Question

Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable parameter pl(s) Dal(sKp+ g) Assuming W-0, find the transfer function Y(s)/R(s) h) Assuming R-0, find the transfer function Y(s)/W(s) i) What is the type of the system (with respect to steady-state error)? j) What is the steady-state error when rt)u(t) (unit-step) and w(t)-0 k) What is the s.s. error when r(t) t u(t) and w(t)-0 ) Assume r(t)-0, what is the response of the system to w(t) ut) (unit-step)? What is the steady- state response to the disturbance? m) Determine the range of constants Kp and Ki such that the rise-time of the closed-loop system is equal (or less than) 0.18 s and so that the damping factor ξ is equal to (or greater than) 0.8. Use the textbook approximation for the rise-time. For the values of constants Kp and Ki that correspond to the borderline cases of rise-time and damping-factor in problem 2m), determine the settling time of the closed-loop system to within 1% of the final value n)

Answer 1

R f CI ssu PI RU

pi) 2 2S

the of kmwih pet to Y (S) (5 2 冫。

(oiTP) K (r) So 闪 dn