模糊控制器设计源码程序

朱雀 2022-09-11 10:28 117阅读 0赞

clear % Clear all variables in memory  
clc;  
close all;

eold=0; % Intial condition used to calculate c  
rold=0; % Intial condition used to calculate r  
yeold=0; % Intial condition used to calculate yc  
ymold=0; % Initial condition for the first order reference model

% Next, initialize parameters for the fuzzy controller

nume=11; % Number of input membership functions for the e  
% universe of discourse  
numc=11; % Number of input membership functions for the c  
% universe of discourse

ge=1/2;,gc=1/2;,gu=5;  
% Scaling gains for tuning membership functions for  
% universes of discourse for e, c and u respectively  
% These are tuned to improve the performance of the FMRLC  
we=0.2\*(1/ge);  
% we is half the width of the triangular input membership  
% function bases (note that if you change ge, the base width  
% will correspondingly change so that we always end  
% up with uniformly distributed input membership functions)  
% Note that if you change nume you will need to adjust the  
% "0.2" factor if you want membership functions that  
% overlap in the same way.  
wc=0.2\*(1/gc);  
% Similar to we but for the c universe of discourse  
base=0.4\*gu;  
% Base width of output membership fuctions of the fuzzy  
% controller

% Place centers of membership functions of the fuzzy controller:

% Centers of input membership functions for the e universe of  
% discourse for of fuzzy controller (a vector of centers)  
ce=\[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1\]\*(1/ge);

% Centers of input membership functions for the c universe of  
% discourse for of fuzzy controller (a vector of centers)  
cc=\[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1\]\*(1/gc);  
gf=0;

fuzzyrules=\[-1 -1 -1 -1 -1 -1 -0.8 -0.6 -0.4 -0.2 0;  
\-1 -1 -1 -1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2;  
\-1 -1 -1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4;  
\-1 -1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6;  
\-1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8;  
\-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1;  
\-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1;  
\-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 1;  
\-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 1 1;  
\-0.2 0 0.2 0.4 0.6 0.8 1 1 1 1 1;  
0 0.2 0.4 0.6 0.8 1 1 1 1 1 1\]\*gu\*gf;

% Next, we define some parameters for the fuzzy inverse model

gye=1/2;,gyc=1/2;  
% Scaling gains for the error and change in error for  
% the inverse model  
% These are tuned to improve the performance of the FMRLC  
gp=0.2;

numye=11; % Number of input membership functions for the ye  
% universe of discourse  
numyc=11; % Number of input membership functions for the yc  
% universe of discourse

wye=0.2\*(1/gye); % Sets the width of the membership functions for  
% ye from center to extremes  
wyc=0.2\*(1/gyc); % Sets the width of the membership functions for  
% yc from center to extremes  
invbase=0.4\*gp; % Sets the base of the output membership functions  
% for the inverse model

% Place centers of inverse model membership functions  
% For error input for learning Mechanism  
cye=\[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1\]\*(1/gye);

% For change in error input for learning mechanism  
cyc=\[-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1\]\*(1/gyc);

% The next matrix contains the rule-base matrix for the fuzzy  
% inverse model. Notice that for simplicity we choose it to have  
% the same structure as the rule-base for the fuzzy controller.  
% While this will work for the control of the simple first order  
% linear system for many nonlinear systems a different structure  
% will be needed for the rule-base. Again, the entries are  
% the centers of the output membership functions, but now for  
% the fuzzy inverse model.

inverrules=\[-1 -1 -1 -1 -1 -1 -0.8 -0.6 -0.4 -0.2 0;  
\-1 -1 -1 -1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2;  
\-1 -1 -1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4;  
\-1 -1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6;  
\-1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8;  
\-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1;  
\-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1;  
\-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 1;  
\-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1 1 1;  
\-0.2 0 0.2 0.4 0.6 0.8 1 1 1 1 1;  
0 0.2 0.4 0.6 0.8 1 1 1 1 1 1\]\*gp;

% Next, we set up some parameters/variables for the  
% knowledge-base modifier

d=1;  
% This sets the number of steps the knowledge-base modifier looks  
% back in time. For this program it must be an integer  
% less than or equal to 10 (but this is easy to make larger)

% The next four vectors are used to store the information about  
% which rules were on 1 step in the past, 2 steps in the past, ....,  
% 10 steps in the past (so that picking 0<= d <= 10 can be used).

