Fuzzy Logic Controller

Not really my field, but presumably we use it because it works!
The thing you are controlling may be proportional to a simple error but may be proportional to the rate of change of the error thus some form of derivative is called for.
As an example if you were trying to control something falling with your latest antigravity ray then ray drive power based on the objects position might not be adequate, but basing it on the velocity or even the acceleration of the object would be useful.
Del
_{(Other uninvented rays are also unavailable, terms and condition apply, all antigravity ray operatives must be 18 years or over)}

An example of derivative control:

• A heavy boat is proceeding into a lock with a forward velocity and the gap between the prow of the boat and the forward lock gate is reducing. The helm increases reverse thrust in proportion to the rate of decrease of the gap so as not to thump the lock gate with the prow of the boat.

Any correlation with the process that "we" are carrying out?

The derivative can provide a "predictive" control variable so the system can begin to adjust before the error becomes too large.

You may want to look up PID control techniques. It will shed some light on the purpose of using the 'derivative' term.

The following may apply to your application...

http://en.wikipedia.org/wiki/Fuzzy_Control_System

Fuzzy logic is a generalized statistical system. As it is generalized, it is usually wrong or ineffective. Substituting understanding and hard won expertise usually is. Look at your profession for a proof.

In either fuzzy logic controller or a Auto tuning PID controller, the P, I and D are employed for error correction.

In P or Proportional band, an imaginary band is created around the set point. Say for example, the value is 50% (always the range of the controller, which assume as 1000 Deg., so the band value is 500 Deg.) This 500 Deg. envelopes the set point. Let the set point again be 750 Deg. So we have this band of 500 Deg. enveloping the set point, above and below the set point by equal measure, hence, we have250 deg above and 250 deg. below the set point, implies, the band starts at 500 deg. and ends at 1000 deg. The power output decided by the controller based on either direct or inverse action, shall be spread over this band. For inverse action, the % power output is 100% at 500 deg. and 0 at 1000 deg. Note that 50% of power is at the set point.

Analogy: You want to drive the car at 90kmph. Once you reach 90 kmph, if you remove your foot off the gas pedal, the speed drops, you still need some power to keep going at 90 kmph continuous.

Now, the I or Integral part is ommitted and your question of derivative part and its function. The derivative of any constant is 0. Once the error is constant (PV = SP), the D or derivative parameters ensures that the output of its individual action is zero, or so as it seems, but the moment , the PV changes, the % output changes and forces back the error to be zero with the P & I actions. The ability of the controller to anticipate the posssile error changes, and its ability to bring back the temperature to the SP is an indication and measure of the correct tuning of the controller. similarly for a furnace temperature to be controlled, if the furnace has zero losses, the controller cannot tune itself. In other words, the controller has to focus the output in a manner the furnace losses have to be met, to hold the temperature stable and at set point.

I trust your query is answered. The thanks for this answer goes to my brother, teacher, mentor, guide and well wisher, Mr. V. Ramakrishna, without whose help and guidance, I would have been a dumber guy than I am now.

A certain amount of confusion here. A fuzzy logic controller is not the same as a PID controller. A fuzzy logic system takes an analogue variable, like temperature, and assigns the value to one of a set of groups, like hot, warm, medium, cool, cold. The groups overlap, so that the assignment may be based on other happenings. That is the fuzzy part. Once in a group, the variable is processed with strictly digital logic.

A PID controller, on the other hand, uses analogue logic all the way. The Proportional error is the amount the signal differs from the required value at the present moment. The Derivative of the error indicates how rapidly the error signal is changing, which may be used to slam the brakes on harder than would otherwise be the case. Using the Integral function is looking at the history of the error signal, like saying "the last time the error was this, I put the brakes on like this, but it wasn't enough, so i'll put the brakes on a bit more this time".