Oussama Hadoune

If your training is successful, then the ANFIS controller will perform almost exactly like the PID controller. The ANFIS controller inherits the performance data from the PID controller, and its training algorithm only learns to approximate control manifold of the PID controller. So, at best, the ANFIS controller performs on a par with the PID controller.

If you hope to enhance the system response, then you should consider tuning the PID gains, or implementing an algorithm that automatically adjust the PID gains according to the control error. In other words, the gains are not static, but a nonlinear function of the error, cumulative error, and rate of change in error:

KPID = f(e, ∫e, de).

Yew-Chung Chak Thank you for clarifying. In that case, won't the fuzzy controller inherit the performance of an auto-tuned PID controller ?

What do you mean by an auto-tuned PID controller? If you are training the ANFIS to mimic the auto-tuning algorithm (not the PID controller itself) and it is successful, perhaps the ANFIS can tune the PID controller as good as the auto-tuner.

I mean a PID controller who changes its parameters according to the error value.

Yew-Chung Chak Thus, the correct way to train an ANFIS is to get the dataset from A Fuzzy controller ?

Oussama Hadoune, I'm unsure of the structure of the PID controller that you are talking about. If you are referring to a Nonlinear PID controller (not an Auto-tuning PID Controller) that adjusts its control parameters like this (almost like a Gain-scheduler):

uPID = KP(e, ∫e, de)·e + KI(e, ∫e, de)·∫e + KD(e, ∫e, de)·de,

then I think you can possibly train the ANFIS to perform almost as good as the Nonlinear PID controller with sufficient data. What is your purpose of training an ANFIS when the Nonlinear PID controller can do the same job, and the ANFIS cannot outperform the Nonlinear PID controller?

Regarding your 3rd post, why did you suggest getting the dataset from a Fuzzy controller? Also, you did not clarify what kind of dataset it is.

For PID controller you have as input: e(t), de(t)/dt; ⎰e(t).dt, and u(t) as output. You can use the dataset of these inputs and output for anfis training