Hi,

If you are able to design a linear PID controller for your system, you can use the PID gains to calculate the scaling factors required in Fuzzy controller the way that I have explained in this paper. This calculations give you a good starting point for the scaling factors but not the optimal ones. I have also proposed a PID-type fuzzy controller which gives you zero-steady state error and needs much less rule-based to be assigned compared to common three input fuzzy PID controller.

https://www.researchgate.net/publication/265786851_PID-type_Fuzzy_Logic_Controller_for_Active_Magnetic_Bearing_System

Regards,

Conference Paper PID-type Fuzzy Logic Controller for Active Magnetic Bearing System

Dear Amin

Thank's for your comment. your paper is very comprehensive. 

All the best

Because of this situation it is usually desirable and often necessary to scale, or normalise, the universe of discourse of an input/output variable. Normalisation means applying the standard range of [–1,+1] for the universe of discourse both for the inputs

and the outputs.

In the case of the normalised universe, an appropriate choice of specific operating areas requires scaling factors. An input scaling factor transforms a crisp input into a normalised input inorder to keep its value within the universe. An output scaling

factor provides a transformation of the defuzzified crisp output from the normalised universe of the controller output into an actual physical output. But an important question is; What do these scaling factors affect?

The following Article on Fuzzy Adaptive Controllers for Speed Control of PMSM Drive

where The objective of the FAC is to tune the scaling factors in the FLC, according to the comparison between a reference signal and the system output, throws some Light on Tuning the Scaling Factor.

©2010 International Journal of Computer Applications (0975–8887) Volume 1 –No. 11

Fuzzy Adaptive Controllers for Speed Control of PMSM Drive

N. J. Patil, Dr. R. H. Chile, Dr. L. M. Waghmare

The PMSM is preferred, in industrial servo applications, to the DC motor due to considerations of the cost, size, low maintenance, maximum speed capability, and simplicity of design.Fuzzy logic can be considered as a mathematical theory

combining multi-valued logic, probability theory, and artificial intelligence to simulate the human approach in the solution of various problems by using an approximate reasoning to relate different data sets and to make decisions. In this paper, the adaptive control of fuzzy logic controller for a vector controlled PMSM is investigated . First FLC principle is presented and its application to the speed control is considered .

P.S.

Most of the research works on FLC have either neglected this issue by directly

 applying a set of scaling factors (SFs) without explanation or simply given some rough idea to guide the choice of the SFs to a specific problem, their adopted solutions are essentially empirical and with the trial and error nature . Different types of adaptive FLC’s such as self tuning and self organizing controllers have also been developed and implemented for various practical processes. Of the various tunable parameters, SF’s have the highest priority due to their global effect on the control performance. However, relative importance of the input and output SF’s to the performance of a

fuzzy logic control system is yet to be fully established.

A Fuzzy Adaptive Scheme is proposed in which the Adaptation mechanism is executed by fuzzy logic based on the error and change of error measured between the motor speed and the reference signal. The control performance of the adaptive fuzzy controller is evaluated by simulation for various operating conditions.

Link:  http://www.ijcaonline.org/allpdf/pxc387387.pdf

In control systems applications, many people use to scale both input and outputs by taking into account min/max constraints. That is, when sensory data are at minimum values and output values turns to Zero. And, when sensory data are at maximum values and output values turn to maximum. This constraints gives you and appropiate set of factor scales values. Often, problems arises related to Zero-output state because of "dead-zone" of motors or actuators... but this is another topic.

Why be fuzzy when you don't have to be? Why not consider using multiple model adaptive control instead? You have, I think, the same types of support points as in fuzzy, but it is quantitative and more precise. Indeed, you can have a controller that maximizes the precision with which a desired target goal is hit. You might see Jelliffe R, Schumitzky A, Bayard D, Milman M, Van Guilder M, Wang X, Jiang F, Barbaut X, and Maire P: Model-Based, Goal-Oriented, Individualized Drug Therapy: Linkage of Population Modeling, New "Multiple Model" Dosage Design, Bayesian Feedback, and Individualized Target Goals. Clin. Pharmacokinet. 34: 57-77, 1998.

Or,

Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens. Therap. Drug Monit. 22: 346-353, 2000.

And also

Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.

Hope this is useful for you,

Roger Jelliffe

There is no convincing answer .. unfortunately !!!

based on your problem ,input,output nature

Sometimes,it is better to consider an adaptative system which consider the modification od the scaling value

It could be intersting to apply a sensitivity analysis to see the appropiate scaling factor for your particular application

You can do it using any optimization technique such as GA, PSO, .....etc.

It's not difficult.

Good Luck