Question

B. Controller Design Consider the positional robotic system and its BD. Assume: H-1 and G,-3/(s+4). B.1 Design a steady state error es10 % due to a unit step input. Initials: PD-type controller to ensure a time constant of 0.25 sec., and Controller Plant R G, G. H Sensor to ensure -0.5 and o,-10 rad/s. B2. Design a Pl-type controller B3. Design a PID-type controller to ensure co,-5 rad/s, E-0.5 and e2 % due to a unit ramp input.

B2 and B3

Answer 1

Phent Controllex C. Sensoy Sensor, H StH PI type Conter G = Ks+K clased foop tranfer funèbion = Hdyy 3(K, *Kp) sfS)H(kpSt513 (nts)s Kps +K) (n+s)s 30st Ks) Chacbistc etion Denoninbr finc ton closed hof Trfr

Chaactiste eion s(413K,st3K Standard Characteriste egrution 3KTn 7 2un-4+3Kp o o lo adsec Since e05 lo-4=3,k 2x05 xlo-443K 2 3Kr 3Kr Kp- 33.3 K 3 9s+33.3 PI type cantler ap to G05,wlo ensure K4SKS+Kr PID type conbeller h B3 3kkstk) Clsed op Ts fer fometion aphe Hyy 1+ 3(as) (n+s)s (nts)s

3(KsK) 30 +) s(4)+ 3Ck kss) 3(KsKst) +3K) $4413K, S3K t3K) +3KA sf43 \+3Kr N+3Ka} l+3K\ Characteresibe eaton = s+2wntw, S w3K 443 k +3KA Steady state error, ess= % 0,02 Ro1-Unt ramp 0 02 RS) est SO 0 02 S>0 t 3CKs4Ks) -0 02= K 3x0.02 3KT 3k 'I

Kェミ 6667 wn5 radsec 3Kz Wn 1+3K 25(+3 K)00 3x 66.67 o O 3 KA 2133 2.33 Ka= 子 2 awn 4+3Ke +3KA 05 5= 4+3K 205x5=4+3K +x23) Kp 36- 12 3 40 4+3kp 335+12s+666子 Repirel fID Conbeller b enve e 05, n5d/sec
Feel free to ask if you have any query.Thank you.