Convert transfer function to state-space models

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Diego Garcia 2019-10-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/484735-convert-transfer-function-to-state-space-models

回答： Diego Garcia 2019-10-17

I'm trying to convert a transfer function to state space model. In order to avoid the control toolbox functions since I don't have it's license.

The transfer function that I'm using is quite simple. Is the model for a heatsink temperature.

For this transfer function I have the next values for A,B,C and D.

I've tried to compare the output from the lsim() function and the equations from above but the output differs

Here's the code that I've used

P = rand(1,10)*1000;
t = 0:1:length(P)-1;
A = -400;
B = 0.5;
C = 0.6658;
D = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%    State space    %%%
%%%%%%%%%%%%%%%%%%%%%%%%%
state_space_sys = ss(A,B,C,D);
state_space = lsim(state_space_sys,P,t);
figure
plot(t,state_space)
grid on,grid minor, title('State space')
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%   My function     %%%
%%%%%%%%%%%%%%%%%%%%%%%%%
x(1:length(P)) = 0;
y(1:length(P)) = 0;
u = P;
for k = 1:length(u)
    x(k+1) = A*x(k) + B*u(k);
    y(k) = C*x(k) + D*u(k);
end
figure
plot(t,y)
grid on,grid minor, title('My function')

Is there any mistakes on the approach?

It should be quite simple, but I can't manage to find the solution.

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Walter Roberson 2019-10-16

编辑：Walter Roberson 2019-10-16

Is there a reason not to use tf() and ss() ? That is, if you pass a tf into ss() then it will be converted.

Diego Garcia 2019-10-17

Hello @Akbar. Rth is the thermal resistance of the heatsink. th stands for thermal.

@Akbar & @Walter Roberson , I'm trying to aboid the system control toolbox, since I don't have the license and I can only use the trial for 30 days.

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采纳的回答

Diego Garcia 2019-10-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/484735-convert-transfer-function-to-state-space-models#answer_396780

在 MATLAB Online 中打开

At the end, I found another solution. I'm posting this here, so if someone has the same problem, can use this approach.

If you take the transfer function, and develop it, we reach to the following expresion

Now, we know that 1/s is equal to integrate. So in the end, we have to integrate the right side of the equation. The code would be like this.

Cth = Tau/Rth;
deltaT = zeros(size(P));
for i = 2:length(P)
    deltaT(i) = (1/Cth * (P(i)-deltaT(i-1)/Rth))*(time(i)-time(i-1)) + deltaT(i-1);
end

This integral has the same output as the function tf() and the function lsim() with the A,B,C and D values.

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Control Systems Control System Toolbox Linear Analysis Time and Frequency Domain Analysis

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