Matrix Error

Greetings,

I am trying to model the system X(s)/E(s) = (-20.5s+41)/(s^2+7s+10). Where E(s) = U(s) - (X(s)^2-X(s)). U(s) is an impulse.

It is a negative feedback system in the s-domain.

The line e=... represents the calculation of the error of a feedback.

         E
U --->+---->G(s)----->X(s)
      ^            |
      |            |
       ----(?)------

Where the output of (?) is represented by X(s)^2 - X(s).

So E(s) is the input of G(s) and X(s) is the output of G(s). It is a negative feedback system, so E(s) is represented by U(s)-( X(s)^2 - X(s)).

The block, (?), cannot be treated as X(s)-1.

Best way I could explain it...

I am getting an error

In an assignment  A(I) = B, the number of elements in B and I must be the same.

Error in SysSimHW10p1 (line 45)
    xdot1(2) = -7*x(2) - 10*x(1) + e;

that I am having trouble fixing.

% X(s)    -20.5s + 41
%----- = --------------
% E(s)   s^2 + 7s + 10

% E(s) = U(s) - [ (X(s)^2 - X(s) ]

clear all
close all
clc

N = 450;

T = .01;
X = [0 0];
x = zeros(1,N);
u = zeros(1,N);

xdot1 = x;
xdot2 = xdot1;

for n = 1:N-1

      u(1) = .01;
      e = u - x.*x + x;

      xdot1(1) = x(2);
      xdot1(2) = -7*x(2) - 10*x(1) + e;

      x = x + (T/2)*(3*xdot1 - 1*xdot2);

      xdot2 = xdot1;
      X = [X (-20.5*x(2) + 41*x(1))];

end

t = T*[0:length(X)-1];
plot(t,X)
title('Impulse Response of System')
xlabel('Time')
ylabel('Amplitude')

Any help is appreciated!

Answer 1

[Geoff]

Well, u is a 1x450 vector, and x is a 1x3 vector. You can't add those together.

What is that line of code supposed to mean?

[Kyle]

I added more detail to the problem statement. Thank you

[Geoff]

Okay, and what is 's'? I notice it's not in your code. Is that because you can use vector-operations to compute the entire X(s) without looping, or is that what you're doing with 'n'?

Everywhere else you use 'x', you're taking a scalar out of it (x(1), x(2)). Could it be that you're meant to do this for the line where your error occurs? Or should you be taking u(n) instead of u?

[Kyle]

s just means that the functions are represented in my problem as S-domain functions---Laplace transfer functions. They represent a simplified version of differential equations. To program these equations they are converted back to time-domain representations. Ignore the s and just think of it in terms of X, G, U, E..I guess.