solving odes with changing input
Show older comments
i have a system which need to change its input after reaching certain values and do this until all nine states go to zero.Any help/guidance would be greatly appreciated
my code is as below
function xdot=njc(t,x)
k1=1; k2=1.5; k3=1.5; b1=0.5; b2=0.6; b3=0.75; flag1=1; %flag2=-1;
%Step 1. Drive the system to a nonzero equilibrium such that tan(x4) =/ 0 in finite time using
if flag1==1
uu(1)=0;
uu(2)=-k1*(abs(x(4)-4)).^b1*sign(x(4)-4)-k2*(abs(x(5))).^b2*sign(x(5))-k3*(abs(x(6))).^b3*sign(x(6));
uu=[uu(1);uu(2)]; end %Step 2. Drive the x7 variable to zero while keeping x4 = 4 using
if x(4)==4
flag1=-1;
end
if flag1==-1 uu(1)=-1/tan(4)*(k1*(abs(x(7))).^b1*sign(x(7))+k2*(abs(x(8))).^b2*sign(x(8))+k3*(abs(x(9))).^b3*sign(x(9))); uu(2)=-k1*(abs(x(4)-4)).^b1*sign(x(4)-4)-k2*(abs(x(5))).^b2*sign(x(5))-k3*(abs(x(6))).^b3*sign(x(6)); uu=[uu(1);uu(2)]; end
% % Step 3. Drive the x4 variable to zero while keeping x7 = 0 using
if x(7)==0
flag1=0;
end
%
if flag1==0
uu(1)=-k1*(abs(x(7))).^b1*sign(x(7))-k2*(abs(x(8))).^b2*sign(x(8))-k3*(abs(x(9))).^b3*sign(x(9));
uu(2)=-k1*(abs(x(4))).^b1*sign(x(4))-k2*(abs(x(5))).^b2*sign(x(5))-k3*(abs(x(6))).^b3*sign(x(6));
uu=[uu(1);uu(2)];
end
% % Step 4. Drive the x1 variable to zero while keeping x4 = 0 using
if x(4)==0 flag1=2; end
if flag1==2 uu(1)=-k1*(abs(x(1))).^b1*sign(x(1))-k2*(abs(x(2))).^b2*sign(x(2))-k3*(abs(x(3))).^b3*sign(x(3)); uu(2)=-k1*(abs(x(4))).^b1*sign(x(4))-k2*(abs(x(5))).^b2*sign(x(5))-k3*(abs(x(6))).^b3*sign(x(6)); uu=[uu(1);uu(2)]; end
xdot(1)=x(2); xdot(2)=x(3); xdot(3)=uu(1);
xdot(4)=x(5); xdot(5)=x(6); xdot(6)=uu(2);
xdot(7)=x(8); xdot(8)=x(9); xdot(9)=uu(1)*tan(x(4));
xdot=xdot'; end
clear all close all clc
Tspan =linspace(0,60,250);
IC=[1;0;0;pi/4;0;0;-1;0;0]; %opts = odeset('InitialStep',1e-5,'events',@g); %opts = odeset('InitialStep',1e-15); %options = odeset('RelTol',1e-3,'AbsTol',[1e-3 1e-3 1e-3 1e-3 1e-3 1e-3 1e-3 1e-3 1e-3]); [T,Y] = ode45(@njc, Tspan,IC)
x1 = Y(:,1); x2 = Y(:,2); x3 = Y(:,3); x4 = Y(:,4); x5 = Y(:,5); x6 = Y(:,6); x7 = Y(:,7); x8 = Y(:,8); x9 = Y(:,9);
% if x4==4 % i=3 % end
figure(1) plot(T,x1,T,x2,T,x3,'linewidth',2) legend('x1','x2','x3',3); xlabel('t(s)') ylabel('x_1,x_2,x_3') grid on
figure(2) plot(T,x4,T,x5,T,x6,'linewidth',2) legend('x4','x5','x6',3); xlabel('t(s)') ylabel('x_4,x_5,x_6') grid on
figure(3) plot(T,x7,'+',T,x8,'o',T,x9,'linewidth',2) legend('x7','x8','x9',3); xlabel('t(s)') ylabel('x_7,x_8,x_9') grid on
Answers (0)
Categories
Find more on Programming in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!