Ricoh USA, Inc., PacWest

What is the difference between usual toner control and fuzzy toner control? Simply put, fuzzy control means that toner control is designed following a mathematical theory known as fuzzy logic.

Fuzzy logic is a way to formalize everyday concepts like "a little" and "a lot". Traditional logic makes use of only two concepts: true and false, and makes no allowance for things that could be a little true, or a little false.

Other process control methods make use of this: if the machine senses a low toner condition, it sends a fixed amount of toner to the development unit. The copier checks to see if toner concentration is above or below a certain threshold. If it is below the threshold, the copier adds toner.

It doesn't matter if toner concentration is much lower, or a little lower than the threshold, the copier would add the same amount of toner in both cases. Further, if toner density is just a bit above the threshold, no toner is added at all. Fuzzy control rectifies this situation and leads to methods that go like this:

For this model, toner is supplied at every copy cycle, and an extra corrective check is made every 10 cycles.

Fuzzy control is so simple a concept that you may wonder why it's so new. There are two reasons for this. First, the mathematical formulation for it is pretty recent: less than 30 years. Engineers and scientists simply weren't comfortable with concepts like "just a bit".

Second, though simple enough to explain and formulate in everyday language, fuzzy control requires a fair bit of computer power. Power that wasn't affordable until seven or eight years ago, when fuzzy control technology was just making its appearance.

Conventional logic works with two values: true and false. These two values are interchangeable with yes and no, or 1 and 0. We assign one of these two values to every statement. We can say the statement "Caesar is dead" is true, and say it has a truth value of 1.

With fuzzy logic, we assign a truth value between 0 and 1 to assess how true a statement. If the statement is about a variable, like a person's age or a sensor response, then the truth value will usually change along with the variable.

The relationship between a statement about a variable, and the statement's truth value is defined by something called a membership function. (It's called a membership function because fuzzy math was first developed for a set theory, not logic, otherwise we could call it a truth value function.) You can see a typical membership function illustrated above.

As John's age increases, the truth value of the statement "John is an old man" increases. This should be of no surprise, since we defined it that way. We can define similar membership functions for a variety of statements.

Notice the shape of the two functions. What determines them? Simply our definition of the words.

Since the word "old" denotes an extreme, something final, where there is no going back, we expect a function that never decreases. On the other hand the word "average" denotes a middle value, so we expect a function that increases, reaches a peak, and then decreases.

It is important not to confuse membership function with probability functions. At this point, they might look similar, but for each method, the way of combining statements is completely different.

In conventional logic, we can compound statements. We say "John is old" and "John is healthy". If John were an active 35 year old man, conventional logic would say the combined statement is false, or that it had a truth value of 0. In fuzzy logic however each statement would have a truth value, suppose 0.1 for "John is an old man""and 0.95 for "John is healthy".

For this model, the sensor responses monitored by the machine come from two sources: an ID sensor and a TD sensor.

First, the ID sensor measures the reflectivity of ID sensor patterns made on the drum. Second, the TD sensor measures the toner concentration (toner/carrier ratio) of the developer.

Sensor responses are processed before they are used by the fuzzy algorithm. Two results come from the ID sensor. These are called Vsg and Vsp. The fuzzy algorithm uses the difference between them, Vref - VT.

Vref is the threshold that determines if toner is added or not. The process output of the fuzzy algorithm is a change for Vref. This change is called D Vref, or delta Vref.

The Vref - VT difference is also linked to seven similar statements. Finally, the statements are combined into rules to obtain seven statements about D Vref, again similar to the ones for the Vsg/Vsp ratio.

Diagrams on the following pages illustrate the membership functions for all 21 statements, and provide an example of how toner supply is determined.

The list on the last page made statements about how large or small the Vsg/Vsp ratio was.

The states described by the first and last statements are negative large and positive large. These are extreme states, and the corresponding membership functions (see NL and PL in the diagram) have the kind of shape we'd expect.

The five middle statements are about middle states, so the membership functions are shaped like peaks.

Suppose the Vsg/Vsp ratio is equal to 0.12. The table below shows the truth of each statement when applied to our example.

Vsg/Vsp = 0.12
Vsg/Vsp is &	M(x)
Negative Large (NL)	0.00
Negative Medium (NM)	0.00
Negative Small (NS)	0.00
About Zero (ZO)	0.34
Positive Small (PS)	0.66
Positive Medium (PM)	0.00
Positive Large (PL)	0.00

So we can say the ratio is positive but pretty small, in fact kind of close to zero.

