Question

Kc = (s + zc) / (s + pc)

g(s) = (0.4s + 0.8)(s + 14) / (s + pc)

Where OS = 4.33, Ts = 0.5, and the compensator zero is on the s-plane at -12.

(i) For the system in aboove with the designed compensator pole and zero (pc and zc) and Ke, determine the steady-state error ess due to the unit step input.

Answer 1

To determine the steady-state error ess due to a unit step input, calculate the closed-loop transfer function and use the final value theorem.

Step-by-step explanation:

In order to determine the steady-state error ess due to a unit step input for the given system, we need to calculate the closed-loop transfer function (T(s)) and then find the value of ess using the final value theorem.

First, let's calculate the closed-loop transfer function using the given equations:

T(s) = kc * g(s) = [(s + zc) / (s + pc)] * [(0.4s + 0.8)(s + 14) / (s + pc)]

Once we have the closed-loop transfer function T(s), we can then find the steady-state error ess using the final value theorem:

ess = lim(s→0) s * T(s) = lim(s→0) s * [(s + zc) / (s + pc)] * [(0.4s + 0.8)(s + 14) / (s + pc)]