solving odes with changing input

Question

samee baig 2016-8-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/300356-solving-odes-with-changing-input

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

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solving odes with changing input

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solving odes with changing input

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