A Modified Sychronous Current Regulator for Brushless Motor Control

A Modified Sychronous Current Regulator for Brushless Motor Control Shane Colton <scolton@mit.edu> Graduate Student, Department of Mechanical Engineering Massachusetts Institute of Technology Rev0 - Doctoral Qualifying Examination, January 26, 20

Overview This work details a torque controller for brushless Permanent Magnet Synchronous Motors (PMSM). Methods of controlling PMSM: Brushless DC Control Field-Oriented Control (FOC): Synchronous Current Regulator (SCR) The author s contribution is a modified SCR that: uses Hall effect sensors (instead of an encoder). is more computational efficient (low-cost processing). has the potential for improved transient response. The design of the controller and an experimental application to low-cost personal transportation will be detailed. 2

Outline Theoretical Analysis Permanent Manget Synchronous Motor Model Field Oriented Control Principles Synchronous Current Regulator (SCR) Modified Synchronous Current Regulator (mscr) Applied Analysis Plant Information Controller Hardware Controller Design Controller Simulations: SCR and mscr Experimental Testing and Data Future Work Questions / Feedback Motor Control Overview Current Sensing Simplified Plant Closed-Loop Transfer Function and Root-Locus A more fair transient response comparison. High-Speed Operation Error Handling and Failsafes Connection to Adaptive Feed-Forward Cancellation (AFC) 3

PMSM Model Three-phase permanent magnet synchronous motor (PMSM) electromechanical model: PMSM ~ I a L R ~ V a ~ I b L R E a ~ V b ~ I c L R E b ~ τ, Ω V c E c Power Conversion: I a E a I b E b I c E c 4

PMSM Model To control torque, both the phase and the magnitude of current must be controlled. One option: high-bandwidth current controllers on each phase of the brushless motor. The closed-loop bandwidth must be significantly faster than the commutation of the motor (the AC frequency): AC References: I xr I x { a, b, c} sin( t ), x I ar I br + - + - G c (s) G c (s) V a V b Z ( s) Z ( s) I a I b I cr + - G c (s) V c Z ( s) I c 5

Field-Oriented Control Principles By exploiting symmetry of the three-phase variables and transforming to the reference frame of the rotor, the controller can act on quantities which are DC in steady-state operation. (Similar to adaptive feed-forward cancellation with sinusoidal input.) Field-Oriented Current control works without the need for high-bandwidth control loops. Easier to implement on fixed-point, lowcost microcontrollers. Better high-speed performance. 6

Field-Oriented Control Principles Vector Motor Quantities, D/Q Axes Controller operates in a two-dimensional coordinate system that is attached to the rotor: rotor/synchronous reference frame. A Q Direct (D) Axis: Aligned with a North magnet pole. Quadrature (Q) Axis: Exactly between two magnet poles. In a two-pole motor, they are physically perpendicular. C D B South-Face Magnet North-Face Magnet Steel Copper Winding 7

Field-Oriented Control Principles Vector Motor Quantities, D/Q Axes Controller operates in a two-dimensional coordinate system that is attached to the rotor: rotor reference frame. Direct (D) Axis: Aligned with a North magnet pole. A Quadrature (Q) Axis: Exactly between two magnet poles. Ω Q D The axes are attached to the rotor. Q always leads D in the direction of rotation. C B South-Face Magnet North-Face Magnet Steel Copper Winding 8

Field-Oriented Control Principles Vector Motor Quantities, D/Q Axes Controller operates in a two-dimensional coordinate system that is attached to the rotor: rotor reference frame. A Q Direct (D) Axis: Aligned with a North magnet pole. Quadrature (Q) Axis: Exactly between two magnet poles. In a four-pole motor, they are separated by 45º mechanical. They are always separated by 90º electrical. C D B South-Face Magnet North-Face Magnet Steel Copper Winding 9

Field-Oriented Control Principles Vector Motor Quantities, D/Q Axes All motor quantities that have direction can be projected onto the d/q axes as vectors: Back EMF: Always on the q- axis. d E E dt Ω Q I A Stator Current / Flux: Vector sum of coil current/flux defined by right hand rule. D λ Rotor Flux Linkage: Always on the d-axis for a permanent magnet motor. N C I E B South-Face Magnet North-Face Magnet Steel Copper Winding 0

