Creating Symbolic state space model and transforming to canonical form?
4 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
Johnathon Street
le 17 Avr 2021
Commenté : Johnathon Street
le 17 Avr 2021
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
0 commentaires
Réponse acceptée
Paul
le 17 Avr 2021
Modifié(e) : Paul
le 17 Avr 2021
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
6 commentaires
Walter Roberson
le 17 Avr 2021
A=sym('a',3)
B=sym('b',[3 1])
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)
Bc = simplify(Tinv*B)
Works for me. I just copied Paul's code exactly.
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Symbolic Math Toolbox dans Help Center et File Exchange
Produits
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!