# calculation for the response of fourth order transfer function from step input

I need some help to verify my calculation. Following is the transfer function of a control circuit $$H(s)=\dfrac{1+0.145s+0.0019s^2}{1+\dfrac{0.8}{150 }s+\dfrac{1}{150²}s²}×\dfrac{1}{1+0.0012s}×\dfrac{1}{1+0.008s}$$

I simulated the above by plotting its step response the settling time I found is 79ms, this is a fourth order system, do I need to handle it differently? Is this the time when the output of the filter will become equal to the step input magnitude?

I believe settling time is not really easy to define. Mathematically speaking, the settling time is infinite, because the filter tends asymptotically to its steady state value. In terms of engineering, it's usually the time needed for the filter to be in a certain margin from the steady state. Commonly 2% to 5% according to a source in Wiki, but it's very arbitrary.

A common rule-of-thumb to estimate it is to take 4 to 8 times of the dominant time constant of the system as the settling time, being the time constant defined exactly on the time taken to reach steady-state value (1 time constant is about 63%). But this is less intuitive with higher-than-2nd-order systems.

An even more common rule-of-work is to look at the response and just decide for yourself (as arbitrarily as you like as the definition is loose) when you're there. 