Page 114 - Control Theory in Biomedical Engineering

100 Control theory in biomedical engineering

+mu*E(i+1)));
else
lambda1(N1+2*m+1–i)=lambda1(N1+2*m+2–i)–...
h*(–1+lambda1(N1+2*m+2–i)*(delta+...
a1*(1–exp(–u(i+1))))+lambda2(N1+2*m+2–i)*n*T(i+1));
lambda2(N1+2*m+1–i)=lambda2(N1+2*m+2–i)–...
h*(1+lambda2(N1+2*m+2–i)*(–r2+2*r2*...
b*T(i+1)+n*E(i+1)+c1*N(i+1)+a2*(1–exp(–u(i+1))))+...
lambda3(N1+2*m+2–i)*c2*N(i+1));
end

if(N(i+1)<=0.75)
lambda3(N1+2*m+1–i)=lambda3(N1+2*m+2–i)–...
h*(lambda2(N1+2*m+2– i )* c1 * T ( i +1)+...
lambda3 ( N1 +2* m +2– i )*(– r3 +2* r3 * N ( i +1)+...
c2 * T ( i +1)+ a3 *(1– exp (– u ( i +1))))–1);
else

lambda3 ( N1 +2* m +1– i )= lambda3 ( N1 +2* m +2– i)–...
h *( lambda2 ( N1 +2* m +2– i )* c1 * T ( i +1)+...
lambda3 ( N1 +2* m +2– i )*(– r3 +2* r3 * N ( i +1)+...
c2 * T ( i +1)+ a3 *(1– exp (– u ( i +1)))));
end

lambda4 ( N1 +2* m +1– i )= lambda4 ( N1 +2* m +2– i)–...
h*( lambda1 (N1 +2*m+2– i)* a1 * E(i+1)* exp (– u(i+1))+...
lambda2 ( N1 +2* m +2– i )* a2 * T ( i +1)* exp (– u ( i +1))+...
lambda3 ( N1 +2* m +2– i )* a3 * N ( i +1)* exp (– u ( i +1))+ lambda4
(N1+2* m+2– i)*d);
v ( i +1)= min (3, lambda4 ( N1 +2* m +1– i)/B);
w ( i +1)= min (2, lambda1 ( N1 +2* m +1– i )* s1 / B2 );
r ( i +1)=( i +1)* h – m*h ;
end

figure (1)
hold off
plot ( r, E,’ r –.’,’ LineWidth ’,3)
hold on
plot ( sol . x, sol . y (1,:),’ LineWidth ’,2)
legend (’ With Control ’,’ Without Control ’);
xlim ([0 30])