meme\_int=\[0 0 0 0 0 0 0 0 0 0\];  
% sets up the vector to store up to 10 values of e\_int  
meme\_count=\[0 0 0 0 0 0 0 0 0 0\];  
% sets up the vector to store up to 10 values of e\_count  
memc\_int=\[0 0 0 0 0 0 0 0 0 0\];  
% sets up the vector to store up to 10 values of c\_int  
memc\_count=\[0 0 0 0 0 0 0 0 0 0\];  
% sets up the vector to store up to 10 values of c\_count

%  
% Next, we intialize the simulation of the closed-loop system.  
%

k\_p=1; % The numerator of the plant. Change this value to study  
% the ability of the FMRLC to control other plants. Also,  
% you can make this a time-varying parameter.  
zeta\_p=.707;  
% Damping ratio for the second order plant (could change this  
% to see how the system will adapt to it)  
w\_p=1; % Undamped natural frequency for the plant (could change this  
% to see how the system will adapt to it)  
k\_r=1;  
% The numerator of the reference model. Change this value to study  
% the ability of the FMRLC to meet other performance specifications.  
a\_r=1;  
% The value of -a\_r is the pole position for the reference model.  
% Change this value to study the ability of the FMRLC to meet  
% other performance specifications (e.g., a faster response).

t=0; % Reset time to zero  
index=1; % This is time's index (not time, its index).  
tstop=64; % Stopping time for the simulation (in seconds)  
step=0.01; % Integration step size  
x=\[0;0\]; % Intial condition on state of the plant

% Need a state space representation for the plant. Since our  
% plant is linear we use the standard form of xdot=Ax+Bu, y=Cx+Du  
% Matrix A of state space representation of plant

A=\[0 1;  
\-w\_p^2 -2\*zeta\_p\*w\_p\];  
B=\[0; 1\]; % Matrix B of state space representation of plant  
C=\[k\_p 0\]; % Matrix C of state space representation of plant

%  
% Next, we start the simulation of the system. This is the main  
% loop for the simulation of the FMRLC.  
%  
while t <= tstop  
y(index)=C\*x; % Output of the plant

% Next, we define the reference input r as a sine wave

r(index)=sin(.6\*t);

ym(index)=(1/(2+a\_r\*step))\*((2-a\_r\*step)\*ymold+...  
k\_r\*step\*(r(index)+rold));

ymold=ym(index);  
rold=r(index);  
% This saves the past value of the ym (r) so that we can use it  
% the next time around the loop

% Now that we have simulated the next step for the plant and reference  
% model we will focus on the two fuzzy components.

% First, for the given fuzzy controller inputs we determine  
% the extent at which the error membership functions  
% of the fuzzy controller are on (this is the fuzzification part).

c\_count=0;,e\_count=0; % These are used to count the number of  
% non-zero mf certainitie of e and c  
e=r(index)-y(index);  
% Calculates the error input for the fuzzy controller  
c=(e-eold)/step;  
% Calculates the change in error input for the fuzzy controller  
eold=e;  
% Saves the past value of e for use in the next time through the  
% loop

% The following if-then structure fills the vector mfe  
% with the certainty of each membership fucntion of e for the  
% current input e

if e<=ce(1) % Takes care of saturation of the left-most  
% membership function  
mfe=\[1 0 0 0 0 0 0 0 0 0 0\]; % i.e., the only one on is the  
%left-most one  
e\_count=e\_count+1;,e\_int=1; % One mf on, it is the  
%left-most one.  
elseif e>=ce(nume) % Takes care ofsaturation  
%of the right-most mf  
mfe=\[0 0 0 0 0 0 0 0 0 0 1\];  
e\_count=e\_count+1;,e\_int=nume; % One mf on, it is the  
%right-most one  
else % In this case the input is on the middle part of the  
% universe of discourse for e  
% Next, we are going to cycle through the mfs to  
% find all that are on  
for i=1:nume  
if e<=ce(i)  
mfe(i)=max(\[0 1+(e-ce(i))/we\]);  
% In this case the input isto the  
% left of the center ce(i)and we compute  
% the value of the mfcentered at ce(i)  
% for this input e  
if mfe(i)~=0  
% If the certainty is not equal to zerothen say  
% that have one mf on by incrementing our count  
e\_count=e\_count+1;  
e\_int=i; % This term holds the index last entry  
% with a non-zero term  
end  
else  
mfe(i)=max(\[0,1+(ce(i)-e)/we\]);  
% In thiscase the input is to the  
% right ofthe center ce(i)  
if mfe(i)~=0  
e\_count=e\_count+1;  
e\_int=i; % This term holds the index of the  
% last entry with a non-zero term  
end  
end  
end  
end

