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# EEP301: AC and DC servo motor study

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Control Lab experiment EEP301, 5th sem electrical engineering @ IIT Delhi

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### EEP301: AC and DC servo motor study

1. 1. EEP301 LAB REPORT AC AND DC SERVOMOTOR STUDY Submitted by: Aastha Dua (2009EE ) Akshay Gupta (2009EE ) Indra Bhushan (2010EE50548) Kumar Saurav (2009EE ) Mehul Mittal (2010EE50553) Umang Gupta (2010EE50564) VIVEK MANGAL (2010EE50566)
2. 2. Experiment AC SERVOMOTOR STUDY Objective: To study the characteristics of small ac servomotor and determine its transfer function. Introduction: In A/C servo system Actual motor toque Tm(s)=K1Ec(s)-K2ω(s),Where Tl=constant load torque,ω is shaft speed ,Ec is voltage applied We in this experiment are going to verify motor characteristics. Observations and results: Steady State Operation : Determination of Generator constant: KG=load step-1 /motor speed INPUT STEP MOTOR SPEED NR, rpm LOAD STEP-1 (NO LOAD) Voltage GENERATOR CONTANT,Kg Volt/rpm 1. 1053 2.16 0.002051 2. 1676 3.44 0.002052 3. 1810 3.71 0.002049 Result: Average Generator Coefficient, KG=0.00205 Volts/rpm Determination of Motor Parameters: Input Load Step-1 Load Step-2 Load Step-3 Ec V E0 V Il A N rpm TL= (30.Eo.I L)/N.π Il A N rpm TL= (30.KG.Il)/π Il Amp N rpm TL 1 3.73 2.16 0 1053 0 0.04 576 0.000783 0.059 377 0.0011 2 7.41 3.44 0 1676 0 0.078 1141 0.00152 0.115 820 0.0022 3 10.9 3.71 0 1810 0 0.093 1382 0.00182 0.148 1072 0.0028
3. 3. Calculations KM=(Wss/Ec=N.π/30Ec) At Ec=3.73 Volts and E0=2.16V Km1=32.14 rad/volt-sec At Ec=7.41 V and E0=3.44 V Km2=23.68 5 rad/volt-sec At Ec=10.92 V and E0=3.71 V Km3=17.35 rad/volt-sec Result: On averaging Km=24.45 rad/volt-sec The Km obtained is different from each other due to the motor non linearity ωss1=KmEc-KnTL1 ωss2=KmEc-KnTL2 Kn=( ωss1- ωss2)/( TL2- TL1) Transient Operation : At E0=3.73 V Time constant, τm=105 ms Transfer Function=Km/s. (sτm+1) =17.35/s(0.105s+1) At E0=2.22V Time constant, τm1=212 ms τm2=210ms Transfer Function=Km/s.(sτm+1)=32.14/s(0.211s+1) At E0=3.48V Time constant , τm=145ms Transfer Function=Km/s.(sτm+1)=23.685/s(0.145s+1) Time Constants obtained above have error due to non-linear friction present.
4. 4. DC SERVOMOTOR STUDY Objective: To study the torque speed characteristics and determine transfer function of d.c motor. Observations and results: Motor and Generator Characteristics S.No. Ea,Volts Ia,amp N,rpm Eg,Volts 1 3.04 85 1250 2.32 2 3.51 83 1465 2.73 3 3.99 85 1682 3.14 4 5.02 89 2146 4.00 5 6.00 95 2574 4.80 6 7.03 99 3032 5.65 7 8.00 104 3466 6.46 8 8.98 109 3890 7.25 9 10.01 115 4315 8.04 10 11.01 120 4720 8.79
5. 5. KM=(4720-1250)/(11.01-3.04)=435.38
6. 6. KG=(8.79-2.32)/(4720-1250)=0.00186 volt/rpm
