Question

11- The unity feedback system has an Ess 1/6000 for an input of 10tu(t). Given: k(s2 3s 30) s (s 5) Find k and n that satisfies the given specifications.

Answer 1

Given Transfer function: G(s) = k(s^3 + 3s + 30)/s^n(s + 5) Steady state error: E_ss = 1/6000: Input = 10 t - u(t) Ramp Input rightarrow Steady state error exists for ramp input only for constant 'Type - 1' system therefore: n = 1 rightarrow steady state error constant for unit ramp input K_v = 1/E_ss (velocity error constant) doublerightarrow therefore K_v for (0.t u(t)) = 10/E_ss = 10/1/6000 K_v doublerightarrow 60,000 therefore K_v doublerightarrow lt_s rightarrow 0 S.G(s) = 60,000 therefore lt_s rightarrow 0 middot s middot K(s^2 + 3s + 30)/s(s + 5) = 60,000 therefore k(0 + 0 + 30)/0 + 5 = 60,000 therefore 6k = 60,000 k = 10,000

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