Question

Consider the system whose differential equation is as follows.

?′′′ − 9?′′ + 27?′ + 21? = 66?′ + 44?

       Find the transient and steady state for the step and impulse response using MATLAB.

I understand how to get the coefficients, the roots, the impulse response, the step response and the transfer functions itself but its not clear on how to isolate the transient and steady state response by themselves. Maybe I am misunderstanding what those terms mean?

Answer 1

Hello,
          Please find the answer attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

The system that you have attached in your question is an unstable system, and the terms steady state and transient do not apply to unstable systems. Execute the folowing matlab code to find the poles:

sys = tf([66 44],[1 -9 27 21]);
pole(sys)

Matlab gives:

ans =

   4.8171 + 3.1473i
   4.8171 - 3.1473i
-0.6342 + 0.0000i

Note that the first 2 poles are on the right hand side of the s plane. This indicates that the output blows up, and there is no transient or steady state.

NOTE: For a stable system, its easy to find the steady state and transient. The steady state value is the final value of the output after the output settles down. This can be easily found from the matlab plot by looking at what value the output settles down. Once you find this value, just subtract this value from the total output to get the transient response.

*****************************************************************
PS: Please do not forget the thumbs up!