2016 Kappa Electronics Motor Control Training Series Kappa Electronics LLC. -V th. Dave Wilson Co-Owner Kappa Electronics.

Transcription

1 2016 Kappa Electronics Motor Control Training Series 2016 Kappa Electronics C V th CoOwner Kappa Electronics

2 Benefits of Field Oriented Control

3 NewtonMeters Maximum Torque Per Amp (MTPA) Maximum torque per amp (MTPA) 200V 200 V(treaction) V 100V 50V Simulated Reactance Torque as a function of angle delta from 2005 Prius Traction Motor 0 0V 50 50V V V o 200V 0.0s 0.3s 0.6s 0.9s 1.2s 1.5s 1.8s 2.1s 2.4s 2.7s 3.0s 3.3s 3.6s 150 o 120 o 90 o 60 o 30 o 0 o 30 o 60 o 90 o 120 o 150 o 180 o

4 Field Oriented Control in Real Time A B C Torque Currents Constant 3 2 P 2 dr I qs Constant (for now) Adjustable Torque expression based on amplitude invariant form of Clarke Transform. Interrupt: Measure rotor flux angle Regulate current vector to be 90 o wrt rotor flux Exit ISR Interrupt: Measure new rotor flux angle Regulate current vector to be 90 o wrt rotor flux Exit ISR Interrupt: Measure new rotor flux angle Regulate current vector to be 90 o wrt rotor flux Exit ISR

5 Establishing Space Vector Conventions b B Direction of positive rotation Direction of positive speed Direction of positive torque a A a Phase A leads phase B Phase B leads phase C Phase C leads phase A C b Motor shaft axis

6 How Do You Control Torque on a DC Motor? Brush DC Motor Desired Current Error Signal PI Controller PWM Power Stage Dave s Motor Control Center Measured Current ADC1 Commutator keeps rotor and stator fields properly aligned! Measure current already flowing in the motor. Compare the measured current with the desired current, and generate an error signal. Amplify the error signal to generate a correction voltage. Modulate the correction voltage onto the motor terminals.

7 1. Measure currents already flowing in the motor. Only 2 phases are measured! WHY? A, B, and C axes are fixed with respect to the motor housing. This reference frame is also called the stationary frame or stator frame. net current vector B i a i b A i c (implied) B C Dave s Motor Control Center i b i c i a A Controller with A/D i a i b i c C

8 2. Compare the measured current (vector) with the desired current (vector), and generate error signals. The desired phase currents can be calculated via these equations: i a = I m sin(q ) i b = I m sin(q 120 o ) i c = I m sin(q 240 o ) I m is proportional to motor torque q is the angle of the rotor flux B C Commanded i s i b i a Error i s i c A So how do we find q?

9 2. Compare the measured current (vector) with the desired current (vector), and generate error signals. q or q d Magnetic axis for phase A Usually accomplished with a resolver or encoder.

10 3Phase Stationary Frame Current Regulators q = rotor flux angle Phase A PI i a V a I m sin(q ) Reference current waveforms synchronized to rotor position q Phase B PI i b V b V c I m sin(q 120 o ) Phase C PI i c I m sin(q 240 o )

11 2. Compare the measured current (vector) with the desired current (vector), and generate error signals. The CARKE transform allows us to convert three vectors into two orthogonal vectors that produce the same net vector. B i b i s i c i b In other words, A convert a 3phase i a i a motor into a 2phase motor. This is the Amplitude C Invariant form of the Forward Clarke Clarke Transform a(t) b(t) c(t) a b 1 a t 2 a t b( t) c( t ) b t bt ct 3

12 2Phase Stationary Frame Current Regulators V a 2phase to 3phase transform V b q V c Reference current waveforms synchronized to rotor position V α V β i B i C i A 3phase to 2phase transform i α i β Phase α PI Phase β PI

