Question

neatly, correctly, and fast please! Don't forget the 4H. i am not sure what H is, but I think it is a number bigger than 1.

Problem 5. (8+2)(S-a)2 Given: (0S Y (s) X(s) 2 l s-4) Figure 1 a) Find the transfer function of the system (Figure 1). b) Is the system stable? If not, what would it take to stabilize it? (E (ed c) For transfer function T)1/(s1 +5 145 + 4) ,ldentify the pole(s) which might cause system instability. Where are the locations of those poles and what are their frequency? In ol as bsitibom

Answer 1

y (s)/x (s) = 4H/1 + 4H/s^2 - 4 = 4H (s^2 - 4)/s^2 - 4 + 4H For system to be stable Poles must lie in LHP so, s^2 - 4 + 4H = 0 rightarrow s^2 = 4 - 4H s = squareroot 4 - 4H For stability 4 - 4H < 0 rightarrow 4H > 4 rightarrow H > 1 H must be greater than 1 char eq^n = s^4 + s^3 + 5s^2 + 4s + 4 so, s^4 + s^3 + 5s^2 + 4s + 4 = 0 Solving the we get poles at s_1 s_2 = plusminus 2j s_3, s_4 = -0.5 plusminus 0.86603 j Lies on imaginary so, s_1, s_2 axis so this makes the system marginal stable Frequency s = plusminus 2j w_1 = 2, w_2 = -2