Question

Puge 328 polf prt 33 Question 3 [20 Marks (a) K(s+4) $(s+1)(s+2) 5 KCGTA) Given the unity-feedback system of Figure 3.1 with G(s) = do the following: T9= Construct the Routh-Hurwitz table [2 Marks] Find the range of K that keeps the system stable i. (2 Marks] Find the Value of K that makes the system oscillate [2 Marks iv. find the frequency of oscillation when K is set to the value akes the (4 Marks system oscillate R(S) E(s) Cx) G(s Figure 3.1 (b) Find the value of K for the unity feedback system shown in Figure 3.1, where K(s+3) G(S) s+7) [10 Marks f the input is 10t u(t) and the desired steady-state error is 0.061 for this input

Answer 1

We are given G(s) = K(s + 4)/s(s + 1) (s + 2), H(s) = 1 for routh-Hurwitz table, the characteristic Equation is given as 1 + G(s) H(s) = 1 1 + K(s + 1)/s(s + 1) (s + 2) = 0 s(s + 1) (s + 2) + K(s + 4) = 0 s(s^2 + 3s + 2) + Ks + K_4 = 0 s^3 + 3s^2 + 2s + Ks + K_4 = 0 s^3 + 3s^2 + (2 + K)s + K_4 = 0 Routh-Hurwitz table for system to be stable, all terms in the first column must be positive. \r\n ie. 4k > 0 and 3(2 + K) - 4K/3 > 0 rightarrow K > 0 and 6 + 3K - 4K > 0 6 - K > 0 6 > K rightdoublearrow for 0 < K < 6, the system is stable for system to oscillate K = 6, the system will oscillate to find the freq