How Do You Calculate Settling Time for a Control System?

[chagocal]

1.
a)find time constant of the closed loop system.(take R(s)=1/s and D(s))
G(s)=k/(s+10),k=20

b) find the settling time(within 2% of the final value when R(s)=1/s and D(s)=1/s

solution for part 1a
H(s)=Y(s)/R(s)=G(s)/s/1+G(s)(1/s)/s= (k/s+10)/s/((1+(k/s+10)(1/s)/s)
constant time should equal to 1/30 sec

stuck on 1b need help

 

[Redbelly98]

Welcome to PF.

It has been a long time since I worked with Laplace transforms, but does the signal behave as a straightforward exponential decay towards the final value? If so, simply solve for when the exponential is 2%, using the time constant you have.

 

[CEL]

1.
a)find time constant of the closed loop system.(take R(s)=1/s and D(s))
G(s)=k/(s+10),k=20




b) find the settling time(within 2% of the final value when R(s)=1/s and D(s)=1/s

solution for part 1a
H(s)=Y(s)/R(s)=G(s)/s/1+G(s)(1/s)/s= (k/s+10)/s/((1+(k/s+10)(1/s)/s)
constant time should equal to 1/30 sec

stuck on 1b need help

Find the dominant poles of your TF. They should be of the form $$-\sigma\pm j\omega$$. The settling time is $$\frac{4}{\sigma}$$