequency; and

,

(f) moving said flexible dynamic system from the initial position to the final position at least according to said move time, said velocity profile function, and said at least one values of said parameters.

2. A method of moving a flexible dynamic system from an initial position to a final position according to claim 1, wherein said flexible dynamic system is selected from a group consisting of a disk drive arm and a robot arm.

3. A method of moving a flexible dynamic system from an initial position to a final position according to claim 1, wherein said velocity profile function is selected from a group consisting of a Gaussian function and a prolate spheroid function.

4. A method of moving a flexible dynamic system from an initial position to a final position according to claim 3, wherein said velocity profile function is a Gaussian function h,(t) of the form,

$h_n$

( t ) = ⅇ

- 1 2 ⁢

2 2 ⁢

n ⁢

t 2

wherein n is a parameter associated with said Gaussian function, and t is a variable representing time.

5. A method of moving a flexible dynamic system from an initial position to a final position according to claim 4, wherein step (e) comprises the step of

(e1) using at least said selected move time to determine said parameter n such that a near maximum spectral energy in said velocity profile function is contained within frequencies less than said smallest resonance frequency, parameter n begin determined by at least approximately maximizing a variable J with respect to n, where J is defined to be:

$J=\frac{{\int <br><br>}_0^{{\mathrm{\omega <br><br>}}_0}<br><br>{<br><br>G_{h,n}<br><br>\left(\mathrm{\omega <br><br>}\right)<br><br>}^2<br><br>d<br><br>\mathrm{\omega <br><br>}}{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{<br><br>G_{h,n}<br><br>\left(\mathrm{\omega <br><br>}\right)<br><br>}^2<br><br>d<br><br>\mathrm{\omega <br><br>}}$

wherein ω

₀ is said smallest resonance frequency, and G_h,n(ω

) is a Fourier transform of a time shifted version of h(t),

$g_{h,n}<br><br>\left(t\right)=\{\begin{array}{cc}{h}_n<br><br>\left(t-D\right)& \mathrm{if}<br><br>\text{\hspace{1em}<br><br>}<br><br>0\le <br><br>t\le <br><br>2<br><br>D;<br><br>\\ 0,& \mathrm{otherwise}.\end{array}$

and D is one half of said move time.

11. A method of moving a flexible dynamic system from an initial position to a final position according to claim 3, wherein said velocity profile function is a Gaussian function h,(t) of the form,

$h_n$

( t ) = ⅇ

- 1 2 ⁢

2 2 ⁢

n ⁢

t 2

wherein n is a parameter associated with said Gaussian function, and t is a variable representing time.

12. A method of moving a flexible dynamic system from an initial position to a final position according to claim 11 wherein step (e) comprises the step of

(e1) using at least said selected move time to determine said parameter n such that a near maximum spectral energy in said velocity profile function is contained within frequencies less than said smallest resonance frequency, parameter n begin determined by at least approximately maximizing a variable J with respect to n, where J is defined to be:

$J=\frac{{\int <br><br>}_0^{{\mathrm{\omega <br><br>}}_0}<br><br>{<br><br>G_{h,n}<br><br>\left(\mathrm{\omega <br><br>}\right)<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\omega <br><br>}}{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{<br><br>G_{h,n}<br><br>\left(\mathrm{\omega <br><br>}\right)<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\omega <br><br>}}$

wherein ω

₀ is said smallest resonance frequency, and G_h,n(ω

) is a Fourier transform of a time shifted version of h_n(t),

$g_{h,n}<br><br>\left(t\right)=\{\begin{array}{cc}{h}_n<br><br>\left(t-D\right)& \mathrm{if}<br><br>\text{\hspace{1em}<br><br>}<br><br>0\le <br><br>t\le <br><br>2<br><br>D;<br><br>\\ 0,& \mathrm{otherwise}.\end{array}$

and D is one half of said move time.

