MATLAB：用IF条件在线改变ODE参数

Question

所以，我试图解决描述电力系统响应和稳定性的ODE。精确的方程和理论并不重要。正如标题所暗示的，我希望ode求解器根据一个IF条件改变一些参数。代码如下：

clear; 

E = 10;
X = 10;
R = 0;

T = 5;      % Time Constant
tmax = 100;   
G0 = 0;     % Initial Value

Psc = E^2/X;
P0 = 1.25*Psc; % Power Losses

G = 0:0.001:2;
a = tand (0);
V = E ./ sqrt( (1+R*G+a*X*G).^2 + (X*G-a*R*G).^2 );
P = E^2*G ./ ( (1+R*G+a*X*G).^2 + (X*G-a*R*G).^2 );


% ODE Numerical Solution
[t23, Gsol23s] = ode23s(@(t, G) P0/T - G* (E ./ sqrt( (1+R*G+a*X*G).^2 ...
    + (X*G-a*R*G)).^2 )^2, [0 tmax], G0);

Vsol23s = E ./ sqrt( (1+R*Gsol23s+a*X*Gsol23s).^2 ... 
    + (X*Gsol23s-a*R*Gsol23s).^2 );
Psol23s = E^2*Gsol23s ./ ( (1+R*Gsol23s+a*X*Gsol23s).^2 ...
    + (X*Gsol23s-a*R*Gsol23s).^2 );

figure;
plot(P/Psc, V/E, 'linewidth', 3);
hold on;
grid on;
plot(Psol23s/Psc, Vsol23s/E, 'linewidth', 2);
xlabel('P/Psc'); ylabel('V/E')

figure;
plot(t23, Vsol23s/E, t23, Psol23s/Psc, t23, Gsol23s*X)
legend('V/E', 'P/Psc', 'G*B');

每次V小于0.95*E，我都想把a减5。比如：

if Vsol23s << 0.95*E
a = a - 5;
end

任何想法都非常感谢。

编辑1：一次给出一个ode步骤（而不是tspan的整个矩阵）的解决方案可以做到这一点，但我不知道这是否可能。

Answer 1

参数化您的diffeq，然后根据需要将A的更新值传递给它。

E = 10;
X = 10;
R = 0;

tmax = 100;   
G0 = 0;     % Initial Value

Psc = E^2/X;
P0 = 1.25*Psc; % Power Losses

G = 0:0.001:2;
a = tand (0);
V = E ./ sqrt( (1+R*G+a*X*G).^2 + (X*G-a*R*G).^2 );
P = E^2*G ./ ( (1+R*G+a*X*G).^2 + (X*G-a*R*G).^2 );

[t23, Gsol23s] = ode23s(@(t, G) f(t, G, a), [0 tmax], G0);

Vsol23s = E ./ sqrt( (1+R*Gsol23s+a*X*Gsol23s).^2 + (X*Gsol23s-a*R*Gsol23s).^2 );
Psol23s = E^2*Gsol23s ./ ( (1+R*Gsol23s+a*X*Gsol23s).^2 + (X*Gsol23s-a*R*Gsol23s).^2 );

tIdx = find(Vsol23s < 0.95*E, 1, 'first');
if tIdx
    t0 = t23(tIdx);
    G0 = Gsol23s(tIdx);
    tSol = t23(1:tIdx-1);
    gSol = Gsol23s(1:tIdx-1);
    vSol = Vsol23s(1:tIdx-1);
    pSol = Psol23s(1:tIdx-1);
end

while tIdx

    a = a - 5;

    [t23, Gsol23s] = ode23s(@(t, G) f(t, G, a), [t0 tmax], G0);
    Vsol23s = E ./ sqrt( (1+R*Gsol23s+a*X*Gsol23s).^2 + (X*Gsol23s-a*R*Gsol23s).^2 );
    Psol23s = E^2*Gsol23s ./ ( (1+R*Gsol23s+a*X*Gsol23s).^2 + (X*Gsol23s-a*R*Gsol23s).^2 );
    tIdx = find(Vsol23s < 0.95*E, 1, 'first');
    disp(tIdx)
    if tIdx
        t0 = t23(tIdx);
        G0 = Gsol23s(tIdx);
        tSol = [tSol; t23(1:tIdx-1)];
        gSol = [gSol; Gsol23s(1:tIdx-1)];
        vSol = [vSol; Vsol23s(1:tIdx-1)];
        pSol = [pSol; Psol23s(1:tIdx-1)];
    else
        tSol = [tSol; t23];
        gSol = [gSol; Gsol23s];
        vSol = [vSol; Vsol23s];
        pSol = [pSol; Psol23s];
    end

end

figure;
plot(P/Psc, V/E, 'linewidth', 3);
hold on;
grid on;
plot(pSol/Psc, vSol/E, 'linewidth', 2);
xlabel('P/Psc'); ylabel('V/E')

figure;
plot(tSol, vSol/E, tSol, pSol/Psc, tSol, gSol*X)
legend('V/E', 'P/Psc', 'G*B');


function y = f(t, G, a)
    % parameters
    E = 10;
    X = 10;
    R = 0;

    T = 5;      % Time Constant

    Psc = E^2/X;
    P0 = 1.25*Psc; % Power Losses

    y = P0/T - G* (E ./ sqrt( (1+R*G+a*X*G).^2 + (X*G-a*R*G)).^2 )^2;
end