Fuzzy system should not be used for the class of linear system!

Mr Chaibakhsh can you explain why it can not be used for linear systems?and tell me in general how to identify a system with fuzzy systems?

Dear friend

Please see this files. I hope this helps you.

      Best Regard

I don't quite agree with this statement that "Fuzzy system should not be used for the class of linear system". Although nonlinear control methods such as fuzzy and sliding mode control are designed for nonlinear systems, of course because the controllers are nonlinear, however, I believe as linear controllers such as PID can be used to control nonlinear plants, nonlinear controllers can also be used for linear plants. In fact, most systems are nonlinear in nature and are linearized to make the controller design easier. Therefore, a nonlinear controller such as fuzzy or SMC can be designed based on the linear model (if the actual nonlinear model is not available) and then nonlinear controller can be implemented on the actual nonlinear plant and the designed controller will be robust against nonlinearities that were not taken into account during the controller design stage. 

Anyway, your question is different. Apparently, you want to find the equivalent fuzzy model of your system. suppose your linear system transfer function y(t)=g(t)u(t). You can use smiling and design a general fuzzy system and and send the same input (maybe unit step input) and compare the output from both systems and try to minimise the error between the output of the linear system and the fuzzy system by changing the scaling factors of the fuzzy system.

I have coded this example, which I think it will help you. It models a linear system with a single output Sugeno type fuzzy system. The transfer function is just a fictitious stable transfer function. Keep in mind that your system has to be stable to be able to use this.

t=(0:0.01:10)';

u=ones(length(t),1);

G=tf(10,[1 10]);

y=lsim(G,u,t);

epoch_n = 100;

in_fis = genfis1([t y],5,'gbellmf');

out_fis = anfis([t y],in_fis,epoch_n);

plot(t,y,t,evalfis(t,out_fis));

legend('Training Data','anfis Output');

Regards,

Mr Noshadi thank you so much for your help.could you please tell me what do yo mean by smiling!!???and how can i design a general fuzzy system !! i mean should i get data from my system or not?whats the point in supposing y(t)=g(t)u(t)?? and is the fuzzy system in Mamdani type or Sugeno ?should i define a index(criteria) for it to minimize the error?!!!!!!!!!

Sorry for my typo. I meant you can use either Simulink or MATLAB command line. You can design your own fuzzy system by just typing fuzzy in matlab and construct your fuzzy model. Then, you can compare the output from the actual system to a particular input with the output from the fuzzy system and eventually minimize the error between the two by either manipulating the fuzzy rules or using gains before and after the system (basically range of membership functions). The index could be the IATE or RMSE or so on. This is basically what I have shown in the MATLAB code but by using ANFIS. Here, I assumed your actual system is G(s)=10/(s+10), then I simulated G(s) with a step input U u=ones(length(t),1); for 10 second t=(0:0.01:10)';. Y y=lsim(G,u,t); will be the output from (let's assume your actual system). Then I generated a fuzzy system with 5 bell shape membership functions in_fis = genfis1([t y],5,'gbellmf'); After that I trained my fuzzy system for 100 iteration out_fis = anfis([t y],in_fis,epoch_n); the final out_is fuzzy system 

thanks for your advice