Whаt mоtiоn cаuses the clоse-pаcked position of the sacroiliac joint
Prоblem 1. (24 pts) Given а 3-phаse, 6-pоle inductiоn mаchine. The parameters are rs=0Ω, rr'=1Ω, Llr'=Lls=0 mH, Lm=5 H, ωe=100 rad/s. {"version":"1.1","math":"rs=0Ω, rr'=1Ω, Llr'=Lls=0 mH, Lm=5 H, ωe=100 rad/s. "} The torque/speed curve at a rated voltage of 480 V is shown below. The peak torque occurs at a rotor speed that is 90% of synchronous speed. Fill in the table below (state any approximations made to simplify your effort). Operation Point I~as{"version":"1.1","math":"I~as"} I~ar'{"version":"1.1","math":"I~ar'"} Frequency of rotor currents (physical currents) Frequency of transformed rotor currents if ω{"version":"1.1","math":"ω"} = 10 rad/s A B C Problem 2. (23 pts) Given the 3-phase inverter below. It is operating under sine-triangle modulation. Vdc = 200 V. The switching frequency is much greater than the desired fundamental ac frequency. THE LOAD IS PURELY RESISTIVE with a value of 1 Ω{"version":"1.1","math":"Ω"} (the inductance shown has a value of 0 H). a. If you desire vas=100sin(100t+π4){"version":"1.1","math":"vas=100sin(100t+π4)"} (phase b and c have equal amplitude and are displaced by 120°{"version":"1.1","math":"120°"}). Determine the phase-a duty cycle you would use. (6 pts) b. If at a given instant of time, da = -0.5, db = 0.9, dc = -0.4, and the value of the triangle wave is 0.8, determine the value of ias, ibs, ics, and idc at that instant. (12 pts) c. If the amplitude of your duty cycle waveform in a) is increased to d = 20, express the fast average of vas. (5 pts) Problem 3. (16 pts) A 2-pole, 3-phase wound rotor synchronous machine is operating at rated voltage vas=21000cos(100t){"version":"1.1","math":"vas=21000cos(100t)"}. Ld=Lq=10.0 mH. Lmd=Lmq=9.0 mH{"version":"1.1","math":"Ld=Lq=10.0 mH. Lmd=Lmq=9.0 mH"}. The machine always delivers real power of 3 MW. If the rated stator current is Isr=20002A{"version":"1.1","math":"Isr=20002A"} : a. Determine the maximum value of field current that will be needed for this machine and the value of the reactive power delivered when this field current is applied. (10 pts) b. For the condition in a), determine the value of delta. (6 pts) Note for these problems, simplify to the extent possible, don’t worry about establishing a final numerical value. Problem 4. (14 pts) For the machine shown below: a. Express Lasas{"version":"1.1","math":"Lasas"} and Lasfd{"version":"1.1","math":"Lasfd"}. For Lasas{"version":"1.1","math":"Lasas"}, express in a form using Lls, LA, LB, {"version":"1.1","math":"Lls, LA, LB, "}and θr{"version":"1.1","math":"θr"} as we had done in class. For Lasfd{"version":"1.1","math":"Lasfd"}, express in terms of Lsfd{"version":"1.1","math":"Lsfd"} and θr. (6 pts) b. If the rotor speed is held fixed at 100 rad/s with the field and b- and c-phase windings open-circuited and the phase-a current held constant at 1 A, express Vfd{"version":"1.1","math":"Vfd"} and Vas{"version":"1.1","math":"Vas"}. Assume Lls=0.1 H, LA=1 H, LB=0.4H, Lsfd=1 H{"version":"1.1","math":"Lls=0.1 H, LA=1 H, LB=0.4H, Lsfd=1 H"}. (8 pts) Problem 5. (18 pts) A system is described by the following voltage versus current and flux linkage relationships: v1=i1+pλ1v2=i2+pλ2λ1=0.5i1+1x(i1+i2)1/2λ2=0.5i2+1x(i1+i2)1/2i1, i2>0{"version":"1.1","math":"v1=i1+pλ1v2=i2+pλ2λ1=0.5i1+1x(i1+i2)1/2λ2=0.5i2+1x(i1+i2)1/2i1, i2>0"} a. Express fe(i1, i2, x){"version":"1.1","math":"fe(i1, i2, x)"}. (10 pts) b. If I1=1 A, I2=0 A, {"version":"1.1","math":"I1=1 A, I2=0 A, "}and x = 0.01 m, establish Wf{"version":"1.1","math":"Wf"}. (8 pts) Problem 6. (22 pts) Given a system expressed in a form: vabcs=p100010001iabcs+50sin(10t)50sin(10t-120°)50sin(10t+120°){"version":"1.1","math":"vabcs=p100010001iabcs+50sin(10t)50sin(10t-120°)50sin(10t+120°)"} a. Transform the system model into the arbitrary reference frame. Show all steps. (12 pts) b. If Vabcs=100sin(10t)100sin(10t-120°)100sin(10t+120°){"version":"1.1","math":"Vabcs=100sin(10t)100sin(10t-120°)100sin(10t+120°)"}, determine Iqse{"version":"1.1","math":"Iqse"} and Iqss{"version":"1.1","math":"Iqss"}. (10 pts) Problem 7. (20 pts) A 4-pole, 3-phase permanent magnet synchronous machine with a 1 Ω{"version":"1.1","math":"Ω"} stator resistance has the following current versus flux linkage relationship in the rotor frame of reference: λqsr=0.01iqsrλdsr=0.01idsr+0.1{"version":"1.1","math":"λqsr=0.01iqsrλdsr=0.01idsr+0.1"} The machine is operating at rated torque and speed with Te=30 Nm, Tl=0.1ωr{"version":"1.1","math":"Te=30 Nm, Tl=0.1ωr"}. a. Assume the machine is sourced by an inverter operating under sine-triangle modulation with d = 1. Determine the value of Vdc if a ϕv=0{"version":"1.1","math":"ϕv=0"} control is used and there can be no low frequency harmonics. (10 pts) b. If ϕi=0{"version":"1.1","math":"ϕi=0"}, and hysteresis current control is used to regulate current, determine Ias{"version":"1.1","math":"Ias"} and the minimum Vdc needed to ensure the current can be regulated. (10 pts) Congratulations, you are almost done with this exam. DO NOT end the Honorlock session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). 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Belоw is а definitiоn оf а polymorphic function аnd a class. What will be the outcome of the following code? class Audio(object): def audio_sound(self): print('Boo Boo!') def makeSound(animalType): animalType.sound() #function call a = Audio() makeSound(a) #outcome of this line