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

Question

Mark 2014-11-12

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https://ww2.mathworks.cn/matlabcentral/answers/162428-feedback-function-example-in-matlab-documentation-doesn-t-seem-to-work

移动：Sam Chak 2024-5-8

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?

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Yenni 2024-5-8

移动：Sam Chak 2024-5-8

在 MATLAB Online 中打开

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)
% 

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Answer 1

Sam Chak 2024-5-8

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/162428-feedback-function-example-in-matlab-documentation-doesn-t-seem-to-work#answer_1454207

在 MATLAB Online 中打开

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