6. A method of determining a velocity profile for use in moving a flexible dynamic system from an initial position to a final position, comprising the steps of:

(a) determining at least one resonance frequency of the system;

(b) determining a smallest of said at least one resonance frequencies;

(c) selecting a move time;

(d) selecting a velocity profile function, wherein said velocity profile function has at least one parameter associated therewith;

(e) using at least said selected move time to determine a value for each of said at least one parameters such that a near maximum spectral energy in said velocity profile function is contained within frequencies less than said smallest resonance frequency; and

,

(f) storing in a computer readable medium at least indicia representative of said at least one parameter values and said selected velocity profile function for use in moving said flexible dynamic system from the initial position to the final position.

7. A method of determining a velocity profile for use in moving a flexible dynamic system from an initial position to a final position according to claim 6, comprising the further step of:

(g) reading from said computer readable medium at least said stored indicia representative of said at least one parameter values and said selected velocity profile function; and

,

(h) moving the flexible dynamic system from the initial position to the final position at least according to said move time, said read indicia representative of said selected velocity profile function, and said read indicia of representative of said at least one parameter values.

8. A method according to claim 6, wherein said computer readable medium is selected from a group consisting of a magnetic disk, a magnetic tape, an optical disk, a magneto-optical disk, computer RAM, and non-volatile RAM.

9. A method of moving a flexible dynamic system from an initial position to a final position according to claim 6, wherein said flexible dynamic system is selected from a group consisting of a disk drive arm and a robot arm.

10. A method of moving a flexible dynamic system from an initial position to a final position according to claim 6, wherein said velocity profile function is selected from a group consisting of a Gaussian function and a prolate spheroid function.

13. A method comprising

a step of providing a velocity control profile to describe a near time and frequency-optimal velocity profile for a control object during movement of the control object from an initial position to a final position during a predetermined move time, said control object having at least one resonance frequency,

the velocity profile comprising,

a functional form defined by at least one parameter, said at least one parameter being chosen to at least approximately maximize an amount of spectral energy in said velocity profile function contained within frequencies less than a smallest one of said at least one resonance frequencies based on said move time.

14. The method of claim 13, further comprising a step of moving the control object from the initial position to the final position in accordance with said velocity control profile.

15. The method of claim 13, further comprising a step of deriving from said velocity profile at least a selected one of a control voltage profile, a current profile, an acceleration profile and a displacement profile to describe an associated characteristic trajectory for the control object move from the initial position to the final position.

16. The method of claim 13, further comprising a step of utilizing the at least a selected one of said control voltage profile, current profile, acceleration profile and displacement profile to move the control object from the initial position to the final position.

17. A method of moving a flexible dynamic system from an initial position to a final position according to claim 13, wherein said control object is selected from a group consisting of a disk drive arm and a robot arm.

18. A method of moving a flexible dynamic system from an initial position to a final position according to claim 13, wherein said velocity profile functional form is selected from a group consisting of a Gaussian functional form and a prolate spheroid functional form.

19. A method of moving a flexible dynamic system from an initial position to a final position according to claim 13, wherein said velocity profile functional form is a Gaussian function h_n(t) of the form,

$h_n$

( t ) = ⅇ

- 1 2 ⁢

2 2 ⁢

n ⁢

t 2

wherein n is a parameter defining said Gaussian function, and t is a variable representing time.

20. A method of moving a flexible dynamic system from an initial position to a final position according to claim 16, wherein said parameter n is chosen by at least approximately maximizing a variable J with respect to n, where J is defined to be:

$J=\frac{{\int <br><br>}_0^{{\mathrm{\omega <br><br>}}_0}<br><br>{<br><br>G_{h,n}<br><br>\left(\mathrm{\omega <br><br>}\right)<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\omega <br><br>}}{{\int <br><br>}_0^{\mathrm{\pi <br><br>}}<br><br>{<br><br>G_{h,n}<br><br>\left(\mathrm{\omega <br><br>}\right)<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{\omega <br><br>}}$

wherein ω

₀ is said smallest resonance frequency, and G_h,n(ω

) is a Fourier transform of a time shifted version of h_n(t),

$g_{h,n}<br><br>\left(t\right)=\{\begin{array}{cc}{h}_n<br><br>\left(t-D\right)& \mathrm{if}<br><br>\text{\hspace{1em}<br><br>}<br><br>0\le <br><br>t\le <br><br>2<br><br>D;<br><br>\\ 0,& \mathrm{otherwise}.\end{array}$

and D is one half of said move time.