state space into transformer function ......where is the problem

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belal hariz belgacem 2019-10-27

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/487720-state-space-into-transformer-function-where-is-the-problem

回答： Pavl M. 2024-11-30

clear all, close all, clc;

syms f j k1 k R l

%% State space representation

A = [-f/j k1/j;(-k-k1)/l -R/l];

% the state matrix

B = [0 -1/j;k/j 0];

% the input vector

C = [1 0;0 1];

% the output vector

D = zeros(size(C,2),size(B,2));

% the feedforward

%% Verify the controllability and observability

Mc = ctrb(A,B);

% Controllability matrix

Om = obsv(A,C)

% matrix

the_means_not_controllable = length(A)-length(Mc)

if rank(Mc) == size(A,2)

'It is controllable'

else

'It is not controllable'

end

if rank(Om) == size(A,2)

'It is observable'

else

'It is not observable'

end

%% Transform into transfer function

[num,den] = ss2tf(A,B,C,D)

sys = tf(num,den)

%Order system

Order_system = order(sys)

step(sys,'g')

grid on

.................................................................the problem

Error using ctrb (line 20)

The "ctrb" command cannot be used for models of class "sym".

Error in state_space (line 19)

Mc = ctrb(A,B);

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Answer 1

Pavl M. 2024-11-30

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/487720-state-space-into-transformer-function-where-is-the-problem#answer_1551943

在 MATLAB Online 中打开

I found and corrected it:

clear all, close all, clc;

syms f j k1 k R l

%% State space representation

A = [-f/j k1/j;(-k-k1)/l -R/l];

% the state matrix

B = [0 -1/j;k/j 0];

% the input vector

C = [1 0;0 1];

% the output vector

D = zeros(size(C,2),size(B,2));

A = double(subs(A,{f,j,k1,k,R,l},{1,2,3,4,5,6}))

A = 2×2

-0.5000 1.5000 -1.1667 -0.8333

B = double(subs(B,{j,k},{2,4}))

B = 2×2

0 -0.5000 2.0000 0

% the feedforward

%% Verify the controllability and observability

Mc = ctrb(A,B);

% Controllability matrix

Om = obsv(A,C)

Om = 4×2

1.0000 0 0 1.0000 -0.5000 1.5000 -1.1667 -0.8333

% matrix

the_means_not_controllable = length(A)-length(Mc)

the_means_not_controllable = -2

if rank(Mc) == size(A,2)

'It is controllable'

else

'It is not controllable'

end

ans = 'It is controllable'

if rank(Om) == size(A,2)

'It is observable'

else

'It is not observable'

end

ans = 'It is observable'

%% Transform into transfer function

[num,den] = ss2tf(A,B,C,D,1)

num = 2×3

0 0 3 0 2 1

den = 1×3

1.0000 1.3333 2.1667

sys1 = tf(num(1,:),den)

sys1 = 3 --------------------- s^2 + 1.333 s + 2.167 Continuous-time transfer function.

sys2 = tf(num(2,:),den)

sys2 = 2 s + 1 --------------------- s^2 + 1.333 s + 2.167 Continuous-time transfer function.

%Order system

Order_system1 = order(sys1)

Order_system1 = 2

Order_system2 = order(sys2)

Order_system2 = 2

step(sys1,'g')

hold on

grid on

step(sys2,'b')

grid on

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