Field-Oriented Control Principles Unrealistic Zero-Inductance Motor IR E Q V I λ r D Voltage applied in-phase with back-emf. Current also in-phase with back-emf. Torque per amp is optimal. Reasonable approximation if inductance or speed is low: I L R R ~ V E ~

Field-Oriented Control Principles Motor with Inductance Q Voltage applied in-phase with back-emf. V E IR IωL I Current lags due to the motor inductance. Torque per amp is no longer optimal. Current and back EMF are not in phase: λ r D I E 0 I R L ~ V E ~ 2

Field-Oriented Control Principles Phase Advance to Correct for Inductance Lag IωL V E ϕ Q IR I Voltage applied ahead of back EMF. Current lags due to the motor inductance such that it is in phase with back EMF. Torque per amp is optimal. f ( V, I,, K, R, L,...) t λ r D I R L ~ V E ~ 3

Field-Oriented Control Principles Field Weakening for High-Speed Operation Q Voltage and current both lead back EMF. Stator flux counteracts rotor flux: field weakening V IωL I IR E Torque per amp is not optimal but Maximum achievable speed per volt is higher. λ r D I R L ~ V E ~ 4

5 Field-Oriented Control Principles Park Transform / Inverse Park Transform 2 2 2 3 2 3 2 3 2 3 2 sin sin sin cos cos cos 3 2 T sin cos sin cos sin cos 3 2 3 2 3 2 3 2 T c b a q d x x x T x x x 0 0 x x x T x x x q d c b a Tranforms used to convert from/to stator frame {a,b,c} quantities to/from rotor frame {d,q} quantities. Require rotor position, θ, as an input.

Synchronous Current Regulator θ 0 or I dr I qr + - + - d-axis controller q-axis controller V d V q dq abc Inverse Park Transform PWM a PWM b PWM c M Encoder Park Transform I a I b I d dq I q abc I c = -I a -I b - - θ Park and inverse Park transform convert into and out of rotor reference frame. Two independent controllers for the d- and q-axis. Requires rotor position, typically from an encoder or resolver. 6

Synchronous Current Regulator θ 0 or I dr I qr + - + - d-axis controller q-axis controller V d V q dq abc Inverse Park Transform PWM a PWM b PWM c M Encoder I d s Park Transform dq I a I b I q s abc I c = -I a -I b - - θ Current Filters Because the controllers run in the rotor frame, where values are DC in steady state, the controllers may operate at low bandwidth, below commutation frequency, and long time-constant current filtering can be implemented. 7

Modified Synchronous Current Regulator Initial Motivation For sufficient resolution of rotor position, an encoder or resolver is typically required for field oriented control. (Sensorless techniques also exist.) However, less expensive motors use three Hall effect sensors to derive rotor position with 60º electrical resolution: A A B C C Q A time C B D B Hall Effect Sensor South-Face Magnet North-Face Magnet Steel Copper Winding 8

Modified Synchronous Current Regulator Initial Motivation In sensored brushless DC control, the six Hall effect sensor states directly map to phase voltage outputs. State V a V b V c A B C 2 3 PWM High-Z 0V 0V 0V High-Z High-Z PWM PWM 2 3 4 5 6 4 5 0V High-Z PWM PWM High-Z 0V 6 PWM High-Z 0V Pros: very simple algorithm (state table), can run on low-cost processor. Cons: fixed timing, torque ripple, audible noise Initial Motivation: Can the Synchronous Current Regulator be modified to work with Hall effect sensor inputs, with interpolation? 9

Modified Synchronous Current Regulator Slow Loop (00-,000Hz) Fast Loop (0kHz) Hall Effect Interpolator 3 0 or I dr I + qr - - + d-axis controller q-axis controller ϕ V Sine Wave Generator PWM a PWM b PWM c Synchronous Measurement Hall Effect Sensors M I d s Park Transform dq I a I b I q s abc I c = -I a -I b - - 20

