Question

control systems/answer all parts please

owing reedback control syatems C(s) Go) (s-2)(s + 4) (s2 +12) where: ind: 1- Is the open loop system G(s) stable? why' 2- Find the range values for (x) such that the closed loop system is stable? 3. /Find the (K) value that yields to oscillation, what is the oscillation frequency

Answer 1

Open loop system is: G (s) = (s - 2) (s + 4)/s^2 + 12 stability is decides by pole location poles are at roots of denominator i . e s^2 + 12 = 0 s = plusminus squareroot 12 i = 3.46 i Thus when look system is marginally stable as, poles i .e at imaginary axis Thus close loop transfer function c (s)/R (s) = 3 k G (s)/1 + 3 k G (s) characteristics eqn is given as: 1 + 3 k G (s) = 0 1 + 3 k (s - 2) (s + 4)/s^2 + 12 = 0 s^2 + 12 + 3 k (s^2 + 2 s - 8) = 0 s^2