about why in pole placement gives me error?

Question

azam ghamari 2018-12-26

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评论： oussama sadki 2022-9-5

Hi guys

Does every body knows why in the system :

s=tf('s');
G=(s-2.44)/((s+5)*(s+6)*(s+7));
[A,B,C,D]=tf2ss([1 2.44],[1 18 107 210]);
k_max=1001;
for j=1:k_max
    p(j,:)=[-j-1 -3*j -j-2];
    K(j,:)=place(A,B,p(j,:));
end

with differeing the p value it gives me this error?

Error using place (line 78)

The "place" command cannot place poles with multiplicity greater than rank(B).

Error in test2 (line 33)

K(j,:)=place(A,B,p(j,:));

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Answer 1

Aquatris 2018-12-27

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It is just the error says. Place command cannot place poles with multiplicity greater than rank(B). In your case, rank(B) is 1. However when j=1, you want to place your poles at [-2 -3 -3]. You see the multiplicity of pole at -3 is 2. So place command cannot be used. If you start j from 2 instead of 1, there won't be an issue.

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Aquatris 2018-12-28

I dont know why you think it does not work. You do realize place is for state feedback not output feedback so you need an observer right?

oussama sadki 2022-9-5

hello Aquatris, why then rank(B) and each one poles multiplicity should be equal so that feedback gain could be computed, what relationship is there?

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Answer 2

azam ghamari 2018-12-28

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no, i used it for state feedbackany way when we have somethink like this:

P=p(j,:)=[-j-1 -3*j -j-2];

and B is for example 4x2;

it doesn't work and give me the result.

It gives me this error:

Subscripted assignment dimension mismatch.

Error in test2 (line 31)

K(j,:)=place(A,B,p(j,:));

A=[0.5 0 0.025 0;0 -0.01 0 0.017;0 0 -0.025 0;0 0 0 -0.0178];
B=[0.48 0;0 0.35;0 0.077;0.055 0];
C=[0.5 0 1 0];
D=0;
sys=ss(A,B,C,D);
G=tf(sys)
k_max=1001;
for j=1:k_max
    p(j,:)=[-10*rand(1) -20*rand(1) -15*rand(1) -rand(1)];
    K(j,:)=place(A,B,p(j,:));
end

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Aquatris 2018-12-28

This error is not because of place function. Just check the size of the matrix place() function return with given A and B matrice and you will realize the error.

Since this is a 2 input 4 state system, place() will return a 2x4 matrix. With the line "K(j,:) = place(...)" you are trying to assign 2x4 matrix to a 1x4 matrix, hence the error dimension mismatch. A quick fix is to change the line to;

K(j,:,:)=place(A,B,p(j,:))

azam ghamari 2018-12-29