lvts apc fuzzy controller

Introduction to Fuzzy Logic systems

and Fuzzy logic APC simulator

By LV Tailoring Software

Fuzzy Logic - background

• Western cultures adopted binary logic long time ago as they dealt with the yes or no, guilty or not guilty – vocabulary of the binary Aristotelian logic world.

• Eastern cultures easily accommodate the concept of Fuzziness due to historical background – not the “certain answer” is the just way to express the view of experienced person observing the world.

• In 1965 Prof. Lotfi A. Zadeh introduced fuzzy sets, where many degrees of membership are allowed, and indicated with a number between 0 and 1. The point of departure for fuzzy sets is simply the generalization of the valuation set from the pair of numbers {0,1} to all the numbers in [0,1]. This is called a membership function.

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LV Tailoring Software


• Mitsubishi manufactures a fuzzy air conditioner. While conventional air conditioners use on/off controllers that work and stop working based on a range of temperatures, the Mitsubishi machine takes advantage of fuzzy rules; the machine operates smoother as a result. The machine becomes less mistreated by sudden changes of state, more consistent room temperatures are achieved, and less energy is consumed. These were first released in 1989.

• Sanyo, Panasonic, and Canon make fuzzy video cameras. These have a digital image stabilizer to remove hand jitter, and the video camera can determine the best focus and lightning. Fuzzy decision making is used to control these actions. The present image is compared with the previous frame in memory, stationary objects are detected, and its shift coordinates are computed. This shift is subtracted from the image to compensate for the hand jitter.

• Fujitec and Toshiba have a fuzzy scheme that evaluates the passenger traffic and the elevator variables to determine car announcement and stopping time. This helps reduce the waiting time and improves the efficiency and reliability of the systems.

• The automotive industry has also taken advantage of the theory. Nissan has had an anti-lock braking system since 1997 that senses wheel speed, road conditions, and driving pattern, and the fuzzy ABS determines the braking action, with skid control.

• Since 1988 Hitachi has turned over the control of the Sendai subway system to a fuzzy system. It has reduced the judgment on errors in acceleration and braking by 70%. The Ministry of International Trade and Industry estimates that in 1992 Japan produced about $2 billion worth of fuzzy products. US and European companies still lag far behind. The market of products is enormous, ranging from fuzzy toasters to fuzzy golf diagnostic systems..

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• Example of Fuzzy logic reasoning:

• Everyone who is 60 to 70 years old is old, but very old if 71 years old or above; everyone who is 20 to 39 is young but very young if 19 years old or below.

• Given - Hiram is 70 years old and Miriam is 39 years old.

• 3. Hiram is old but not very old; Miriam is young but not very young.

• This is an example of approximate reasoning; in order to deal with an imprecise inference, fuzzy logic can be employed. It allows imprecise linguistic terms such as:

• • Fuzzy predicates: rare, expensive, fast, high

• • Fuzzy quantifiers: few, usually, much, little

• • Fuzzy truth values: true, unlikely true, false, and mostly false.

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• Fuzzy set where the right part is singleton

• Example

• For Logic set - it is union of numbers

• For Fuzzy set – each number has it “degree of belonging” or certainty, some could treat it as probability – but better way to express it as possibility.

• Often Fuzzy logic theory refers as the theory of possibility - analogous and yet conceptually different from the theory of probability. Probability is a measure of frequency of occurrence of an event, which has a physical event basis. Thus, probabilities have a physical event basis and are related to statistical experiments; they are primarily used for quantifying how frequently a sample occurs in a population.

• Possibility theory attempts to quantify how accurately a sample resembles a stereotype element of a population. This stereotype is a prototypical class of the population and is known as a fuzzy set. This theory focuses more on the imprecision intrinsic in the language, while probability theory focuses more on the uncertainty of events, in the sense of its randomness in nature.

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Fuzzy Logic - background• Fuzzy variables

• First step in build up of Fuzzy control system – creation of membership function for all related variables (input and output).

• If we are going to use graph for representation of Fuzzy logic set we coming to detention of the membership function.

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Fuzzy Logic - background• Main Fuzzy logic mathematical operation – similar to binary.

• Union

• Intersection

• Negation

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Fuzzy Logic - background• We just defined membership function for input data we need to operate on.

• We need to apply input data on certain function which in turn will be in turn the fuzzy function – what is the rules of conversion?

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Fuzzy Logic - background• Fuzzy rules

• It is possible that Fuzzy system we want to build has some input variable, each of them represented by it’s own membership function.

• Inner relationship of this variables is not defined strictly by mathematical rules, they should not be mutually independed, they just need to be relevant to our application.

• Increasing number of the input variables has better definition of the system, but could in turn complicate creation of the behavioral rules.

• Second step in build up of Fuzzy control system – creation of Fuzzy Linguistic Descriptions or Fuzzy rules.

• IF (a set of conditions is satisfied) THEN (a set of consequences can be inferred)

• A general fuzzy IF–THEN rule has the form:

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Fuzzy Logic - background• Simplest Fuzzy logic controller

• What is Defuzzification?

• Simplest system – one input one output

• Center of Mass formula

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Fuzzy Logic –vehicle example

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Simulation of Fuzzy and WA APC

system• In order to check performance of Fuzzy APC vs. WA APC simulation of the

system performed (Labview).

• Dose values were taken as input variables, also Focus values are present, but not used in simulation.

• Membership function were created as well as for Dose and Focus variables.

• Rules includes Dose and Focus impact, but feedback loop updates just Dose performance (close simulation for FAB Litho tool activity).

• Actual simulation not included any translation of Dose values to CD values for given Focus, it assumes that any inconsistencies are added as WN or trend in the final measurement.

• WA APC simulated as 5 tag window with 0.35/0.25/0.2/0.14/0.06 weights accordingly which is effectively matched NSO exponential weights average approach.

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Area CD division Fuzzy APC controller -

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Membership function of Fuzzy APC

controller - Dose

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Membership function of Fuzzy APC

controller - Focus

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Rules of Fuzzy APC controller

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Test Surface Fuzzy APC controller

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Schematic Labview presentation of

Fuzzy APC controller

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GUI Labview presentation of Fuzzy vs.

Weighted average APC controllers

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Brief conclusions:

• Fuzzy APC operation depends just on current sample, no history sample required to perform noise reduction

• WA APC need historical sample to perform, which could be irrelevant for RT operation sequence.

• Fuzzy APC better performed as WN cancellator, reducing noise power significantly compared to WA APC (~factor of 2)

• WA APC has better signal trend tracking.• In Fuzzy APC signal trend contaminated noise

cancellation ability.

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Thank you for your attention

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lvts apc fuzzy controller

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