Question

control system

Question No.4 Derive the value of k , a and b by designing the steady state error for a ramp input u) equals 0.1 and the poles of the system are located at-2 3j : (CS-PLO3) state error for a ramp input u(1) Y(s) U(s) G(s) (s+a) Where, G(s) s(s+b)

Answer 1

Given where G(s) = (s + a)/s (s + b) (1) given steady state error of a ramp Input v(t) equals to 0.1 and the poles of the system are located at -2 plusminus 3j For ramp Input r(t) = A t prime u(t) Input = 1 when type = Input = > E_ss = constant type > Input = > E_ss = 0 type < Input = > E_ss = infinity E_ss = A/k_v = 0.1 k_v - velocity constant = lt_s rightarrow 0 s G(s) lt_s rightarrow 0 s [s + 1/s (s + b)] = a/b k_v = a/b given amplitude of ramp Input A = 1 E_ss = 1/k_v = 0.1 k_v = 1/0.1 = 10 Therefore k_v = 10 a/b = 10 = > a = 10 b \r\n poles are complex conjugate -2 + 3j, -2 - 3j [s - (-2 + 3j)] [s - (-2 - 3j)] G(s) = s + a/[(s + 2) - 3j] [(s + 2) + 3j)]
$a=10$