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Using 'connect' command to simplify MIMO model

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Vehzan Rustomji
Vehzan Rustomji on 4 Dec 2019
Edited: Vehzan Rustomji on 4 Dec 2019
Consider the 3x3 MIMO model P_sys (see attachment for state space model) with inputs and outputs as shown:
K is a PI controller that is used to stabilize the third output,i.e., loop 1 is closed first.
I wish to include the dynamics of the controller K in the reduced 2x2 MIMO model with inputs , and outputs ,ν
Please confirm if I have used the command connect properly in the code as follows:
load P_sys.mat
s = tf('s')
k_p = 1;
k_i = 18.8496;
K = k_p + k_i/s;
K.u = 'e_omega';
K.y = 'T_e';
Sum = sumblk('e_omega = omega_p_ref - \omega_p');
T = connect(P_sys,K,Sum,{'I_1','I_2','omega_p_ref'},{'r_g','\nu'});
I understand that T is now a 3x2 system, but if I simply ignore the input 'omega_p_ref', I end up with a 2x2 system
Someone who has experience of using this command, please confirm if what I have done is correct.
Thanks a bunch!
PS: For your reference, the structure of the plant P is:
P_sys.Inputname = {'I_1','I_2','T_e'};
P_sys.Outputname = {'r_g','\nu','\omega_p'};
P_sys.Statename = {'r_g','\nu','p_p','p_s','\omega_p'};

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