System of Nonlinear Equations are failing to be solved

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Labid Bin Bashar 2022-9-25

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https://ww2.mathworks.cn/matlabcentral/answers/1811845-system-of-nonlinear-equations-are-failing-to-be-solved

评论： Labid Bin Bashar 2022-9-26

Hello Altruists,

I am trying to solve the system of nonlinear equations using both fsolve() and vpasolve(). However, they are failing to provide any result and end up in some empty symbolic variables (for vpasolve()) or just stopped iteration at some point (for fslove()). The code given below is a simplified version of my code. In this case, I have to solve two equations (in reality 5 equations) eq1 and eq2 to find out the roots Kp, Ki. How can I solve this problem?

    syms Kp ;
    syms Ki ;
    Kd = 0.2023;
    lm = 1.1477;
    mu = 0.9973;
    
    phi_m = 80;
    w_gc = 0.3;
    
    
    
    L = 0.2694;
    K = 0.42456;
    p2zw = 1.2157;
    wn = 0.50679;
    a = 2.109;
    b = 1.015;
    
    P_mag = K / ((w_gc^(a)*cos(a*pi/2) + p2zw*w_gc^(b)*cos(b*pi/2) + wn^2)^2 + (w_gc^(a)*sin(a*pi/2) + p2zw*w_gc^(b)*sin(b*pi/2))^2);
    P_arg = -w_gc*L-atan((w_gc^a*sin(a*pi/2))+(p2zw*w_gc^b*sin(b*pi/2))/(w_gc^a*cos(a*pi/2))+(p2zw*w_gc^b*cos(b*pi/2)+w_gc^2));
    C_mag = sqrt((Kp + (Ki*w_gc^(-lm)*cos(lm*pi/2)) + Kd*w_gc^mu*cos(mu*pi/2))^2+((-Ki*w_gc^(-lm)*cos(lm*pi/2)) + Kd*w_gc^mu*sin(mu*pi/2))^2);
    C_arg = atan(((-Ki*w_gc^(-lm)*cos(lm*pi/2)) + Kd*w_gc^mu*sin(mu*pi/2))/(Kp + (Ki*w_gc^(-lm)*cos(lm*pi/2)) + Kd*w_gc^mu*cos(mu*pi/2)));
    
    
    eq1 = C_arg + P_arg == pi-phi_m*pi/180;
    eq2 = C_mag*P_mag == 1;
    [sol1, sol2] = vpasolve([eq1 eq2],[Kp Ki])
sol1 = 0.40751782462346212168748687200968
sol2 = 0.1065888515318568220223455502278