Question

Figure below shows a general second order feedback control system. Use your own wording, by
employing any method (mathematically/description) you know, explain clearly that why increasing
the gain K of the P-action contrller, increase system response oscillations. ( ?? is system natural frequency and ? is damping ratio)

+ K G(s) = - g s(s + 25g) R(S) Input E(s) Error He C(s) Output

Answer 1

2 ധ് RE K () ES |S(3+28 wn) The closed loob. transfer function, C() Kwo? RS) s(s+26Wn)+kwons 2 kwa (18) R (6) s²+28 wast kws without Let's take a closed loop controller P-Combolles R(S) S (5+28W 2 wo R(S) s²+2qWns two CoG So, o = with controller is $2+28 Wns + k.ws and Cot without controller is s²+28wnst wi with 2 cscanned with CamScanner

with het wall = matrural free of system con boller So from egr 0 2 Wong - kwa 22 |wn = Sk. wn 3 Let Who Why = natural freg. of system without conboller. So, foroon eya who = with 9 ปาก = Wh WP can see that So, from ③ and 4 wn Jk whe If K increases Wni natural freg. with controller increases a the will increase So, Increasing CScannet hos en Camsegnet gain LK) response oscillations Issystem