Why does transforming transfer matrix into complex vector transfer function lead to NaN ?

Question

Merve Can 2021-10-27

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1573113-why-does-transforming-transfer-matrix-into-complex-vector-transfer-function-lead-to-nan

评论： Paul 2021-11-2

Hi,

I am currently trying to transform my transfer matrix into compex vector form. The following picture shows how it is theoretically done.

My

is Z_2 and has quite a high order. So when I try to use eq. (F2) to get

Matlab returns Z_2_cmplx = NaN. Here is my code:

%% Calculation of Transfer Function

% Parameters

Lf_1 = 5.6e-3;

Rf_1 = 0.1;

Cf_1 = 1.61e-05;

L_1 = 1.46e-3 ;

R_1 = 0.053;

wn = 2*pi*50;

Kpc_1 = 35.839999999999996;

Kic_1 = 8.789333333333335e+02;

Kpv_1 = 0.027560488364344;

Kiv_1 = 12.664025834171640;

F_i = 0.9;

% Calculating Transfer Functions

s = tf('s');

Z_PIi = (Kpc_1 + Kic_1 * 1/s) ;

Z_CDi = (-wn*Lf_1) * [0 -1;1 0];

Z_inner = (Z_PIi + (s*Lf_1 + Rf_1))*[1 0;0 1] + (wn*Lf_1)*[0 -1;1 0] + Z_CDi;

Z_inner_inv = inv(Z_inner);

G_I = Z_PIi / Z_inner;

Z_PIv = 1/(G_I * ((Kpv_1 + Kiv_1 * 1/s) * [1 0;0 1]));

Z_PIv_inv = inv(Z_PIv); %Removes extra s

Z_CDv = -1/((wn*Cf_1*[0 -1;1 0])*G_I);

Z_CDv_inv = inv(Z_CDv);

Z_parallel_inv = Z_PIv_inv + Z_CDv_inv + [s*Cf_1 -wn*Cf_1;wn*Cf_1 s*Cf_1] + Z_inner_inv; %equal to Zinner//Zpar mentioned in the notes

Z_parallel = 1/Z_parallel_inv;

Z_1 = Z_parallel/Z_PIv;

Z_ov = [R_1, -wn*Lv_1;

wn*Lv_1, R_1];

Z_Fi = -Z_parallel / inv(G_I)*F_i;

%% Transformation into complex vector form

Z_2 = Z_parallel + Z_Fi + (Z_ov * Z_1);

Z_2_cmplx = (Z_2(1,1)+Z_2(2,2))/2 + 1i * (Z_2(2,1)+Z_2(1,2))/2 % This yields NaN :/

Can anyone please help me with this? I am really out of ideas on how to solve this issue.

Thanks a lot!!!!

Merve

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Paul 2021-10-27

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Can't run the code because, variable Lv_1 is undefined.

Also, the expression for Z_2_cmplx doesn't follow the equation in the picture. It should be

Z_2_cmplx = (Z_2(1,1)+Z_2(2,2))/2 + 1i * (Z_2(2,1) - Z_2(1,2))/2

Because Z_2_cmplx is supposed to be G_dq_plus (I think).

Merve Can 2021-10-27

在 MATLAB Online 中打开

Hi Paul,

thank you for your answer. Yes, sorry it should be a “-“.Nevertheless, I am getting NaN.

Lv_1 = (5.6e-3)*3;

Can you run the code now?

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Answer 1

Paul 2021-10-27

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1573113-why-does-transforming-transfer-matrix-into-complex-vector-transfer-function-lead-to-nan#answer_818228

在 MATLAB Online 中打开

Recreating the result

%% Calculation of Transfer Function
% Parameters
Lf_1  = 5.6e-3;
Rf_1  = 0.1;
Cf_1  = 1.61e-05;
L_1   = 1.46e-3 ;
R_1   = 0.053;
Lv_1 = (5.6e-3)*3;
wn    = 2*pi*50;
Kpc_1 = 35.839999999999996;
Kic_1 = 8.789333333333335e+02;
Kpv_1 = 0.027560488364344;
Kiv_1 = 12.664025834171640;
F_i   = 0.9; 
% Calculating Transfer Functions
s = tf('s');  
Z_PIi               = (Kpc_1 + Kic_1 * 1/s) ;
Z_CDi               = (-wn*Lf_1) * [0 -1;1 0];
Z_inner             = (Z_PIi + (s*Lf_1 + Rf_1))*[1 0;0 1] + (wn*Lf_1)*[0 -1;1 0] + Z_CDi;
Z_inner_inv         = inv(Z_inner);
G_I                 = Z_PIi / Z_inner; 
Z_PIv               = 1/(G_I * ((Kpv_1 + Kiv_1 * 1/s) * [1 0;0 1]));
Z_PIv_inv           = inv(Z_PIv);                                                               %Removes extra s
Z_CDv               = -1/((wn*Cf_1*[0 -1;1 0])*G_I);
Z_CDv_inv           = inv(Z_CDv);
Z_parallel_inv      = Z_PIv_inv + Z_CDv_inv  + [s*Cf_1 -wn*Cf_1;wn*Cf_1 s*Cf_1] + Z_inner_inv;  %equal to Zinner//Zpar mentioned in the notes
Z_parallel          = 1/Z_parallel_inv;
Z_1                 = Z_parallel/Z_PIv;
Z_ov                = [R_1, -wn*Lv_1;
                       wn*Lv_1, R_1];
Z_Fi                = -Z_parallel / inv(G_I)*F_i;
Z_2                 = Z_parallel + Z_Fi + (Z_ov * Z_1);
Z_2_cmplx           = (Z_2(1,1)+Z_2(2,2))/2 + 1i * (Z_2(2,1)-Z_2(1,2))/2 % This yields NaN :/
Z_2_cmplx =
 
  NaN
 
Static gain.

