"feedback" function example in Matlab documentation doesn't seem to work?

I am trying to reproduce Example 2 in the documentation for the function "feedback" in Matlab2014a.

The example :

Consider a state-space plant P with five inputs and four outputs and a state-space feedback controller K with three inputs and two outputs. To connect outputs 1, 3, and 4 of the plant to the controller inputs, and the controller outputs to inputs 4 and 2 of the plant, use

feedin = [4 2];
feedout = [1 3 4];
Cloop = feedback(P,K,feedin,feedout)

My code :

P = rss(4,4,5); 
K = rss(2,2,3); 
feedin = [4 2]; 
feedout = [1 3 4]; 
Cloop = feedback(P,K,feedin,feedout);
size(Cloop)

Result:

Instead of returning a 3 input, 1 output closed-loop system, Matlab gives a system of the same size as P:

State-space model with 4 outputs, 5 inputs, and 6 states.

Why isn't this working properly?

[Yenni]

clc
clear all
close all
close all hidden
%
% Fungsi Alih Lingkar Tertutup
disp('Fungsi Alih Lingkar Tertutup Tanpa Pengendali Proporsional (P)')

Fungsi Alih Lingkar Tertutup Tanpa Pengendali Proporsional (P)

[num_op,den_op] = cloop(num_ol,den_ol,-1);

Unrecognized function or variable 'num_ol'.

sys_cl = tf(num_op,den_op)
% 

Answer 1

[Sam Chak]

Hi @Mark

Using the 'feedback()' command to compute the closed-loop model with the specified input and output connections doesn't affect the number of inputs and outputs. However, if there are any cancellable poles and zeros, some states will be eliminated. The number of outputs and inputs is reflected in the tiled chart layout, which has the number of rows (outputs) by columns (inputs) of tiles in the response plot.

%% State-space Proces 
Ap      = [0, 1; -1, -2];
Bp      = [0; 1];
Cp      = eye(size(Ap));
Dp      =  0*Cp*Bp;
P       = ss(Ap, Bp, Cp, Dp);
size(P)

State-space model with 2 outputs, 1 inputs, and 2 states.

%% State-space Kontroler 
Ak      = [0, 1; 0, -2];
Bk      = [0; 1];
Ck      = [1, 0];
Dk      =  1;
K       = ss(Ak, Bk, Ck, Dk);
size(K)

State-space model with 1 outputs, 1 inputs, and 2 states.

%% Closed-loop system (before pole-zero cancellation)
feedin  = [1];  % feed [Pin(1)] from [Kout(1)]
feedout = [1];  % feed [Pout(1)] to  [Kin(1)]
Cloop   = feedback(K*P, 1, feedin, feedout, -1);
size(Cloop)

State-space model with 2 outputs, 1 inputs, and 4 states.

%% Closed-loop system (after pole-zero cancellation)
Cloop   = minreal(Cloop)

2 states removed.

Cloop =
 
  A = 
            x1       x2
   x1   -1.565  -0.1752
   x2    1.825  -0.4346
 
  B = 
           u1
   x1  -1.251
   x2  0.6592
 
  C = 
            x1       x2
   y1  -0.3296  -0.6256
   y2  -0.6256   0.3296
 
  D = 
       u1
   y1   0
   y2   0
 
Continuous-time state-space model.

size(Cloop)

State-space model with 2 outputs, 1 inputs, and 2 states.

%% Step response
step(Cloop), grid on