% Next we will save the number of mfs that are on and the pointer  
% e\_int as to which rules were on. This vector of length  
% 10 saves the last 10 values of e\_count and e\_int as time  
% progresses (hence, it is a moving window).  
% These will be used by the FMRLC knowledge-base modifier.

meme\_count=\[e\_count meme\_count(1:9)\];  
meme\_int=\[e\_int meme\_int(1:9)\];

% The following if-then structure fills the vector mfc with the  
% certainty of each membership fucntion of c for the current  
% value of c (to understand this part of the code see the above  
% similar code for computing mfe)

if c<=cc(1) % Takes care of saturation of left-most mf  
mfc=\[1 0 0 0 0 0 0 0 0 0 0\];  
c\_count=c\_count+1;  
c\_int=1;  
elseif c>=cc(numc)  
% Takes care of saturation of the right-most mf  
mfc=\[0 0 0 0 0 0 0 0 0 0 1\];  
c\_count=c\_count+1;  
c\_int=numc;  
else  
for i=1:numc  
if c<=cc(i)  
mfc(i)=max(\[0,1+(c-cc(i))/wc\]);  
if mfc(i)~=0  
c\_count=c\_count+1;  
c\_int=i; % This term holds last entry  
% with a non-zero term  
end  
else  
mfc(i)=max(\[0,1+(cc(i)-c)/wc\]);  
if mfc(i)~=0  
c\_count=c\_count+1;  
c\_int=i; % This term holds last entry  
% with a non-zero term  
end  
end  
end  
end  
% Next we will save the number of mfs that are on and the pointer  
% c\_int as to which rules were on. This vector of length 10  
% saves the last 10 values of c\_count and e\_int as time progresses  
% (hence, it is a moving window). These will be used by the FMRLC  
% knowledge-base modifier.

memc\_count=\[c\_count memc\_count(1:9)\];  
memc\_int=\[c\_int memc\_int(1:9)\];

% These for loops calculate the crisp output using only the non-  
% zero premise of error,e, and change in error,c. This cuts down  
% computation time since we will only compute  
% the contribution from the rules that are on (i.e., a maximum of  
% four rules for our case). Minimum is used for the premise  
% and implication.

num=0;  
den=0;  
for k=(e\_int-e\_count+1):e\_int  
% Scan over e indices ofmfs that are on  
for l=(c\_int-c\_count+1):c\_int  
% Scan over c indices ofmfs that are on  
prem=min(\[mfe(k) mfc(l)\]);  
% Value of premisemembership function  
% This next calculation of num adds up the numerator for the  
% defuzzification formula. fuzzyrules(k,l) is the output center  
% for the rule.base\*(prem-(prem)^2/2 is the area of a symmetric  
% triangle with base width "base" and that is chopped off at  
% a height of prem (since we use minimum to represent the  
% implication). Computation of den is similar but without  
% fuzzyrules(k,l).  
num=num+fuzzyrules(k,l)\*base\*(prem-(prem)^2/2);  
den=den+base\*(prem-(prem)^2/2);  
end  
end

u(index)=num/den;  
% Crisp output of fuzzy controller that is the input  
% to the plant

% Next, we perform computations for the fuzzy inverse model.

ye=ym(index)-y(index); % Calculates ye  
yc=(ye-yeold)/step; % Calculates yc  
yeold=ye; % Saves the value of ye for use the  
% next time

ye\_count=0;,yc\_count=0; % Counts the non-zero certainties  
% of ye and ycsimilar to how we did  
% for the fuzzycontroller

