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convert equation to matrix for 3d plot

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Shane Palmer
Shane Palmer on 11 Jun 2020
Commented: Shane Palmer on 12 Jun 2020
Hello,
I am trying to represent this function in 3D as a surface, been doing some more experimenting here. I am having problems with turning my P_ave_output into a matrix. It is a bit of a complicated equation and I was hoping matlab had an easy command to do this for me. As I understand it, my R_l and C variables are matrices, and therefore the P_ave_output also needs to be a matrix. I am not quite sure how to do that. The end goal is again to represent a 3d surface plot relating the 3 matrices. Would you have any pointers for this?
I appreciate your help.
Thanks,
Shane
clear all
syms omega t R_l s A_in Y C
%Inputs
A_o = 3;
R_c = 40;
L_c = 0.051;
f=186;
omega_in = 2*pi*f;
A = A_o*sin(omega*t);
M=0.01;
%Theta from part a)
theta = 0.244;
%Spring coefficient (N/m)
k = 13660;
%Damping coefficient (N*s/m)
C_d = 0.07;
%Capacitance Assumption
%C=14*10^-6;
%Impedance equations
Z1 = R_c+R_l+L_c*s+1/(s*C);
Z2 = C_d+k/s+M*s;
%From part a) transfer function
%Output voltage V_l
V_l = (theta*(Y*s)*R_l)/Z1;
%Input excitation force Z_in
A_in=(Y*s*Z2+theta*V_l/R_l)/(M);
%output voltage ratio to input force
Transfer_func = simplify(V_l/A_in);
Transfer_func(s) = vpa(simplify(V_l/A_in),5);
Transfer_func(omega) = subs(Transfer_func, {s},{1j*omega});
amplitude_TF = A_o*abs(Transfer_func(omega_in));
angle_TF = angle(Transfer_func(omega_in));
V_l_steady_state = amplitude_TF*(sin(omega_in*t+angle_TF));
P_ave_output = (amplitude_TF/(sqrt(2)))^2/R_l;
P_ave_diff = diff(P_ave_output);
P_ave_diff = simplify(P_ave_diff, 'Steps',500);
P_ave_max = P_ave_diff == 0;
%R_l_optimal = vpa(abs((solve(P_ave_max, R_l))),3)
%fplot(P_ave_output,[10 200])
%xticks([10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200])
%xline(72.3)
%ylabel('Average Power (Watts)')
%xlabel('Load Resistance R_l (Ohms)')
%Plotmax = vpa(subs(P_ave_output,{R_l},{R_l_optimal}),8)
R_l= [10:10:200];
C=[2:2:20];
ZZ=P_ave_output
surf(R_l,C,ZZ)
  4 Comments
Star Strider
Star Strider on 11 Jun 2020
In order for the surf call to work, ‘Y’ needs to be defined (or removed). (It’s quadratic in ‘A_in’, so it doesn’t cancel in ‘Transfer_func’.)
It would then be straightforward to calculate ‘ZZ’, and produce the plot.
Shane Palmer
Shane Palmer on 12 Jun 2020
Okay, thank you for the clarification. I'll see if I can include that information in a better way.

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