impulse response with the commande lsim

hello everyone

i try to get the impulse response of first order transfert function with the commande lsim

sys = tf(1,[0.5,1]);

t = [0:0.1:3];

input = zeros(size(t));

input(1)=inf ;% when t=0 the input is inf

output = lsim(sys,input,t);

plot(t,output)

that lines of commandes dont give me same result as

>> sys = tf (1,[0.5 1])

>> impulse(sys)

why????????????

Answer 1

[Mathieu NOE]

hello

your first implementation is a discrete time impulse

For discrete-time systems, the impulse response is the response to a unit area pulse of length Ts and height 1/Ts, where Ts is the sample time of the system.

so the "dirac" area" must remain = 1 , that is the amplitude is not inf but the inverse of the time increment (0.1 s in your code)

further reducing the time increment makes the code getting closer to the "true" impulse response

try with dt = 0.01 like below :

sys = tf(1,[0.5,1]); 
dt = 0.01;
 t = [0:dt:3]; 
input = zeros(size(t)); 
input(1)=1/dt ;% dirac area = 1 
output = lsim(sys,input,t);
plot(t,output)