7. 7. Ea=6V, Ra=4.42Ω TORQUE SPEED CHARACTERISTICS: S.No. Load Step Ia,mA N,rpm ω=Nπ/30 Eb=Ea- IaRa Volt Kb=Eb/ω TM=KbIa Newton.m 1 0 94 2578 269.96 5.584 0.0207 0.001946 2 1 129 2503 262.11 5.43 0.0207 0.00267 3 2 155 2433 254.78 5.315 0.0208 0.00324 4 3 183 2367 247.87 5.19 0.0209 0.003843 5 4 213 2300 240.85 5.058 0.0210 0.00473 6 5 248 2275 238.23 4.90 0.0206 0.00508
8. 8. B=98.7*10-6 newton.meter.sec/rad STEP RESPONSE STUDY: S.No. Ea,Volts EG,Volts N,rpm Es=0.632Eg Time contant,τm Gain constant,Km 1 6 4.83 2591 3.04 92 45.22 Average Kb= 20.78 *10-3 volts rad/sec Thus, J=τm(B+Kb 2 /Ra)=18.07*10-6 N.m/radsec2 Motor transfer function G(s)=Km/sτm+1=45.22/(0.092s+1)
9. 9. Ea=8V ,Ra=4.42Ω TORQUE SPEED CHARACTERISTICS: S.No. Load Step Ia,mA N,rpm ω=Nπ/30 Eb=Ea- IaRa Volt Kb=Eb/ω TM=KbIa Newton.m 1 0 106 3460 362.33 7.53 0.0207 0.00219 2 1 146 3359 351.75 7.355 0.0209 0.00305 3 2 184 3260 341.4 7.187 0.0210 0.003864 4 3 221 3167 331.65 7.023 0.0212 0.00468 5 4 258 3071 321.59 6.86 0.0213 0.0055 6 5 301 2960 309.97 6.67 0.0215 0.00647
10. 10. B=81.7*10-6 NEWTON.METER.SEC/RAD STEP RESPONSE STUDY: S.No. Ea,Volts EG,Volts N,rpm Es=0.632Eg Time contant,τm Gain constant,Km 2 8 6.43 3464 4.05 93 45.34 Average Kb= 21.1 *10-3 volts rad/sec Thus J=τm(B+Kb 2 /Ra)=16.9*10-6 N.m/radsec2 Motor transfer function G(s)=Km/sτm+1=45.34/(0.093s+1)
11. 11. At Ea=10V, Ra=4.42Ω TORQUE SPEED CHARACTERISTICS: S.No. Load Step Ia,mA N,rpm ω=Nπ/30 Eb=Ea- IaRa Volt Kb=Eb/ω TM=KbIa Newton.m 1 0 113 4325 452.9 9.5 0.0210 0.00237 2 1 163 4195 439.3 9.28 0.0211 0.00344 3 2 212 4074 426.63 9.063 0.0212 0.00449 4 3 257 3965 415.21 8.86 0.0213 0.00547 5 4 302 3857 403.9 8.66 0.0214 0.00646 6 5 354 3739 391.55 8.44 0.0215 0.007611
12. 12. B=85.4*10-6 NEWTON.METER.SEC/RAD STEP RESPONSE STUDY: S.No. Ea,Volts EG,Volts N,rpm Es=0.632Eg Time contant,τm Gain constant,Km 3 10 8.02 4319 5.05 93 45.22 Average Kb= 21.25 *10-3 volts rad/sec Thus J=τm(B+Kb 2 /Ra)=17.44*10-6 N.m/radsec2 Motor transfer function G(s)=Km/sτm+1=45.22/(0.093s+1)
13. 13. At Ea=11.5V ,Ra=4.42Ω TORQUE SPEED CHARACTERISTICS: S.No. Load Step Ia,mA N,rpm ω=Nπ/30 Eb=Ea- IaRa Volt Kb=Eb/ω TM=KbIa Newton.m 1 0 129 4902 513.34 10.92 0.0212 0.002735 2 1 183 4747 497.1 10.69 0.0215 0.00393 3 2 236 4611 482.86 10.457 0.0216 0.0051 4 3 284 4484 469.56 10.245 0.0218 0.00619 5 4 332 4371 457.73 10.03 0.0219 0.00727 6 5 387 4240 444.01 9.789 0.0220 0.00853
14. 14. B=83.5*10-6 NEWTON.METER.SEC/RAD STEP RESPONSE STUDY: S.No. Ea,Volts EG,Volts N,rpm Es=0.632Eg Time contant,τm Gain constant,Km 4 11.5 9.1 4900 5.733 94 44.62 Average Kb= 21.7 *10-3 volts rad/sec Thus J=τm(B+Kb 2 /Ra)=17.86*10-6 N.m/radsec2 Motor transfer function G(s)=Km/sτm+1=44.62/(0.094s+1) Additional Experiments: At Ea=8V and Eg=6.43V we record time for voltage to rise to 10-100% of Eg. voltage level (V) time (ms) 1.286 38 1.929 47 2.572 58 3.215 71 3.858 87 4.501 106 5.144 136 5.787 186
15. 15. This is the graph for the variation in voltage with time. Note the exponential nature of the plot.