As we did for the Vsg/Vsp ratio, we can make and evaluate statements about the Vref -VT difference. Again, the shapes are essentially what we'd expect: a plateau for each extreme state, and peaks for the rest.

Suppose now that the Vref VT difference is equal to -0.4. The table below shows the truth of each statement when applied to our example.

Vref VT = -0.4
Vref - VT is &	M(x)
Negative Large (NL)	0.00
Negative Medium (NM)	0.78
Negative Small (NS)	0.22
About Zero (ZO)	0.00
Positive Small (PS)	0.00
Positive Medium (PM)	0.00
Positive Large (PL)	0.00

So, we can say the difference is negative but leaning just a bit on the small side.

The Vsg/Vsp ratio and the Vref - VT difference are the inputs used by the fuzzy algorithm. The algorithm then needs to produce an output. It does this using rules that output a conclusion based on the inputs. For instance:

There are seven possible conclusions for each rule. Each conclusion is a statement which itself has a membership function, shown below.

Notice two things about the rules: they are all of the form "if (A and B) then C. Therefore the lesser of the two truth values will be chosen for the conclusion.

To get back to our example, Vsg/Vsp is ZO and PS with truth values 0.34 and 0.66, while Vref - VT is NM with truth values 0.78 and 0.22. Since all other are completely false (i.e. have truth value zero) we can forget them. This leaves us with four statements to combine and assign truth values.

The results are illustrated in the diagram. We combine them to get a new membership function, outlined in bold. This function describes the truth value of a fuzzy statement, but to use it, we need to defuzzy it: the system needs a real number to work with.

The copier gets this number by calculating the center of gravity of this function (a kind of average value). We obtain the value 0.19, which we use as D Vref.

The F400 compensates for changes in the OPC drum characteristics through a process control method here called latent image control. The process measures voltages on the drum directly, rather than through developed patches. Hence the latent image is controlled, rather than the developed one.

Latent image control compensates for changes in the drum's ability to hold a charge and to dissipate it. These changes are measured by measuring various voltages: VD, VL, VR (dark potential, light potential, and residual voltage).

The process measures voltages on the drum directly, rather than through developed patches. Hence the latent image is controlled, rather than the developed one.

This particular method of latent image control was developed and designed using the help of an artificial neural network.

Artificial neural networks (ANN's) imitate the human brain: they can learn things. It's easy to write a program that plays perfect Tic Tac Toe, but an ANN program can actually learn to play and win. It will begin by losing, and quickly learn what works and what doesn't.

A network is a collection of linked nodes. Nodes hold information, typically Yes or No. The nodes are linked so that their setting will have influence on other nodes.

Nodes could be anything. They could be transistors, vacuum tubes, or even variables in a computer program. One way to use ANN's is to design a software simulation of one.

What makes a network neural, is to connect the nodes in a manner than imitates the neurons of a brain, which is a natural neural network.

Four elements distinguish neural networks: input, processing, output, and feedback. The nodes of the network are distributed over three layers: an input layer, a processing layer, and an output layer. The ANN learns by analyzing the feed back from the output, which makes feed back an ANN's most essential feature.

The input layer receives information. The output layer returns it. The processing layer generates the output using the information from the input layer.

Feedback alters the processing layer. At first the processing layer turns input into output more or less at random, and results are terrible. But once in a while, a good result occurs. Feed back allows the processing layer to keep what works and change what doesn't, and the output gradually improves.

An ANN was used to design the latent image control process for a laboratory prototype of the F400.

The input was drum voltage readings (VD, VL, VR) the output was bias voltage values. The processing layer of the ANN determined the bias values from the drum voltage readings.

The bias results from the ANN were implemented on the F400 prototype and evaluated by the design team. The evaluation was then coded and given to the ANN. The ANN then altered the methods by which it had obtained the previous output, and a new series of parameters was output.

This process was repeated many times and under varying operating conditions, until the design team was satisfied with the results. Each time these steps are run, the process alters itself this point, the processing layer of the network is recorded.

The processing layer is the ANN's final output: it embodies the methods by which a slew of sensor readings determine the optimal bias voltages.