Abstract

In part I of a previous study [Appl. Opt. 37, 6937 (1998)] we introduced what is believed to be a novel two-dimensional (2-D) fuzzy-logic optical controller. The complexity of such a setup when we deal with an N-dimensional control procedure leads to a more compact version both in planning demands and in space. Viewing the pros and cons of the 2-D setup, we seek a simpler model and find it in a one- dimensional (1-D) multilayer setup. Here we explain the process of finding the optimal 1-D setup and support the concept with true optical results. The new 1-D optical controller is modular and easy to build, and the results that it yields are quite satisfactory.

© 1999 Optical Society of America

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References

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  1. L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
    [CrossRef]
  2. M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 3, pp. 24–35.
  3. W. Pritzik, Fuzzy Control and Fuzzy Systems, 2nd extended ed. (Research Studies Press, Taunton, Somerset, UK; Wiley, New York, 1993) Chap. 2, pp. 68–77.
  4. E. Gur, D. Mendlovic, Z. Zalevsky, “Optical implementation of fuzzy-logic controllers. Part I,” Appl. Opt. 37, 6937–6945 (1998).
    [CrossRef]
  5. H. Itoh, S. Mukai, H. Yagima, “Optoelectronic fuzzy inference system based on beam-scanning architecture,” Appl. Opt. 33, 1485–1490 (1994).
    [CrossRef] [PubMed]

1998 (1)

1994 (1)

1965 (1)

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Chew, G.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 3, pp. 24–35.

Gur, E.

Itoh, H.

Kandel, A.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 3, pp. 24–35.

Langholz, G.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 3, pp. 24–35.

Mendlovic, D.

Mukai, S.

Pritzik, W.

W. Pritzik, Fuzzy Control and Fuzzy Systems, 2nd extended ed. (Research Studies Press, Taunton, Somerset, UK; Wiley, New York, 1993) Chap. 2, pp. 68–77.

Schneider, M.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 3, pp. 24–35.

Yagima, H.

Zadeh, L. A.

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Zalevsky, Z.

Appl. Opt. (2)

Inf. Control (1)

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Other (2)

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 3, pp. 24–35.

W. Pritzik, Fuzzy Control and Fuzzy Systems, 2nd extended ed. (Research Studies Press, Taunton, Somerset, UK; Wiley, New York, 1993) Chap. 2, pp. 68–77.

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Figures (6)

Fig. 1
Fig. 1

2-D optical fuzzy controller, as suggested in Part I.4 POF, phase-only filter; I, input (data); O, output (result).

Fig. 2
Fig. 2

Simple 1-D optical controllers, based on fuzzy logic (a) with a single PSD and (b) with two separate PSD’s. PBS, polarized beam splitter; BS, beam splitter; MIR, mirror; AMP, amplifier; I, input (data).

Fig. 3
Fig. 3

COG (a) with a single PSD and (b) with two separate PSD’s.

Fig. 4
Fig. 4

Table of rules for an inverted pendulum on a cart. E, error; CE, change in error; CD, cart displacement; P/NVL, positive/negative very large; P/NL, positive/negative large; P/NM, positive/negative medium; P/NS, positive/negative small; Z, zero.

Fig. 5
Fig. 5

Effect of ratio between two inputs on the 1-D controller output: I 1/I 2 = 5 (solid curve); 8 (dashed curve); 10 (dotted–dashed curve); 20 (dotted curve), where I 1 is the error (pendulum tilt angle) and I 2 is the change of error (1st derivative).

Fig. 6
Fig. 6

Results of optical experiments. (a) Different widths of Gaussian beam: narrow (solid curve), medium (dashed curve), wide (dotted–dashed curve); (b) different beam shapes: Gaussian (solid curve), triangle (dashed curve); and (c) different rule structures: nine rules (solid curve), five rules (dashed curve), and no rule plates (dotted–dashed curve).

Equations (3)

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Out=8Out1+1Out28+1,
T=maxTx, Ty.
T=Td+Ts,

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