Question

The model of a position control system using a DC motor is shown below. Find the K1 and K2 values so that the system will have a peak time of 0.4 s and 5% overshoot. R(S) K $(s + 1) Y(s) 1+K28

Answer 1

the The model of a position control system using a 0.6 motor is shown below. Find the ki and Ka values so that system will have a peak time of 0.4 see and 5%. Over shoot. RIS KI SIS+) >Y(S) 1+k₂S Solution- As per question, peak time (Tp) = 0.4 sec Peak overshoot (mp) = 5% =0.05 ki G(s) sist) H(s) = 1+k2s we know that, -n& X100 Mp = (edi-qz -n & e re-p2 0.05 = n → In (0.05) - T& ſi-qz > + 2.9957 = ti & 1-82 (2.9957) [1-42 = 18

गांव V A n n Squaring on both side then weget, ((2.4957) J-$2) (2.9957)*(1-3) = 1 8.9744 (1-3) = (3-141652 8.9744 -8.97448 = 9.869682 8.9744 - 9.869682 +8.970482 8.9744 = 18.844ę? 18-844$= - 8.9744 U V W 2 re 8.97 44 18.844 > & -0.47624 0.47624 re E = 0.6901 we also know that, ㅠ Peal time : (Tp) = wd (Tp) = conseq? 3.1416 0.4 = wn Ji-(0.690172

Of X on Ji-(0.6901)2 = 3.1416 3.1416 wun 2 0.4 JT-(0.6901) wn = 10.85 rad/see so, C($ 2. Y(S) RCS) 1 +61)H(s) Scsti) y(s) R(S) It Ki (1+Kys) sisti) KI Yls) R(S) SCS+) S(+1)+KI (it K25) SCS+) Y) s²stk, tk, K2S RO y(s) = 5² + K, KS+stki RCS) KI Y() R(5) $+(ki*2+1)s+ki

Standard second order tromsfer formation Y($) RCS2 02² st gewenst won Comparing then weget, ki = wg² 2 K, -(10.85) ki -117.77 Approximate. And, 2&wn Kikatt IN 2 x (0.6901) (10.85) = 117.77 K2+ 14.97517 = 117.77K2+ → 117.77K2+1 = 14.97517 > 117.77K2 -14.97517-1 = 117.77K2 = 13.97517 k = 13.97517 N 117.77 K₂ = 0.1186649 → Approximate