Transfer Function to State Space Using Prediction Error Method

Question

Muhammad 2023-10-15

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2034889-transfer-function-to-state-space-using-prediction-error-method

评论： Muhammad 2023-11-17

E7i_CSV.csv

Hi Everyone,

I have Experiemental Data (Bode Plot), using MATLAB I found the Transfer Function of my plant. I have attached my E7i_CSV file.

T2 = readtable('E7i_CSV.csv');   
                                                                       % Fill With Actual Sampling Frequency
FHz = T2.F;
Ts = 1/(2*(max(FHz)+10000))
for k = 1:size(T2,1)-1
    if FHz(k+1) == FHz(k)
        FHz(k+1) = FHz(k+1)+0.5;                                                % 'Brute Force' Interpolation 
    end
end
Mag = T2.G;
PhDeg = T2.P;
Response = Mag.*exp(1j*deg2rad(PhDeg));                                         % Complex Vector
sysfr = idfrd(Response, FHz, Ts, 'FrequencyUnit','Hz')
%bode(sysfr)
%tfsys = tfest(sysfr,4,3) This is much better
tfsys = tfest(sysfr,4,3) %82.69%
%tfsys = tfest(sysfr,6,3)
figure
compare(sysfr, tfsys)
is_stable = isstable(tfsys);
disp(is_stable);

I want to convert this transfer function to statespace equations, which will be used for Model Predictive Control Design. Simple tf2ss command give me TF but it doesn't look very accrurate.

[A, B, C, D] = tf2ss(num,den)

So, I was reading a paper which i will follow, they have mentioned that they had FRF (Frequency Response Function) data and they find state space model/equations using Prediction Error Method (PEM). But I am unable to understand how I can used Bode Plot data and convert it state space using PEM. I will appreciate your help.

Secondy I verified the paper StateSpace Model by first converting it to Transfer Function and then using tf2ss command. which shows inaccurate results similiar to my results. I am looking for your help. Following is the verification code for paper i am following

%Rana Paper State Space Equations Coversion to
                            %Transfer Function for Validation Reason
% Define state-space matrices
Ax = [-49.3277, -980.7648, 618.2198;
      567.3557, -120.2273, 651.7342;
      -45.8885, -415.4194, -115.7522];
Bx = [-1.8122; 3.901370; 4.3011];
Cx = [14.9368, 16.9208, -23.6827];
Dx = 0;
% Create a state-space model
sys = ss(Ax, Bx, Cx, Dx);
% Display the state-space model
disp('State-Space Model:');
disp(sys);
% Convert the state-space model to a transfer function
tf_sys = tf(sys);
% Display the transfer function
disp('Transfer Function:');
disp(tf_sys);
                        %TF to StateSpace Rana Model
num_rana = [ -62.92 3.625*10^4 -1.065*10^8];
den_rana = [ 1 285.3 8.811*10^5 1.982*10^8];
tff_rana = tf(num_rana,den_rana);
tffss_rana = tf2ss(num_rana,den_rana);
[Arana,Brana,Crana,Drana] = tf2

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Mathieu NOE 2023-10-19

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2034889-transfer-function-to-state-space-using-prediction-error-method#answer_1336766

在 MATLAB Online 中打开

hello

a tried some coding around your data

I don't know why you have "accuracy" problem when you go from TF to SS models

here I use a low order model , you can see TF and SS are matching well

I also opted for a different sampling rate (Ts is one fourth of the nyquist rate)

T2 = readtable('E7i_CSV.csv');   
                                                                       % Fill With Actual Sampling Frequency
FHz = T2.F;
Mag = T2.G;
PhDeg = T2.P;
Response = Mag.*exp(1j*pi/180*PhDeg);                                         % Complex Vector
Ts = 0.25*1/(2*(max(FHz)));
% Ts = 1/(2*(max(FHz)+10000));
Fs = 1/Ts;
% TF  design
NA = 6;
NB = NA-2; 
W = 2*pi*FHz;
[num,den] = invfreqs(Response,W,NB,NA,[],100);
hverif = freqs(num,den,W);
% convert to SS
[A,B,C,D]=tf2ss(num,den);
[Ad,Bd,Cd,Dd] = c2dm(A,B,C,D,Ts,'tustin');
SYS = ss(Ad,Bd,Cd,Dd,Ts);
[M,P] = bode(SYS,W);
 
M = squeeze(M);
P = squeeze(P);
P = wrapTo180(P);
figure(1)
subplot(2,1,1),semilogx(FHz,20*log10(Mag),'b',FHz,20*log10(abs(hverif)),'r',FHz,20*log10(M),'c');
legend('data','TF ','SS '); 
xlabel('Frequency (Hz)');
ylabel('modulus (dB)');
subplot(2,1,2),semilogx(FHz,PhDeg,'b',FHz,180/pi*(angle(hverif)),'r',FHz,(P),'c');
legend('data','TF ','SS '); 
xlabel('Frequency (Hz)');
ylabel('modulus (dB)');

5 个评论
显示 3更早的评论隐藏 3更早的评论

Mathieu NOE 2023-10-19

在 MATLAB Online 中打开

here a higher order model - if it's what you're after :

T2 = readtable('E7i_CSV.csv');   
                                                                       % Fill With Actual Sampling Frequency
FHz = T2.F;
Mag = T2.G;
PhDeg = T2.P;
Response = Mag.*exp(1j*pi/180*PhDeg);                                         % Complex Vector
Ts = 0.25*1/(2*(max(FHz)));
% Ts = 1/(2*(max(FHz)+10000));
Fs = 1/Ts;
% TF  design
NA = 22;
NB = NA-2; 
W = 2*pi*FHz;
[num,den] = invfreqs(Response,W,NB,NA,[],100);
hverif = freqs(num,den,W);
% convert to SS
[A,B,C,D]=tf2ss(num,den);
[Ad,Bd,Cd,Dd] = c2dm(A,B,C,D,Ts,'tustin');
SYS = ss(Ad,Bd,Cd,Dd,Ts);
[M,P] = bode(SYS,W);
 
M = squeeze(M);
P = squeeze(P);
P = wrapTo180(P);
figure(1)
subplot(2,1,1),semilogx(FHz,20*log10(Mag),'b',FHz,20*log10(abs(hverif)),'r',FHz,20*log10(M),'c');
legend('data','TF ','SS '); 
xlabel('Frequency (Hz)');
ylabel('modulus (dB)');
subplot(2,1,2),semilogx(FHz,PhDeg,'b',FHz,180/pi*(angle(hverif)),'r',FHz,(P),'c');
legend('data','TF ','SS '); 
xlabel('Frequency (Hz)');
ylabel('modulus (dB)');

Mathieu NOE 2023-11-16

hello @Muhammad

problem solved ?

Muhammad 2023-11-17

Hi @Mathieu NOE

I read the document and try to understand all the six discretization methods, for frequency domain they used Tustin Approximation but I was not able to understand it fully, and still I have confusion that why c2dm(A,B,C,D,Ts,'tustin'); doesn't follow my TF completely. For now I am using c2dm without tustin approximation.

Thanks for follow up. Please help me in this regard for choosing right one

请先登录，再进行评论。

Transfer Function to State Space Using Prediction Error Method

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

5 个评论
显示 3更早的评论隐藏 3更早的评论

另请参阅

类别

标签

Community Treasure Hunt

Transfer Function to State Space Using Prediction Error Method

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

5 个评论 显示 3更早的评论隐藏 3更早的评论

另请参阅

类别

标签

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

5 个评论
显示 3更早的评论隐藏 3更早的评论