Why are some of the outputs' first values not equal to zero?

Question

Volkan Yangin 2020-12-1

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评论： Ameer Hamza 2020-12-1

Hi,

My state space system contains 6 outputs and some of them's first values are not zero. In my opinion, when t=0; first values of outputs should be zero, but step command doesn't give me all of them as 0.

It may be because of D, but i'm not sure.

Is there any point which i miss? How can i make first values of y1 an y4 zero? Can it be possible?

Thanks,

clear all
clc
A=[-7.4 -10.6;-0.7 -16.9];
B=[37.3;63.8];
C=[-7.4 0;0 1;1 0;-0.1 -0.14;-0.1 0.13;0.1 0];
D=[37.3;0;0;1;0;0];
sys=ss(A,B,C,D);
t=0:0.01:10;
[y,t]=step(sys,t)

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Answer 1

Ameer Hamza 2020-12-1

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Yes, it is because of matrix 'D'. At t=0, the values of all the states 'x' will be zero, but the value of output 'y' will not be equal to zero for your system. For example, change the line to

[y,t,x]=step(sys,t);

and check the value of 'x'. It starts at 0.