Abstract

In recent years fuzzy-logic-based controllers have become the preferred tool for implementing control mechanisms in high-complexity systems. We suggest novel implementations of a basic fuzzy controller. First, we show the principles of fuzzy-logic control and explain the concept behind the optical controller. Next we review a one-dimensional fuzzy-logic-based optoelectronic controller that was suggested in 1994. Finally, we present a novel two-dimensional optical control approach accompanied by computer simulations of an inverted pendulum. The two-dimensional setup is first given for a dual-input controller and then expanded to a multi-input controller.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1955).
    [CrossRef]
  2. H. Itoh, S. Mukai, H. Yagima, “Optoelectronic fuzzy inference system based on beam-scanning architecture,” Appl. Opt. 33, 1485–1490 (1994).
    [CrossRef] [PubMed]
  3. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  4. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  5. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).
  6. E. Carcole, J. Campos, S. Bosch, “Diffraction theory of Fresnel lenses encoded in low-resolution devices,” Appl. Opt. 33, 162–174 (1994).
    [CrossRef] [PubMed]

1994 (2)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1967 (1)

1955 (1)

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1955).
[CrossRef]

Bosch, S.

Campos, J.

Carcole, E.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Itoh, H.

Lohmann, A. W.

Mukai, S.

Paris, D. P.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

Yagima, H.

Zadeh, L. A.

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1955).
[CrossRef]

Appl. Opt. (3)

Inf. Control (1)

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1955).
[CrossRef]

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Other (1)

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

MG’s for (a) a classical set and (b) a fuzzy set.

Fig. 2
Fig. 2

Five MF’s covering the range [x n , x m ].

Fig. 3
Fig. 3

Fuzzy sets for temperature (x), pressure (y), and torque (z). Sets {μ} and {η} are the MG’s for the input data x 0 and y 0, respectively.

Fig. 4
Fig. 4

Procedure for finding the output torque value as a COG of the surfaces beneath the {χ} MG’s.

Fig. 5
Fig. 5

One-dimensional optoelectronic control setup proposed by Itoh et al.2 PL, positive large; PM, positive medium; PS, positive small; Z, zero; NS, negative small; NM, negative medium; NL, negative large.

Fig. 6
Fig. 6

Calculation of MG’s by use of (a) a single-input, multiple-MF setup and (b) a single-MF, multiple-input setup. MG’s: a = c and b = d.

Fig. 7
Fig. 7

One-dimensional setup for optical beam displacement by use of an AOD.

Fig. 8
Fig. 8

Rule scheme (9 × 9) for an inverted pendulum: x represents the pendulum tilt, y represents the first derivative of the tilt, and out represents the required cart displacement. P, positive; N, negative; Z, zero; L, large; M, medium; S, small.

Fig. 9
Fig. 9

Beam allocation of a microprism array in the Fourier plane. If the DOE depth resolution is high, more energy is in the first order, and less is in the other orders. PVL, positive very large; NVL, negative very large.

Fig. 10
Fig. 10

Two-dimensional optical fuzzy controller. The data inputs are fed to AOD’s, and the outcome of the PSD is the controller’s output.

Fig. 11
Fig. 11

Simulation results for the 2-D setup: (a) fluctuations resulting from the beam width and (b) fluctuations resulting from the rule structure.

Fig. 12
Fig. 12

Multidimensional setup in a 2-D representation.

Fig. 13
Fig. 13

Mistake in the conclusion as a result of the consecutive rule plates.

Equations (7)

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

Rule   1 :   if   x MF 3 temp   and   y MF 3 pres ,   then   z MF 3 torq . Rule   2 :   if   x MF 4 temp   and   y MF 3 pres ,   then   z MF 4 torq .
μ 3   AND   η 3   χ 3 , μ 4   AND   η 3   χ 4 ,
min μ 3 ,   η 3 = χ 3 = μ 3 , min μ 4 ,   η 3 = χ 4 = η 3 .
θ = α I 1 - I 2 .
ξ = λ F v   kf 0 ,
θ B = λ Λ = λ f 0 2 v ,
  | u x ,   y | 2 d x d y   | U v x ,   v y | 2 d v x d v y ,

Metrics