How to Initialize a Discrete-Time Model?

Question

Daniel Gelman 2016-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/300507-how-to-initialize-a-discrete-time-model

回答： Farouk Moukaddem 2016-8-26

Hello,

I have the following discrete-time model.

num = [0.02884 -0.02844];
den = [1 -1.7298 0.7337];
H = tf(num,den,0.005);
opt = stepDataOptions('StepAmplitude',200,'InputOffset',250);  
figure;
step(H, opt);

Is it possible to set the initial conditions of this transfer function? I would like to initialize the model output (rather than 0) without changing how the input looks like (i.e using InputOffset option in the stepDataOptions for the step()).

Daniel

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Answer 1

Farouk Moukaddem 2016-8-26

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Hi Daniel,

Theoretically speaking, Transfer Functions are defined when all initial conditions on a system are set to zero.

However, if initial conditions need to be changed, it has to be realized in state space (by using integrator in continuous time and unit delays in discrete time).

To specify initial conditions, convert your system to state-space model using the "tf2ss" command and use the State-space block in Simulink.

For more information on this, refer to the following documentation link:

http://www.mathworks.com/help/simulink/slref/transferfcn.html#zmw57dd0e145311

Best,

Farouk