Hello,

For a LTI first order system, the transfer function is H(s)= 1/(s+a).
Determine wither the system response time will increase or decrease, when the pole is moved further away from the origin.

Attempt:
the constant a is the inverse of the settling time. so as a is increased, the system respond quicker.
The pole of the system is jw= - a. Therefore as a is increased, the pole is moved away from the origin (assuming is +ve), and the system respond quicker.


Is my answer correct ?


Thanks,

 

The distance alone cannot tell us about the system responce. If the pole is a=r+jw the response time is dependant on r alone. The more negative r is the faster the system is. But if r is positive then the system is driven in instability and will never settle.