Question

Problem #2 Given the system below: C(s) R(s) s2 (s1) s2 (s +3) (a) Determine the system type. (b) Calculate the steady-state error for an input of 5u(t). [0] (c) Calculate the steady-state error for an input of 5tu(t). [15] (d) Discuss the validity of your answers to part (b) and (c). HINT: Is the system stable?

Answer 1

G_1(s) = 1/s^2 (s + 1)/ 1 + 1/s 1/s^2(s + 1) = 1/s^2 (s + 1)/s^3 (s + 1) + 1/s^3 (s + 1) = 1/s^2 (s + 1) times s^3 (s + 1)/s^3 (s + 1) + 1 G_1(s) = s/s^3(s + 1) + 1 implies G(s) = G_1(s) 1/s^2 (s + 3) = s/s^3(s + 1) + 1 = s/s^3 (s + 1) + 1 1/s^2 (s + 3) = 1/[s^3 (s + 1) + 1] [s^2 + 3s] = 1/(s^4 + s^3 + 1) (s^2 + 3 s) implies G(s) = 1/s^6 = 4 s^5 + 3 s^4 + s^2 3 s implies G(s) = 1/s(s^5 + 4 s^4 + 3 s^3 + s + 3) system type it is the no of open loop poles at origin in the open loop transfer function i e G(s) Here type 1 system steady state errors are valid for only unity feedback E(s) = R(s) - c(s) & E(s)/R(s) = 1/1 + G(s) implies E(s) = R(s)/1 + G(s) steady state error implies e_ss = lt_s rightarrow 0 s E(s) = lt_s rightarrow 0 s R(s)/1 + G(s) given