wern93.m

FISMAT accommodates different arithmetic operators, fuzzification and defuzzification algorithm, imp

function uk = wern93(e,x,T)

% uk = wern93(e,x,T)
% 
% Fuzzy-PID-Controller discribed in Wernstedt,J.;Kuhn,T.;Koch,M.:
% Ein neues Entwurfskonzept fuer Fuzzy-Regelungen. (A new design strategy in
% fuzzy control. In at - Automatisierungstechnik 41 (1993), 5, page 152-158
% R.Oldenbourg Verlag.
% For use with the FUZZY31.M S-function-file from the Fuzzy-Toolbox.
% There are different ways for the realisation:
% If the dynamic part (integration and differentiatio of the error e) is rea-
% lized externally there are three inputs from the system. (e(1),e(2),e(3))
% The approximations are the sum and difference in the discrete controller.
% (only one system input for the controller but three in Simulink (DFLCS3)
% needed). Both ways need three sets for the error (eset), the diffentition
% of the error /difference (deset), the integration/sum of the error (seset) 
% and oset for the controller output. 
% x is the state vector with the last value of e(1)..e(3) and uk =x(1)..x(3)
% and x(4).
% T is the sampling period. 
% The Fuzzy-Sets must be defined outside this function. See the script file
% WERNSET.M
% Maybe there is a mistake in the publication above - a discrepancy beetween
% the step response and the assignment to the output terms. 
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% 23-April-1994 (Not tested)

global eset seset deset oset

% Fuzzification: 
% (discrete approximation of the dynamic elements. In Simulink three inputs
%  used - FUZZY31 - but only one is needed. )
ek  = fuzzifi(eset, e(1));
sek = fuzzifi(seset,e(1)+x(1));
dek = fuzzifi(deset,e(1)-x(1));
% (analog realisation of the dynamic parts. Three inputs to the controller
%  in Simulink are needed)
ek  = fuzzifi(eset, e(1));
sek = fuzzifi(seset,e(2));
dek = fuzzifi(deset,e(3));
neg=1; null=2; pos=3;
rb(neg) = s3ma(s3ma(ek(pos) ,sek(pos)) ,dek(pos));
rb(null)= t3mi(t3mi(ek(null),sek(null)),dek(null));
rb(pos) = s3ma(s3ma(ek(neg) ,sek(neg)) ,dek(neg));
% Defuzzification:
% (Center of Gravity Method and MAX-MIN Inference)
uk=defucoga(rb,oset,'min');