Abstract

This article presents a method for characterizing the system dynamics of a trapped particle in real-time and designing a controller to minimize disturbances to the particle’s position. Specifically, adaptive system identification is used to determine the trap characteristics and the actuator transfer function describing the mirror voltage to trap position path. Using an internal model control scheme combined with a filtered-x least-mean-square algorithm, adaptive control was used to create a controller that minimizes a frequency weighted mean-squared-error. The dynamics associated with multiple particle sizes and materials were experimentally determined under different power levels, each case resulting in different system dynamics and demonstrating positive control results. The adaptive system identification and the controller presented automate the process of system identification and control design, enabling the automation of optical trap controller design.

© 2008 Optical Society of America

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References

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  2. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
    [CrossRef] [PubMed]
  3. C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
    [CrossRef] [PubMed]
  4. J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
    [CrossRef] [PubMed]
  5. K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999).
    [CrossRef] [PubMed]
  6. J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).
  7. K. D. Wulff, D. G. Cole, and R. L. Clark, “Servo control of an optical trap,” Appl. Opt. 46, 4923-4931 (2007).
    [CrossRef] [PubMed]
  8. K. D. Wulff, D. G. Cole, and R. L. Clark, “An adaptive system identification approach to optical trap calibration,” Opt. Express 16, 4420-4425 (2008).
    [CrossRef] [PubMed]
  9. B. Widrow and S. D. Stearns, Adaptive Signal Processing, (Prentice-Hall, 1985).
  10. S. S. Haykin, Adaptive Filter Theory, 2nd ed. (Prentice Hall, 1991).
  11. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7-9 (1998).
    [CrossRef]
  12. K. Svoboda and S. M. Block, “Biological applications of optical forces,”Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
    [CrossRef] [PubMed]

2008 (1)

2007 (2)

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

K. D. Wulff, D. G. Cole, and R. L. Clark, “Servo control of an optical trap,” Appl. Opt. 46, 4923-4931 (2007).
[CrossRef] [PubMed]

2000 (1)

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

1999 (1)

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (1)

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

1995 (1)

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

1994 (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,”Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

1986 (1)

Ashkin, A.

Bjorkholm, J. E.

Block, S. M.

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999).
[CrossRef] [PubMed]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

K. Svoboda and S. M. Block, “Biological applications of optical forces,”Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

Burns, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

Bustamante, C.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Chu, S.

Clark, R. L.

Cole, D. G.

Dziedzic, J. M.

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Gittes, F.

Haykin, S. S.

S. S. Haykin, Adaptive Filter Theory, 2nd ed. (Prentice Hall, 1991).

Kendrickjones, J.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Li, P. T. X.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

Liphardt, J.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Manosas, M.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

Molloy, J. E.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

Ritort, F.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

Schmidt, C. F.

Schnitzer, M. J.

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999).
[CrossRef] [PubMed]

Smith, D.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Smith, S. B.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Sparrow, J. C.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

Stearns, S. D.

B. Widrow and S. D. Stearns, Adaptive Signal Processing, (Prentice-Hall, 1985).

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,”Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

Tinoco, I.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

Tregear, R. T.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

Visscher, K.

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999).
[CrossRef] [PubMed]

Wang, M. D.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Wen, J. D.

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

White, D. C. S.

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

Widrow, B.

B. Widrow and S. D. Stearns, Adaptive Signal Processing, (Prentice-Hall, 1985).

Wulff, K. D.

Yin, H.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,”Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (3)

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrickjones, and D. C. S. White, “Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers,” Biophys. J. 68, S298-S305 (1995).

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

J. D. Wen, M. Manosas, P. T. X. Li, S. B. Smith, C. Bustamante, F. Ritort, and I. Tinoco, “Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results,” Biophys. J. 92, 2996-3009 (2007).
[CrossRef] [PubMed]

Curr. Opin. Struct. Biol. (1)

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Nature (1)

K. Visscher, M. J. Schnitzer, and S. M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184-189 (1999).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

B. Widrow and S. D. Stearns, Adaptive Signal Processing, (Prentice-Hall, 1985).

S. S. Haykin, Adaptive Filter Theory, 2nd ed. (Prentice Hall, 1991).

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Figures (3)

Fig. 1
Fig. 1

Filtered-x LMS model-matching scheme for estimating the actuator dynamics. Here, G 2 is the plant dynamics, G ^ 2 the estimated plant dynamics, and F the FIR filter to replicate the actuator dynamics, G A .

Fig. 2
Fig. 2

Internal model control scheme for the adaptive controller. Free parameter Q is adapted using the filtered-x LMS algorithm to minimize the weighted mean-squared-error.

Fig. 3
Fig. 3

Example of the steps for the construction of an adaptive controller using a 1 μm polystyrene sphere trapped in a 20 mW laser. (a) System identification of the plant dynamics, G 1 . The corner frequency, Ω, is 632 Hz . (b) Combined plant and actuator dynamics, as well as the identified actuator dynamics. (c) Open-loop and closed-loop results.

Tables (1)

Tables Icon

Table 1 Open-Loop and Closed-Loop RMS Displacements of Particles Trapped under Multiple Power Levels a

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

J = 1 2 E { e ( n ) 2 } ,
w = J / w [ e ( n ) / w ] e ( n ) .
F ( z ) = w 0 + w 1 z - 1 + w 2 z - 2 + + w M - 1 z 1 - M ,
e / w n = - G ^ 2 z - n v ( n ) .
w - e x z - n .
w ( n + 1 ) = w ( n ) - μ x ( n ) e ( n ) ,
z = G A G 1 v + d ,
K = Q 1 + G Q , Q stable ,
e = W ( 1 + G Q ) d ,
x = W G ^ A G ^ 1 d ^
d ^ = z G A ^ G ^ 1 v ,
e = W z = W ( 1 ( G A G 1 ) Q ) d ,
x = W G ^ A G ^ 1 d ^ .

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