13 Stationary Frame Tracking

14 Synchronous Frame Tracking

15 2. Compare the measured current (vector) with the desired current (vector), and generate error signals. Jump up on the rotating reference frame, whose xaxis is the rotor flux axis. B i q i b i s i d This is called the Park Transform i a A q C a b i d i a cosq i b sinq i q i a sinq i b cosq

16 2. Compare the measured current (vector) with the desired current (vector), and generate error signals. i d i q and are handled independently. Since the comparison is performed in the synchronous frame, motor AC frequency is not seen. Thus, they are DC quantities! Under normal conditions, we have all the flux we need supplied by the permanent magnets on the rotor. So commanded i d is set to zero. i d (commanded) i d (measured) error d (t) This is how much torque we want! i q (commanded) i q (measured) error q (t) Since i d is directly aligned with the rotor flux, it can be used to control the effect of the rotor flux on the stator coils. i q controls the amount of torque generated by the motor

17 3. (Finally!) Amplify the error signals to generate correction voltages. PI Controller (daxis) Commanded I d Measured I d Error K a K b V d PI Controller (qaxis) Commanded I q Measured I q Error K a K b V q K a Current Bandwidth (rad / sec) K b Motor Rd Rq d q PMSM Rs Rs s s ACIM Rs RsRr, IPM Rs Rs s_d s_q R s 1 2 m r s s 1 2 m r s

18 4. Modulate the correction voltages onto the motor terminals. Before we can apply the voltages to the motor windings, we must first jump off of the rotating reference frame. B v b v q v d Voltage vector q v a A Part A. Transfer the voltage vectors back to the stationary rectangular coordinate system. C v d (t) v q (t) v v a b v v d d cosq sinq v v q q sinq cosq a b

19 4. Modulate the correction voltages onto the motor terminals. Part B. Next, we transform the voltage vectors from the rectangular coordinate system to three phase vectors. B v b v b v c v a v a Voltage Vector A C Reverse Clarke Transformation A a a b A B C B C a a b b

20 4. Modulate the correction voltages onto the motor terminals. Phase A top Phase A bottom Phase B top Phase B bottom Phase C top Phase C bottom Over time, under steadystate conditions, the correction voltages v a, v b, and v c will be sine waves phase shifted by 120 o.

21 FOC in a Nutshell V a Torque Current Wilson Flux Current q Reverse ClarkePark Transforms V b q V c V q V d i B i Forward C ClarkePark i A Transforms i q i d Desired Torque PI q Desired Flux PI

22 2016 Kappa Electronics Motor Control Training Series 2016 Kappa Electronics C V th Owner Kappa Electronics

23 ACIM Circuit Representation with Arbitrary Turns Ratio a r j s s a m 2 j a r a m ja m 2 a r r S General equivalent circuit showing arbitrary value of referral ratio a (a=1 corresponds to a turns ratio of N s /N r, which yields the conventional circuit.) If the real value of rotor current isn t required, a can be any value except zero or infinity, resulting in a multitude of possible circuits!

24 ACIM Circuit Representation with Turns Ratio a=m/r Torque current i q Rotor Flux current i d Stator current Rotor leakage inductor is gone! This implies that a reference frame exists where the stator current can be resolved into torque current and flux current. Source: Vector Control and Dynamics of AC Drives, by Don Novotny and Tom ipo, Oxford University Press, 2000

25 Torque Production in an ACIM Stator current is resolved into flux producing and torque producing components. i q Rotor flux is NOT fixed w.r.t. rotor. It is asynchronous to rotor position. i d i s T 3P m e m d q 4 rotor flux r P equals the number of poles 3 4 r m i i P id iq 2 r m i d Both i d and i q produce torque. So why is torque usually set by i q only? Hint: There are two reasons.

26 Dynamic Response of Rotor Referenced Field Orientation Step change in i q Step change in i d i qr m r i qs i qs i dr i qr i qs i qr i qs i ds i ds i ds dr Torque instantaneously changed. dr dr Torque slowly changed.

