Question

[control engineering] The steady-state error, eₛₛ , of a closed loop system is given by

eₛₛ =lim s→0 to 1 s[1+G(s)]
For G(s)= s(s+2)/3(s+1)
​
, evaluate eₛₛ
.

Answer 1

The steady-state error (e₉ₛ) for the closed-loop system with transfer function G(s) = s(s+2)/3(s+1) is calculated using the limit s approaches 0 of 1/s[1 + G(s)], resulting in a steady-state error of 1/3.

Step-by-step explanation:

The student is asking how to calculate the steady-state error (ess) of a closed-loop system with a given transfer function G(s). To find ess, you need to use the formula ess = lim s→0 to 1/s[1 + G(s)]. Plugging in the provided transfer function G(s) = s(s+2)/3(s+1), we can simplify the expression for ess.

1. Calculate 1 + G(s): 1 + s(s+2)/3(s+1).
2. Find the limit as s approaches 0 of 1/s times the expression from step 1.
3. After simplification, the steady-state error becomes ess = 1/3 (since the limit as s approaches 0 for s(s+2)/3(s+1) simplifies to 2/3 and 1 + 2/3 = 5/3, then 1/s × 5/3 as s approaches 0 results in 1/3).

Therefore, the steady-state error for the given system is 1/3.