1. Rules: DO NOT DISCUSS THIS EXAM WITH ANYONE UNTIL RECEIVING Canvas Announcement!! 2. Open book, open notes, etc. 3. Calculators Needed and Allowed. 4. Exam is given under the College of Engineering Honor Code principles and practices. 5. No communications of any kind are allowed. Use of cell phones, cameras, personal data assistants, or any other electronic communication devices, will be treated as an Honor Code violation. 6. Show your work and briefly explain major steps to maximize partial credit. NO CREDIT WILL BE GIVEN IF NO WORK IS SHOWN. This Exam Contains 4 problems over 16 pages (including ample workspace). Sign the College of Engineering Honor Code Below. (NO credit will be given for an exam without a signed pledge): I have neither given nor received aid on this examination. Signed: 1 Surface Mount Permanent Magnet Machines The following control algorithm for a surface-mount permanent magnet machine should be used in Problems 1 and 2. The synchronous current regulator uses Proportional-Integral (PI) feedback control with EMF feedback compensation. Assume that it has been appropriately designed and works well. Duty cycles are calculated using Space Vector Modulation. ωρ Field Weak. i Synch. 1 3NP Apm 4 Inverse vd. da Duty Curr. Clarke id in Park Reg. vr 9- ia Park Trans-Vq. form Cycle db Calc. de Trans- iq Trans-i ib form form 22 2 Wre Are Apm Or 2 The machine is a three-phase surface mount permanent magnet machine with the following equivalent two-phase parameters: Poles (NP): Phase Resistance (R): 4 18m9 2mH Phase Inductance (L): Permanent Magnet Flux Linkage (APM) 0.4V-sec The inverter that drives the machine has a bus voltage of 250V, a peak line current rating of 3004, and a switching frequency of 15kHz. 2 Problem 1 (35 Points) The machine and drive have been operating for some time at a constant torque and speed of 2-100 rad/sec. At a specific instant of time, the rotor position is measured to be 0-30°, and the duty cycles are da=0.1152, d₁=0.6943, and de=0.8848. Determine (i) the three-phase currents ia, ib, and ic, (ii) the electromagnetic torque T3ph, (iii) the electrical power Pelec, (iv) the mechanical power Pmech, and (v) the efficiency η of the machine (5 pts apiece). 3 Workspace for Problem 1 4 Extra workspace for Problem 1 15

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1. Rules: DO NOT DISCUSS THIS EXAM WITH ANYONE UNTIL RECEIVING Canvas Announcement!! 2. Open book, open notes, etc. 3. Calculators Needed and Allowed. 4. Exam is given under the College of Engineering Honor Code principles and practices. 5. No communications of any kind are allowed. Use of cell phones, cameras, person