Modified Synchronous Current Regulator There are several practical differences: The controller is explicity split into fast and slow loops; only PWM generation and rotor position estimatation need be in the fast loop. PWM generation is done by a sine table look-up, which is faster to compute than an inverse Park transform. The rotor position is estimated by interpolating between Hall effect sensor absolute states using the last known speed. As long as rotor position and phase currents are sampled synchronously by the slow loop, the slow loop bandwidth can be arbitrarily low. The modified synchronous current regulator can be run on fixed-point processors to control low-cost motors with Hall effect sensors. It can achieve AC servo motor-like control with brushless DC motors. 2

Modified Synchronous Current Regulator The primary theoretical difference is the controller outputs: I qr + 0 - + - d-axis controller q-axis controller V d V q Standard SCR V d and V q fully-define a voltage vector. D-axis gain: [V/A] Q-axis gain: [V/A] Simulate with: I q I d 0 I + qr - - + d-axis controller q-axis controller ϕ = V V Modified SCR V and V fully-define a voltage vector. D-axis gain: [rad/a] Q-axis gain: [V/A] Simulate with: I q I d 22

Modified Synchronous Current Regulator Consider a step increase in torque command via I qr : Q SCR: ΔV mscr V 2 ΔV SCR IωL V E ϕ IR I 0 + - + - K d s s V d V q I q I d λ r D mscr: 0 + - - + K d s s ϕ V I q I d 23

Applied Analysis 24

Plant Information Overview The controller presented here has been tested on several plants. The example used for this presentation is a 500W electric kick scooter. Custom-designed and built hub motor. Rear wheel direct drive, :. 33V, 4.4Ah LiFePO4 battery. Torque command by hand throttle. 25

Plant Information Important Specifications Symbol Description Value Units 2p Number of poles. 4 - R a Per-phase motor resistance. 0.084 Ω L s Synchronous inductance. 0.2 0-3 H K t Per-phase torque/back EMF constant. 0.0 V/(rad/s) V Nominal DC voltage. 33.0 V J Plant inertia, reflected to rotational. 0.40 kg m² 26

Controller Hardware Overview Custom 48V/40A three-phase inverter drive Hall effect-based current sensing (phase and DC). v,2: Texas Instruments MSP430F2274 (6-bit, no hardware multiplier) v3: STMicroelectronics STM32F03 (32-bit, w/ hardware multiplier) 2.4GHz wireless link for data acquisition. 27

Controller Hardware Important Specifications Symbol Description Value Units R ds On-resistance of each phase leg. 7.50-3 Ω f sw PWM switching frequency. 5,625 Hz f fast Fast-loop frequency. Handles position estimate, sine wave generation. MSP430: 4,500 STM32: 0,000 Hz f slow Slow-loop frequency. Handles current sampling, control computation. MSP430: 22 STM32:,000 Hz f tx Data transmit frequency. For data display and logging. 20 Hz 28

Controller Design Overview Synchronous Current Regulator: (I dr I d ) D-Axis V d Controller (I qr I q ) Q-Axis Controller V q dq abc V{abc} M Controllers Inverse Park Transform Amplifier Motor Modified Synchronous Current Regulator: (I dr I d ) (I qr I q ) D-Axis Controller Q-Axis Controller V V V {abc} M Controllers Sine Wave Generator Amplifier Motor 29

Controller Design Simplified Plant: Q-Axis Only, Stalled At stall, both the d-axis and the q-axis look like resistors. Modeling the q-axis (torque-producing) controller and plant: I qr + - I qe s V q R a I q G c (s) G p (s) I qf d s H(s) Closed-loop poles can be placed anywhere in the left half-plane, bandwidth set by filter frequency and damping ratio set by. 30

Controller Design Simplified Plant: Q-Axis Only, Stalled Magnitude (db) Phase (deg) 40 20 0-20 -40-60 -80 0-45 -90-35 L(s) System: L Frequency (rad/sec): 4.5 Magnitude (db): -.97 System: L Frequency (rad/sec): 4.5 Phase (deg): -05-80 0 0 0 0 2 0 3 Frequency (rad/sec) L( s) ( R s)( a d s ) To leave 75º phase margin:. 2 V A s m 75 0.75 3