27 ACIM Flux Angle Calculation Dave s Motor Control Center Slip Calculator Encoder Commanded i d Commanded i q 1 1 St r t r N D ^ s r ^ q d B Recall that the rotor flux sweeps across the surface of the rotor at a speed equal to the slip frequency, i.e., it is asynchronous to the rotor. q d A C

28 Synchronous Frame Regulation i q and i d are still regulated independently. However, we now need a nonzero i d value, since the rotor doesn t produce any flux on its own (i.e., it doesn t have a permanent magnet) P i (commanded) d error(t) I i d (measured) v d i q (commanded) i q (measured) error(t) P I v q i d i q controls rotor flux magnitude. controls amount of torque generated by motor

29 P Commanded Rotor Speed Commanded i d (flux) Commanded i q (torque) P I P V d V q Reverse ClarkePark Transform θ d V a V b V c Dave s Motor Control Center I i d i q i a I Forward ClarkePark Transform θ d i b i c Commanded i d Commanded i q Slip Calculator Slip Frequency θ d Actual Rotor Speed Control Diagram of a Variable Speed Control System Utilizing Field Oriented Control.

30 Motor DQ Coupling 1/ d 1/ q

31 Stator Voltage Differential Equations Voltage equations from the block diagram: daxis qaxis V sd rs isd sq s dt isd sd K V sq rs isq sd s dt isq sq sq Taking the derivative of both sides: sd daxis qaxis V V sd sq r s r s i i sd sq sq sd s s sd sq d dt d dt i i sd sq Substituting for flux terms and rearranging: daxis V sd r s i sd sq i sq s sd d dt i sd 0 qaxis V sq r s i sq d i K i 0 sd sd s sq dt sq

32 Current Regulator Decoupling Permanent Magnet Motors Commanded i d K a V d K b i d V d compensation s i q Commanded i q V q compensation K a K b V q K E

33 Current Regulator Decoupling AC Induction Motors i d R r r m m / r s 2 m r V d compensation i q R r / r m / r V q compensation s 2 m r

34 Crosscoupling Effect with FOC Current Regulators Decoupling Compensation OFF Commanded Iq Actual Iq 400ms 420ms 440ms 460ms 480ms 500ms 520ms 540ms 560ms 580ms 600ms 620ms 640ms 660ms 680ms Decoupling Compensation ON Commanded Iq Actual Iq 400ms 420ms 440ms 460ms 480ms 500ms 520ms 540ms 560ms 580ms 600ms 620ms 640ms 660ms 680ms

35 2016 Kappa Electronics Motor Control Training Series 2016 Kappa Electronics C V th Owner Kappa Electronics

36 Flux is reluctant to jump through air because air has high permeability. i Reluctance Torque The magnet exerts force on the knife in an effort to minimize the reluctance of the flux path. N Torque S

37 Total Motor Torque I qs I ds Permanent Magnet Rotor Reaction Torque Reluctance Torque 3 P Torque driqs ds 2 2 qs I ds I qs Torque expression based on amplitude invariant form of Clarke Transform.

38 Buried Magnets Create NEW Torque Buried rotor magnets produce different inductances on the dq axes. This results in a NEW torque component proportional to the difference in these inductances.

39 CW CCW Torque ocked Rotor D Torque vs. Angle Q Q Reaction Torque (magnet to magnet) D D Stable Stable Unstable 0 o Unstable 45 o 90 o 135 o Unstable 180 o Q D Q Reluctance Torque (magnet to metal) The magnets exerts force on the rotor in an effort to minimize the resistance (reluctance) of the flux path.

40 Effect of Saliency on Optimum Torque Angle Positive I ds Negative I ds

41 MTPA Control of IPM Motors Commanded i d Commanded Speed Actual Speed imit i T i d 1 r 4 d q i d 2 r 8i 2 T d q 2 i d Current Controller V d Reverse ClarkePark Transform V a V b V c IPM Dave s Motor Control Center q 2 2 i i i i sign T T d Current Controller V q θ d Commanded i q d/dt i d i q i a Forward ClarkePark Transform i b i c θ d Rotor Flux Angle