## 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
### Equations (7)

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

(1)
$$\begin{array}{l}\mathrm{Rule}1:\mathrm{if}x\in {\mathrm{MF}}_{3}^{\mathrm{temp}}\mathrm{and}y\in {\mathrm{MF}}_{3}^{\mathrm{pres}},\mathrm{then}z\in {\mathrm{MF}}_{3}^{\mathrm{torq}}.\\ \mathrm{Rule}2:\mathrm{if}x\in {\mathrm{MF}}_{4}^{\mathrm{temp}}\mathrm{and}y\in {\mathrm{MF}}_{3}^{\mathrm{pres}},\mathrm{then}z\in {\mathrm{MF}}_{4}^{\mathrm{torq}}.\end{array}$$
(2)
$${\mathrm{\mu}}_{3}\mathrm{AND}{\mathrm{\eta}}_{3}\Rightarrow {\mathrm{\chi}}_{3},{\mathrm{\mu}}_{4}\mathrm{AND}{\mathrm{\eta}}_{3}\Rightarrow {\mathrm{\chi}}_{4},$$
(3)
$$min\left({\mathrm{\mu}}_{3},{\mathrm{\eta}}_{3}\right)={\mathrm{\chi}}_{3}={\mathrm{\mu}}_{3},min\left({\mathrm{\mu}}_{4},{\mathrm{\eta}}_{3}\right)={\mathrm{\chi}}_{4}={\mathrm{\eta}}_{3}.$$
(4)
$$\mathrm{\theta}=\mathrm{\alpha}\left({I}_{1}-{I}_{2}\right).$$
(5)
$$\mathrm{\xi}=\frac{\mathrm{\lambda}F}{v}{\mathit{kf}}_{0},$$
(6)
$${\mathrm{\theta}}_{B}=\frac{\mathrm{\lambda}}{\mathrm{\Lambda}}=\frac{\mathrm{\lambda}{f}_{0}}{2v},$$
(7)
$$\iint |u\left(x,y\right){|}^{2}\mathrm{d}x\mathrm{d}y\equiv \iint |U\left({v}_{x},{v}_{y}\right){|}^{2}\mathrm{d}{v}_{x}\mathrm{d}{v}_{y},$$