Controller Design Simplified Plant: Q-Axis Only, Stalled.4.2 Simplified Plant Closed-Loop Step Response Kq =.2 V/A/s Kq =.6 V/A/s Kq = 2.5 V/A/s Normalized I q Amplitude 0.8 0.6 0.4 0.2 0 0 0.05 0. 0.5 0.2 0.25 0.3 Time (sec) 32

Controller Simulations Synchronous Current Regulator Full motor simulation with vector quantities and complex impedance using measured motor parameters (R a, L s, K t ). Current filtering as described above. Speed fixed at 500rpm. (Load dynamics not considered.) I dr = 0, I qr steps from 5A to 30A. + 0 - + - K d s s V d V q K d = {.2,.6, 2.5} V/A/s = {.2,.6, 2.5} V/A/s I q I d 33

Controller Simulations Synchronous Current Regulator 9 8.5 SCR: Vector Step Response, Voltage = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 8 V q [V] 7.5 7 6.5 6-3 -2.5-2 -.5 - -0.5 0 V d [V] 34

Controller Simulations Synchronous Current Regulator 9 SCR: Vector Step Response, Voltage = K d =.2 V/A/s 8.5 K = K =.6 V/A/s q d K = K = 2.5 V/A/s q d Q 8 ΔV mscr ΔV SCR V q [V] 7.5 ΔV SCR V 2 7 V 6.5 6-3 -2.5-2 -.5 - -0.5 0 V [V] d D What am I looking at? 35

Controller Simulations Synchronous Current Regulator 9 8.5 SCR: Vector Step Response, Voltage = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 8 V q [V] 7.5 7 6.5 6-3 -2.5-2 -.5 - -0.5 0 V d [V] 36

Controller Simulations Synchronous Current Regulator 34 SCR: Vector Step Response, Current 32 30 28 26 I q [A] 24 22 20 8 6 = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 4-0 -8-6 -4-2 0 2 4 6 8 0 I d [A] 37

Controller Simulations Synchronous Current Regulator 5.5 SCR: Step Response, Torque Torque [Nm] 5 4.5 4 3.5 3 2.5 2.5 0.5 = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 0 5 5. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Time [s] 38

Controller Simulations Modified Synchronous Current Regulator Full motor simulation with vector quantities and complex impedance using measured motor parameters (R a, L s, K t ). Current filtering as described above. Speed fixed at 500rpm. (Load dynamics not considered.) I dr = 0, I qr steps from 5A to 30A. 0 + - - + K d s s ϕ V K d =.0 rad/a/s = {.2,.6, 2.5} V/A/s (Is this fair?) I q I d 39

Controller Simulations Modified Synchronous Current Regulator 9 mscr: Vector Step Response, Voltage 8.5 8 V q [V] 7.5 7 6.5 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 6-3 -2.5-2 -.5 - -0.5 0 V [V] d 40

Controller Simulations Synchronous Current Regulator 9 mscr: Vector Step Response, Voltage 8.5 Q 8 ΔV mscr ΔV SCR V q [V] 7.5 ΔV mscr V 2 V 7 6.5 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 6-3 -2.5-2 -.5 - -0.5 0 V [V] d D What am I looking at? 4

Controller Simulations Modified Synchronous Current Regulator 9 mscr: Vector Step Response, Voltage 8.5 8 V q [V] 7.5 7 6.5 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 6-3 -2.5-2 -.5 - -0.5 0 V [V] d 42

Controller Simulations Modified Synchronous Current Regulator 34 mscr: Vector Step Response, Current 32 30 28 26 I q [A] 24 22 20 8 6 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 4-0 -8-6 -4-2 0 2 4 6 8 0 I [A] d 43

Controller Simulations Modified Synchronous Current Regulator 5.5 mscr: Step Response, Torque Torque [Nm] 5 4.5 4 3.5 3 2.5 2.5 0.5 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 0 5 5. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Time [s] 44

