Can I use "place" function to adaptively update controller gain K when running model in Simulink?

I am running my model in Simulink, then send some information to the Matlab function which is used for updating controller gain K. In Matlab function, I call another m file from Matlab environment which has "place" function inside. The error is "place" is not supported for code generation.

How can I solve that problem?

Answer 1

[Sam Chak]

Hi @Quang Manh

If the place() function is not supported for code generation, you will need to program the computation manually. After all, the essence of the pole placement technique, in mathematical terms, is fundamentally about solving algebraic equations.

%% system
A   = [0,  1            % state matrix
      -6, -5];
B   = [0                % input matrix
       1];
eA  = eig(A)            % eigenvalues of open-loop system

eA = 2×1

-2.0000 -3.0000

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%% Manual Pole Placement
e   = [-5, -7];         % desired closed-loop eigenvalues
p2  = poly(e)           % desired characteristic polynomial

p2 = 1×3

1 12 35

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k1  = p2(3) + A(2,1);   % gain 1 (proportional)
k2  = p2(2) + A(2,2);   % gain 2 (derivative)
K   = [k1, k2]          % control gain matrix

K = 1×2

29 7

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%% verify the result with computational pole placement
K   = place(A, B, e)

K = 1×2

29.0000 7.0000

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Aa  = A - B*K

Aa = 2×2

0 1.0000 -35.0000 -12.0000

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eig(Aa)                 % eigenvalues of closed-loop system

ans = 2×1

-5.0000 -7.0000

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[Quang Manh]

Thanks for your comment. I agree, but the place() function implements a robust pole-placement algorithm that usually yields better results than the conventional approach. As you suggested, one workaround is to code the computation manually; however, re-implementing the robust pole-placement method this way is time-consuming.

[Sam Chak]

Hi @Quang Manh

If you can call MATLAB from your desired programming language, then you can declare the place() command as an extrinsic function using coder.extrinsic. Otherwise, consider using formulas, as most linear algebra functions are supported for code generation.

%% system
A   = [0,  1            % state matrix
      -6, -5];
B   = [0                % input matrix
       1];
eA  = eig(A)            % eigenvalues of open-loop system

eA = 2×1

-2.0000 -3.0000

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

%% Manual Pole Placement
e   = [-5, -7];         % desired closed-loop eigenvalues
p2  = poly(e)           % desired characteristic polynomial

p2 = 1×3

1 12 35

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% control gain matrix
Co  = [B, A*B];
iCo = inv(Co);
K   = [0, 1]*iCo*(p2(1)*A^2 + p2(2)*A + p2(3)*eye(2))

K = 1×2

29 7

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●

%% verify the result with computational pole placement
K   = place(A, B, e)

K = 1×2

29.0000 7.0000

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

Aa  = A - B*K

Aa = 2×2

0 1.0000 -35.0000 -12.0000

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

eig(Aa)                 % eigenvalues of closed-loop system

ans = 2×1

-5.0000 -7.0000

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[Quang Manh]

again, program "place" function manually is more complicated than I thought as it is robust pole placement algorithm.

I tried to use coder.extrinsic before, however, the simulation time is much more slower. :(

[Sam Chak]

Please consult with the technical support team. They should be able to help you.

[Quang Manh]

Anw, thank you so much for your help!