Creating Symbolic state space model and transforming to canonical form?

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Johnathon Street 2021-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/805126-creating-symbolic-state-space-model-and-transforming-to-canonical-form

评论： Johnathon Street 2021-4-17

Hi all,

Is it possible to create a state space model based on symbolic parameters?... and then convert this model into controllable cannonical form?

Thanks,

Johnathon Street

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Answer 1

Paul 2021-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/805126-creating-symbolic-state-space-model-and-transforming-to-canonical-form#answer_677821

编辑：Paul 2021-4-17

在 MATLAB Online 中打开

Yes, at least in principle. For example:

>> A=sym('a',3)
 
A =
 
[ a1_1, a1_2, a1_3]
[ a2_1, a2_2, a2_3]
[ a3_1, a3_2, a3_3]
 
>> B=sym('b',[3 1])
 
B =
 
 b1
 b2
 b3
 
>> C=[B A*B A^2*B];  % controllability matrix
>> t3 = [0 0 1]/C;
>> Tinv=[t3;t3*A;t3*A^2]; % state transformation
>> Ac = simplify(Tinv*A/Tinv,100)
 
Ac =
 
[                                                                                                   0,                                                                     1,                  0]
[                                                                                                   0,                                                                     0,                  1]
[ a1_1*a2_2*a3_3 - a1_1*a2_3*a3_2 - a1_2*a2_1*a3_3 + a1_2*a2_3*a3_1 + a1_3*a2_1*a3_2 - a1_3*a2_2*a3_1, a1_2*a2_1 - a1_1*a2_2 - a1_1*a3_3 + a1_3*a3_1 - a2_2*a3_3 + a2_3*a3_2, a1_1 + a2_2 + a3_3]
 
>> Bc = simplify(Tinv*B)
 
Bc =
 
 0
 0
 1