Controller Simulations Comparison V q [V] 9 8.5 8 7.5 7 6.5 Voltage Current Torque SCR: Vector Step Response, Voltage = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 6-3 -2.5-2 -.5 - -0.5 0 V d [V] I q [A] 34 32 30 28 26 24 22 20 8 6 SCR: Vector Step Response, Current = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 4-0 -8-6 -4-2 0 2 4 6 8 0 I d [A] Torque [Nm] 5.5 5 4.5 4 3.5 3 2.5 2.5 0.5 SCR: Step Response, Torque = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 0 5 5. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Time [s] 9 mscr: Vector Step Response, Voltage 34 mscr: Vector Step Response, Current 5.5 mscr: Step Response, Torque V q [V] 8.5 8 7.5 7 6.5 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 6-3 -2.5-2 -.5 - -0.5 0 V d [V] I q [A] 32 30 28 26 24 22 20 8 6 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 4-0 -8-6 -4-2 0 2 4 6 8 0 I d [A] Torque [Nm] 5 4.5 4 3.5 3 2.5 2.5 0.5 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 0 5 5. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Time [s] 45

Experimental Testing and Data Baseline: Q-axis Control Only Speed [rpm] 800 700 600 500 400 300 200 00 0 Q-axis Control Only (Fixed Phase) 40 60 80 00 20 40 Q-axis (torque producing) current controlled. D-axis current increases with speed. Current [A] 40 30 20 0 0-0 -20-30 -40 I q I d 40 60 80 00 20 40 Time [s] 46

Experimental Testing and Data Baseline: Q-axis Control Only 40 30 20 Q-Axis Control Only (Fixed Phase) Q-axis (torque producing) current controlled. D-axis current increases with speed. 0 I q 0-0 -20-30 -40-40 -30-20 -0 0 0 20 30 40 I d 47

Speed [rpm] Current [A] Experimental Testing and Data Full mscr Phase [deg] Full mscr 800 700 600 500 400 300 200 00 0 0 50 00 50 200 40 30 20 0 0-0 -20 I -30 q -40 I 0 d 50 00 50 200 30 Time [s] 20 0 0 0 50 00 50 200 Time [s] D-axis current controlled to be zero. Phase advanced as speed increases. 48

Experimental Testing and Data Full mscr 40 30 20 0 Full mscr In the postive torque quadrant, I d is effectively regulated. Negative torque still needs work, but it s better than open-loop. I q [A] 0-0 -20-30 -40-40 -30-20 -0 0 0 20 30 40 I [A] d 49

Future Work Range testing (or directly measure energy consumption) with SCR vs. mscr in real-world use. Controlled dynamometer experiment of SCR vs. mscr transient torque response, to verify simulations. (Requires high-speed data acquisition.) Sensorless control using a state observer for rotor position. Fault detection and recovery to increase controller robustness, possibly using sensorless control as a back-up in the event of sensor failure. More high-speed testing. Larger-scaled motor and controllers. 50

Questions / Feedback 5

References [] J.R. Mevey. Sensorless Field Oriented Control of Brushless Permanent Magnet Motors. M.S. Thesis. Kansas State University, Manhattan, 2009. [2] J.L Kirtley. Permanent Magnet Brushless DC Motors. Chapter 7 of Course Notes for 6.685 - Electric Machines. Massachusetts Institute of Technology, Cambridge, 2005. [3] A. Hughes. Electric Motors and Drives: Fundamentals, Types, and Applications. Third Edition. Newness, TK, 2005. [4] T.M. Rowan, R.J. Kerkman. A new synchronous current regulator and an analysis of current-regulated PWM inverters, IEEE Transactions on Industry Applications, vol. IA-22, no. 4, pp. 678-690, Jul./Aug. 986. [5] F. Briz, M.W. Degner, R.D. Lorenz. Analysis and Design of Current Regulators Using Complex Vectors. IEEE Transactions on Industry Applications, vol. 36, no. 3, pp. 87-825, May/Jun. 2000. 52

Motor Control Overview Electric motors convert electrical power (voltage, current) to mechanical power (torque, speed), with some power lost as heat in the motor. I L R + + V E - - I K t I E K t τ, Ω Brushed DC Motor Model The torque constant (K t ) and back EMF constant are identical due to power conservation. The conversion from current and back EMF to torque and speed is lossless; all losses are accounted for externally. 53

