how to simulate using lsim command I am receiving error because of variable 't'(time).

s = -14.5 

A = [-3, 5, -7, 0; 0.5, -1.5, 0.5, -7.5; -5, 0, -3, 0; -0.5, -5, 0, -7];

B = [1, 0; 0, -1; -2, 0; 0, 1];

C = [1, 0, 0, 0; 0, -1, 0, 0];

D = [-1, 0; 2, 0];
sys = ss(A,B,C,D);

M = (s*eye(4,4) - A);


P = [ M, -B; C, D]

k = rank(P)


d = det(P)

uM = null(P,'r')

sys2 = tf( sys );

[y,t] = lsim(sys2 ,uM , t)
size(y)

Error that I am receiving:-

When simulating the response to a specific input signal, the input

data U must be a matrix with as many rows as samples in the time

vector T, and as many columns as input channels.

Unrecognized function or variable 't'.

Error in antiresonance_part_two (line 40)

[y,t] = lsim(sys2 ,uM , t)

Answer 1

[Star Strider]

The input ‘u’ must have the same number of columns as ‘B’.

I have no idea what you actually want to do (or what your ‘u’ is), so in their absence, try this as a relevant (and working) example with your system:

A = [-3, 5, -7, 0; 0.5, -1.5, 0.5, -7.5; -5, 0, -3, 0; -0.5, -5, 0, -7];
B = [1, 0; 0, -1; -2, 0; 0, 1];
C = [1, 0, 0, 0; 0, -1, 0, 0];
D = [-1, 0; 2, 0];
sys = ss(A,B,C,D);

t = linspace(0, 2.5, 250).';
u = sin(2*pi*t*[1 5]);

[y,t] = lsim(sys, u, t);

figure
yyaxis left
plot(t, u(:,1), '--b')
hold on
plot(t, u(:,2), '--r')
hold off
yyaxis right
plot(t, y(:,1), '-b')
hold on
plot(t, y(:,2), '-r')
hold off
grid
xlabel('Time')
ylabel('Amplitude')
legend('u_1', 'u_2', 'y_1', 'y_2', 'Location','N')

Make appropriate changes to get the result you want.

[Virendra Kowale]

thank you so much I treid but in my question

u(t) = p*exp(zt)

where,

p = x0

x0 = transpose([0,0,0,-0.1333])

z = invariant zero, which i got i.e. (z = -14.5)

t is time which I am taking as t = 0:0.1:10;

and when i try to run this command [y,t] = lsim(sys ,u , t)

I receive the following error

Matrix dimensions must agree.

Error in antiresonance_part_two (line 38)

u = x_zero.*exp(-14.5*t)

[Virendra Kowale]

here is the entire code

clear all

close all

clc

s = -14.5

A = [-3, 5, -7, 0; 0.5, -1.5, 0.5, -7.5; -5, 0, -3, 0; -0.5, -5, 0, -7];

B = [1, 0; 0, -1; -2, 0; 0, 1];

C = [1, 0, 0, 0; 0, -1, 0, 0];

D = [-1, 0; 2, 0];

sys = ss(A,B,C,D);

M = (s*eye(4,4) - A);

P = [ M, -B; C, D]

k = rank(P)

uM = null(P,'r')

I = transpose(uM)

%sys2 = tf( sys );

t = linspace(0, 2.5, 10).';

x_zero = transpose([0,0,0,-0.1333])

u = x_zero.*exp(-14.5*t)

x0= initial(sys,x_zero)

[y,t] = lsim(sys ,u , t)

[Star Strider]

As always, my pleasure!

Experiment with this:

s = -14.5; 
A = [-3, 5, -7, 0; 0.5, -1.5, 0.5, -7.5; -5, 0, -3, 0; -0.5, -5, 0, -7];
B = [1, 0; 0, -1; -2, 0; 0, 1];
C = [1, 0, 0, 0; 0, -1, 0, 0];
D = [-1, 0; 2, 0];
sys = ss(A,B,C,D);
M = (s*eye(4,4) - A);
P = [ M, -B; C, D];
k = rank(P);
uM = null(P,'r');
I = transpose(uM);
%sys2 = tf( sys );
t = linspace(0, 2.5, 10).';
x_zero = transpose([0,0,0,-0.1333]);
u = (x_zero([3 4],:)*exp(-14.5*t.')).';                 % Changed To Match Dimensions Of ‘B’
x0= initial(sys,x_zero);
[y,t] = lsim(sys ,u , t);

figure
yyaxis left
plot(t, u, '-')
ylabel('Input')
yyaxis right
plot(t, y, '-')
ylabel('Output')
grid

It runs without error. You will need to determine if it does what you want.

I added the figure so that I could see the result.

[Virendra Kowale]

Thanks a ton. It worked. It does what I want.

[Star Strider]

As always, my pleasure!

I was not certain if my changes were what you wanted, so I appreciate your follow-up!