Look at the coefficients of the numerator and denominator of Z_2(1,1). They are enormous, here's the five largest. Same thing with Z_2(2,2)

[num,den] = tfdata(Z_2(1,1));
sortnum = sort(num{:});
sortden = sort(num{:});
sortnum(end-5:end)
ans = 1×6
	1.0e+186 *

    0.0271    0.1262    0.4510    1.1589    1.4996    1.9038
sortden(end-5:end)
ans = 1×6
	1.0e+186 *

    0.0271    0.1262    0.4510    1.1589    1.4996    1.9038

When Z_2(1,1) and Z_2(2,2) are combined, problems result with the coefficients getting too large.

[num,den] = tfdata(Z_2(1,1)+Z_2(2,2));
any(isinf(num{:}))
ans = logical
   1
any(isinf(den{:}))
ans = logical
   1

There may be a better way to do all that transfer function manipulation. Are those equations derived from a block diagram?

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Paul 2021-10-28

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Without looking at the paper, I tried to mimic the original equations, but sticking with ss form wherever possible and finding minimal realizations at each step.

Please check carefully that this code is functionally equivalent to your code.

I didn't take the last step of combining the real and imaginary parts of Z2_cmplx, because, frankly, I've never seen anything where an LTI system is multiplied by 1i

Hopefully you have some idea of what the result should look like and compare to the result achieved below.

%% Calculation of Transfer Function

% Parameters

Lf_1 = 5.6e-3;

Rf_1 = 0.1;

Cf_1 = 1.61e-05;

L_1 = 1.46e-3 ;

R_1 = 0.053;

Lv_1 = (5.6e-3)*3;

wn = 2*pi*50;

Kpc_1 = 35.839999999999996;

Kic_1 = 8.789333333333335e+02;

Kpv_1 = 0.027560488364344;

Kiv_1 = 12.664025834171640;

F_i = 0.9;

% Calculating Transfer Functions

s = tf('s');

Z_PIi = ss(Kpc_1 + Kic_1 * 1/s) ;

Z_CDi = ss((-wn*Lf_1) * [0 -1;1 0]);

Z_inner = (Z_PIi + ((s*Lf_1 + Rf_1))*[1 0;0 1]) + (wn*Lf_1)*[0 -1;1 0] + Z_CDi;

Z_inner_inv = minreal(ss(zpk(inv(Z_inner))));

3 states removed.

% G_I = Z_PIi / Z_inner;

G_I = minreal(ss(zpk(Z_PIi * Z_inner_inv)));

5 states removed.

% Z_PIv = 1/(G_I * ((Kpv_1 + Kiv_1 * 1/s) * [1 0;0 1]));

% Z_PIv_inv = inv(Z_PIv); %Removes extra s

Z_PIv_inv = minreal(ss(zpk(G_I * ((Kpv_1 + Kiv_1 * 1/s) * [1 0;0 1]))));

3 states removed.

% Z_CDv = -1/((wn*Cf_1*[0 -1;1 0])*G_I);

% Z_CDv_inv = inv(Z_CDv);

Z_CDv_inv = -((wn*Cf_1*[0 -1;1 0])*G_I);

Z_parallel_inv = Z_PIv_inv + Z_CDv_inv + [s*Cf_1 -wn*Cf_1;wn*Cf_1 s*Cf_1] + Z_inner_inv; %equal to Zinner//Zpar mentioned in the notes

% Z_parallel = 1/Z_parallel_inv;

Z_parallel = minreal(ss(zpk(inv(Z_parallel_inv))));

18 states removed.

% Z_1 = Z_parallel/Z_PIv;

Z_1 = minreal(Z_parallel*Z_PIv_inv);

3 states removed.

Z_ov = [R_1, -wn*Lv_1;

wn*Lv_1, R_1];

% Z_Fi = -Z_parallel / inv(G_I)*F_i;

Z_Fi = minreal(-Z_parallel * G_I * F_i);

1 state removed.

Z_2 = minreal(Z_parallel + Z_Fi + (Z_ov * Z_1));

10 states removed.

% Z_2_cmplx = (Z_2(1,1)+Z_2(2,2))/2 + 1i * (Z_2(2,1)-Z_2(1,2))/2;

Z_2_cmplx_real = minreal(Z_2(1,1) + Z_2(2,2))/2;

26 states removed.

Z_2_cmplx_imag = minreal(Z_2(2,1) - Z_2(1,2))/2;

26 states removed.

bode(Z_2_cmplx_real)

bode(Z_2_cmplx_imag)

Merve Can 2021-11-2

Maybe I can explain it in a better way in an e-mail. Could you please contact me via merve.can@campus.tu-berlin.de?

Paul 2021-11-2

No, I don't do email exchanges.

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