Motor Control Overview A brushed DC motor can be modeled as a SISO system (voltage to speed) with an internal feedback loop of back EMF: V + - Ls R I τ Ω K (s) t G load E K t 54

Motor Control Overview A current control loop provides the ability to command torque. Current is directly proportional to torque, and easy to measure. Depending on the load, an integral controller may be sufficient to track the reference current with zero steady-state error. I r + - K i s G c (s) V - + Ls R I K (s) t τ G load E K t Ω Plant, G p (s) 55

Current Sensing Overview Digital Rotor Position Estimator θ Latch Value Trigger khz Sampling Analog θ latch I d dq - I a I q abc - I c Digital LPF Park Transform I a I b I c 0 Analog LPF 56

Current Sensing Analog Filtering: Second-Order Low Pass. Buffered output filter on ACS74 Hall effect current sensor. 2. Local 2: voltage divider and RC filter at ADC pin. ACS74 Current Sensor STM32F03 I Signal Cond..7k R 2 ADC In R 2 C 2 C F F( s) s 2 s 2. kc 7 2 R C 2 2 F 57

Current Sensing Analog Filtering: Second-Order Low Pass The goal is to do as little filtering of the AC current signal as possible, so as not to distort the phase of the current. (Less than 5º phase lag desireable.) The PWM frequency (5,625Hz) is an obvious target for filtering.. Actual current ripple will be at this frequency. 2. Power transient-induced noise will be here, too. The filtering after the Park Transform can be much more aggressive, so noise in the AC current signal is acceptable. Component Selection: C F R 2 0nF 0k C2 0nF.7k 2 0nF 2 (0k)(0nF) 7s 50s F( s) s 2 s 58

Current Sensing Analog Filtering: Second-Order Low Pass 0 Current Sensor AC Filter, F(s) Magnitude (db) -20-40 -60-80 -00 0 PWM Frequency -20dB Filtering Phase (deg) -45-90 -35 Maximum Commutation Frequency 4º Phase Lag -80 0 2 0 3 0 4 0 5 0 6 0 7 Frequency (rad/sec) 59

Current Sensing Digital Filtering: First-Order Low Pass The digital filter acts on I d and I q, the outputs of the Park transform. At steady-state, these are DC quantities. The filter time constant can be much slower than the commutation frequency. The bandwidth lower limit is driven by the target performance of the current (torque) controller. The bandwidth upper limit is driven by the sampling frequency. The filter time constant should be much longer than the sampling interval. Where Δt is the sampling interval, a first-order digital low pass filter on I d and I q can be implemented with the following difference equations: I I n q n d a I a I n q n d ( a) I q ( a) I d Equivalent continuous time constant: d a t a 60

Current Sensing Digital Filtering: First-Order Low Pass Parameter Selection: t ms a 0.95 a 0.95 t ms ms d a 0.05 9 The filter time constant is significantly longer than the sampling interval, so a continuous time analysis is appropriate: H ( s) d s The bandwidth is /τ d, 52.6rad/s, or 8.38Hz. 6

Simplified Plant Closed-Loop Transfer Function and Root Locus I qr + - I qe s G c (s) V q R a G p (s) I q I qf d s H(s) jω L( s) G G G cl ( s) c p H G G R a K s s c p q d 2 GcG ph Ra d s d q K s K R a q s K q ζ=0.707 σ 62

Controller Simulations A more fair transient response comparison. 0 + - - + K d s s ϕ V K d =.0 rad/a/s = {.2,.6, 2.5} V/A/s (Is this fair?) I q I d One possible way to make a more fair comparison is by using the initial voltage vector to normalize the new d-axis gain: K d.2.6 V 0 2.2 rad A s K d V 0 63