% The following if-then structure fills the vector mfye with the  
% certainty of each membership fucntion of ye (similar to the  
% fuzzy controller). Notice that we use the same number of  
% input membership functions as in the fuzzy controller -  
% just for convenience - it does not have to be this way

if ye<=cye(1) % Takes care of saturation  
mfye=\[1 0 0 0 0 0 0 0 0 0 0\];  
ye\_count=ye\_count+1;,ye\_int=1;  
elseif ye>=cye(numye) % Takes care of saturation  
mfye=\[0 0 0 0 0 0 0 0 0 0 1\];  
ye\_count=ye\_count+1;,ye\_int=numye;  
else  
for i=1:numye  
if ye<=cye(i)  
mfye(i)=max(\[0 1+(ye-cye(i))/wye\]);  
if mfye(i)~=0  
ye\_count=ye\_count+1;  
ye\_int=i; % This term holds last entry with  
% a non-zero term  
end  
else  
mfye(i)=max(\[0,1+(cye(i)-ye)/wye\]);  
if mfye(i)~=0  
ye\_count=ye\_count+1;  
ye\_int=i; % This term holds last entry with  
% a non-zero term  
end  
end  
end  
end

% The following if-then structure fills the vector mfyc with the  
% certainty of each membership fucntion of yc

if yc<=cyc(1)  
mfyc=\[1 0 0 0 0 0 0 0 0 0 0\];  
yc\_count=yc\_count+1;,yc\_int=1;  
elseif yc>=cyc(numyc)  
mfyc=\[0 0 0 0 0 0 0 0 0 0 1\];  
yc\_count=yc\_count+1;,yc\_int=numyc;  
else  
for i=1:numyc  
if yc<=cyc(i)  
mfyc(i)=max(\[0 1+(yc-cyc(i))/wyc\]);  
if mfyc(i)~=0  
yc\_count=yc\_count+1;  
yc\_int=i;  
end  
else  
mfyc(i)=max(\[0,1+(cyc(i)-yc)/wyc\]);  
if mfyc(i)~=0  
yc\_count=yc\_count+1;  
yc\_int=i;  
end  
end  
end  
end

% These for loops calculate the crisp output of the inverse model  
% using only the non-zero premise of error,ye, and change in  
% error,yc. This cuts down computation time (similar to the  
% fuzzy controller). Minimum is used for the premise and the  
% implication. To understand this part of the code see the  
% similar code for the fuzzy controller.

invnum=0;  
invden=0;  
for k=(ye\_int-ye\_count+1):ye\_int  
for l=(yc\_int-yc\_count+1):yc\_int  
prem=min(\[mfye(k) mfyc(l)\]);  
invnum=invnum+inverrules(k,l)\*invbase\*(prem-(prem)^2/2);  
invden=invden+invbase\*(prem-(prem)^2/2);  
end  
end

% Next we compute the output of the fuzzy inverse model.  
% If you want to let gp=0 to test the fuzzy controller by itself  
% then you will have invden=0 and you will not be able to compute p.  
% To make it possible to let gp=0 we put in the following  
% if-then rule.

if gp==0  
p=0;  
else  
p=invnum/invden; % Crisp output of inverse model  
if abs(p)<.05, p=0; end % robustification term

end

% Next we modify the centers of ouput membership functions  
% associated with the rules that were on d steps ago  
% The indexing sheme is similar to the one used in the  
% computation of the outputs of the fuzzy controller and  
% fuzzy inverse model.

for k=(meme\_int(d)-meme\_count(d)+1):meme\_int(d)  
for l=(memc\_int(d)-memc\_count(d)+1):memc\_int(d)

fuzzyrules(k,l)=fuzzyrules(k,l)+p;  
end  
end

% Next, the Runge-Kutta equations to find the next state.

time(index)=t;  
F=A\*x+B\*u(index);  
k1=step\*F;  
xnew=x+k1/2;  
F=A\*xnew+B\*u(index);  
k2=step\*F;  
xnew=x+k2/2;  
F=A\*xnew+B\*u(index);  
k3=step\*F;  
xnew=x+k3;  
F=A\*xnew+B\*u(index);  
k4=step\*F;  
x=x+(1/6)\*(k1+2\*k2+2\*k3+k4); % Calculated next state

t=t+step; % Increments time  
index=index+1; % Increments the indexing term so that  
% index=1 corresponds to time t=0.

end % This end statement goes with the first "while" statement  
% in the program

%  
% Next, we provide plots of the input and output of the plant  
% and the output of the reference model  
%

subplot(211)  
plot(time,y,'-',time,ym,'--')  
xlabel('Time (sec)')  
title('Output of plant (solid) and reference model (dashed)')  
subplot(212)  
plot(time,u)  
xlabel('Time (sec)')  
title('Output of fuzzy controller (input to the plant)')

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B170

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