MATLAB - Event Location fail to work? - matlab

Question

The event location function fail in finding an easy event when solving a 4 variables system of ode. Here's the code:
options1 = odeset('RelTol',1e-5,'AbsTol',1e-9,'Events',#evento1);
[T_ode1,X_ode1,te]=ode15s(#Seno,[0 2],[0 0 0 0 0],options1);
function [y] = Seno(t,x)
%Parameters
V=20;
R=1e6;
epsilon=8.87e-12;
d=4.5e-5;
k_sp=10;
gamma1=0.04;
gamma2=0.1;
m=66e-3;
A=0.1;
omega=80;
h=3.8e-6;
l=2e-3;
N=142;
%Variable redefinition
%x=[x,xpunto,q,y,ypunto]
X=x(1);
Xp=x(2);
Q=x(3);
Y=x(4);
Yp=x(5);
%sistema eq differenziali
y(1)=Xp; %y1(1)=position1
y(2)=-(2*k_sp*X/m)-(gamma1*Xp/m)+((epsilon*2*d*h*N*l)*X*V^2/((d^2-X^2)^2))+A*sin(omega*t); %y1(2)=velocity1
y(3)=1/R*(V-Q*(d^2-X^2)/(epsilon*2*d*h*N*l)); %y1(3)=charge
y(4)=Yp; %position 2
y(5)=-gamma2*Yp; %velocity2
y=y';
end
function [condition,ends,directions] = evento1(t,y)
a=2e-6;
c=2e-6;
b=1.5e-6;
condition= [(y(1)^2)-(a+c)^2, (y(4)^2)-(y(1)+b)^2, (y(4)^2)-(y(1)-b)^2];
ends = [1, 1, 1]; % Halt integration
directions = [1, -1, 1];
end
Setting all the initial condition to 0, as you can see, the first event that the event function should find is when the tird condition when y(1) pass for 1.5e-6 (y(4) is 0). Unfortunally ode ignore that event and stop the solution when the 1st one is satisfied.
I can't see why this happen! I tryed the debugging mode and the systems properly pass across 1.5e-6 but doesn't consider it as an event (ie it doesn't start to evaluate the solution in more points near the event).
Thanks for your time and sorry for my english.

Answer 1

As I mentioned in the comments, you can plot your event conditions after simulating the system:
options1 = odeset('RelTol',1e-5,'AbsTol',1e-9,'Events',#evento1);
[T_ode1,X_ode1,te] = ode15s(#Seno,[0 2],[0 0 0 0 0],options1);
a = 2e-6;
c = 2e-6;
b = 1.5e-6;
y = X_ode1;
condition = [y(:,1).^2-(a+c)^2 y(:,4).^2-(y(:,1)+b).^2 y(:,4).^2-(y(:,1)-b).^2];
figure;
plot(T_ode1,condition);
hold on;
plot(T_ode1([1 end]),[0 0],'k--',te,0,'k*');
legend('Condition 1','Condition 2','Condition 3','Location','W');
xlabel('Time');
ylabel('State');
ylim([-1.8e-11 2e-12]);
This results in a plot that looks like this:
If you zoom in on the plot you'll see that the third condition (yellow) never crosses zero and thus never triggers an event. Eventually the first event (blue) crosses zero and does trigger an event. Adjusting the integration tolerances doesn't appear to change this behavior (at best the third condition might asymptotically touch, but not cross, zero). If you want the third condition to trigger an event, you'll either need to change your parameters, change the condition, change your initial conditions, or change your ODEs.
I'm not sure if or why you think the third condition should cross zero, but if the system is numerically sensitive, then you may need to compensate for this by specifying parameter more precisely or artificially biasing the point of zero crossing.