Controller Simulations A more fair transient response comparison. 9 SCR: Vector Step Response, Voltage K = K =.2 V/A/s q d 9 mscr Vector Step Response, Voltage K =.2 V/A/s q 8.5 K = K =.6 V/A/s q d K = K = 2.5 V/A/s q d 8.5 K =.6 V/A/s q K = 2.5 V/A/s q 8 8 V q [V] 7.5 V q [V] 7.5 7 7 6.5 6.5 6-3 -2.5-2 -.5 - -0.5 0 V [V] d 6-3 -2.5-2 -.5 - -0.5 0 V [V] d 64

Controller Simulations A more fair transient response comparison. 34 SCR: Vector Step Response, Current 34 mscr Vector Step Response, Current 32 32 30 30 28 28 26 26 I q [A] 24 22 I q [A] 24 22 20 8 6 = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 4-0 -8-6 -4-2 0 2 4 6 8 0 I [A] d 20 8 6 =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 4-0 -8-6 -4-2 0 2 4 6 8 0 I [A] d 65

Controller Simulations A more fair transient response comparison. Torque [Nm] 5.5 5 4.5 4 3.5 3 2.5 2.5 0.5 SCR: Step Response, Torque = K d =.2 V/A/s = K d =.6 V/A/s = K d = 2.5 V/A/s 0 5 5. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Time [s] Torque (Nm) 5.5 5 4.5 4 3.5 3 2.5 2.5 0.5 mscr Step Response, Torque =.2 V/A/s =.6 V/A/s = 2.5 V/A/s 0 5 5. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Time [s] 66

High Speed Operation Sensing and control becomes more difficult as speed increases: ωl R, large phase angle. Significant lag due to current sensing / AC-side filtering. Analysis of digital effects (sampling, fitlering) becomes important. Poles: 2 Max Speed: 35,000RPM (without field weakening) ω = 3,665rad/s, f = 583Hz Current sensor phase lag with components specified: ~20º! 67

High Speed Operation 4 x 04 Speed [rpm] 3 2 0 205 20 25 220 225 230 235 240 245 250 255 Phase Angle (deg) 60 45 30 5 0 200 205 20 25 220 225 230 235 240 245 250 255 Current [A] 40 20 0 I q I d -20 200 205 20 25 220 225 230 235 240 245 250 255 Time [s] 68

Error Handling and Failsafes Hall effect sensor failure presents a significant risk to the controller. Failure Mode The entire sensor cable becomes unplugged. Transient sensor glitch. < /6 cycle (single sensor glitch) Permanent sensor failure. > /6 cycle Effect Comlete loss of ability to commutate the motor. An unexpected state transition, resulting in large current/torque transient when voltage vector is applied at the wrong angle. Repeated loss of two states per cycle. Countermeasure Pull-down resistors take the sensor state to {0,0,0}, which is invalid. The output driver shuts down. Motor coasts. If new state is not as expected, trust rotor speed interpolation for the next 60º segment. Follow same rules as above, but with a counter that talleys unexpected state transitions per unit time. If larger than some threshold, shut down. Sensorless or hybrid techniques will significantly change the FMEA. Future work: Ability to switch to sensorless control if a Hall effect sensor fault is detected. 69

Connection to Adaptive Feed-Forward Cancellation The SCR and mscr are applications of adaptive feed-forward cancellation (AFC) to three-phase variables. In one implementation of AFC, a feed-forward path allows for zero-error tracking of a sinusoidal input at a specific frequency: Reference: Cattell, Joseph H. Adaptive Feedforward Cancellation Viewied from an Oscillator Amplitude Control Perspective. S.M. Thesis, Massachusetts Institute of Technology, 2003. 70

Connection to Adaptive Feed-Forward Cancellation By manipulating the block diagram of a the SCR, focusing on the amplitude of a single phase of current, the SCR can be related to single-oscillator AFC (not proven here). The modified SCR is related to single-oscillator AFC with a phase advance offset, which has been proven to improve transient response. In both cases, the Park Transform provides the sinuosoidal multiplier for the input and output. In AFC with phase advance, ϕ i is set as the plant phase angle (initial voltage vector angle). Reference: Cattell, Joseph H. Adaptive Feedforward Cancellation Viewied from an Oscillator Amplitude Control Perspective. S.M. Thesis, Massachusetts Institute of Technology, 2003. 7