MATLAB: Plot integral equation coming from ode solver

integrationMATLAB

I have an equation that comes from ode solver :

[t1 V1] = ode15s(dV1dt, t1, y1); plot(t1, V1 ,'-b','lineWidth',2)

then I do some basic addition or subtraction on it for eg :

Aout1=(V1-1); plot(t1,Aout1,'-b','lineWidth',2);

Now I wish to integrate the output : So I tried with

final = integral (Aout1, 0, 4.2)

But I get error :

Error using integral (line 82) First input argument must be a function handle.

I tried other things as well; but I don't achieve what I wish. Although 'cumsum' works well on it just like that.

Best Answer

Use the trapz (link) function:

idx = find(t1 <= 0.42);
final = trapz(t1(idx), Aout1(idx))

Since you menitoned cumsum, also see the documentation for cumtrapz (link).

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dydt = @(t,y) some_expression_involving_t_and_y_goes_here;

MATLAB: For loop with linspcace – for a multiple plots

Use nested loops:

beta= 2 : 0.1 : 6;
omega = 2*pi*2856;
Qo = 7E+4 : 500 : 1.2E+5;
U_in1 = 1;
y1 = 0;
alfa = (2*beta)./(1+beta);
t0 = [0 4.2];
dV1dt = @(t,V,beta,Qo,omega_half) ((U_in1*omega*beta)/Qo) - omega_half*V;
for k1 = 1:2%numel(beta)
    for k2 = 1:2%numel(Qo)
        QL = Qo(k2)/(1+beta(k1));
        omega_half = omega/(2*QL);
        [t1 V1] = ode15s(@(t,V)dV1dt(t,V,beta(k1),Qo(k2),omega_half), t0, y1);
        
        
        figure
        plot(t1,V1)
        xlabel('t')
        ylabel('V_1')
        title(sprintf('\\beta = %.1f     Q_o = %6d', beta(k1),Qo(k2)))
        
        figure
        Aout1=V1-1;
        plot(t1, Aout1)
        xlabel('t')
        ylabel('A_{out}')
        title(sprintf('\\beta = %.1f     Q_o = %6d', beta(k1),Qo(k2)))
        
        figure
        P1 = (V1 - U_in1).^2;
        plot(t1, P1)
        xlabel('t')
        ylabel('P_1')
        title(sprintf('\\beta = %.1f     Q_o = %6d', beta(k1),Qo(k2)))
    end
end

Note that this will produce 12423 figures! It will probably be better to combine all of them into one figure for each loop iteration using the subplot function, to reduce that to 4141 figures. .

Best Answer

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