Dave Wilson Co-Owner Kappa Electronics Field... · 2018-04-04 · Keeping your motors spinning....

2016 Kappa Electronics Motor Control Training Series

-Vth

Dave WilsonCo-OwnerKappa Electronicswww.kappaiq.com

© 2016 Kappa Electronics LLC

Dave WilsonKeeping your motors spinning.

Benefits of Field Oriented Control


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

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200VV(treaction)

Simulated Reactance Torque as a function of angle delta

from 2005 Prius Traction Motor

0o 30o 60o 90o 120o 150o 180o-30o-60o-90o-120o-150o-180o

50

100

150

200

0

-50

-100

-150

-200

New

ton-M

ete

rs

Maximum torque per amp(MTPA)

Maximum Torque Per Amp (MTPA)


qsdr IP

Torque 22

3

Field Oriented Control in Real Time

Constant Constant (for now)

Adjustable

Interrupt:Measure rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

Interrupt:Measure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

Interrupt:Measure new rotor flux angleRegulate current vector to be 90o wrt rotor fluxExit ISR

†Torque expression based on amplitude invariant form of Clarke Transform.

†

Currents

A B C


+a

+b

Direction of positive rotationDirection of positive speedDirection of positive torque

-a

-b

A

B

C

Establishing Space Vector Conventions

Motor shaft axis

Phase A leads phase BPhase B leads phase CPhase C leads phase A


PWMPI

Controller+

-

ADC1

Desired Current

Measured Current

Error Signal

Measure current already flowing in the motor.1.

Compare the measured current with the desired current, and generate an error signal.2.

Amplify the error signal to generate a correction voltage.3.

Modulate the correction voltage onto the motor terminals.4.

Commutator keeps rotor and stator fields

properly aligned!

Brush DC Motor

How Do You Control Torqueon a DC Motor?

PowerStage

Dave’sMotor Control

Center


A

B

C

A

B

C

i b

i c

i a

(implied)

Controllerwith A/D

i a

i b

i c

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”.

1. Measure currents already flowing in the motor.

net current vector

ia

ib

ic

Only 2 phases are measured!

WHY?


Center


A

B

C

si

i b

i c

i a

2. Compare the measured current (vector) with the desired current (vector), and generate error signals.

ErrorCommanded i s

So how do we find q?

The desired phase currents can be calculated via these equations:

ia = -Im sin(q)

ib = -Im sin(q - 120o)

ic = -Im sin(q - 240o)

Im is proportional to motor torque

q is the angle of the rotor flux


q or qd

Usually accomplished with a resolver or encoder.


Magnetic axis for phase A


3-Phase Stationary Frame Current Regulators

+

-

Phase A

Phase B

Phase C

+

-

+

-

-

-

PI

PI

PI

Reference current waveforms synchronized to rotor position

Va

Vb

Vc

i a

i b

i c

-Imsin(q)

-Imsin(q -120o)

-Imsin(q -240o)

q = rotor flux angle

q


ai

biThe CLARKE transform allows us to convert three vectors into two orthogonal vectors that produce the same net vector.

A

B

C

si

i b

i c

i a


a(t) b(t) c(t) a bForward Clarke

In other words, convert a 3-phase motor into a 2-phase motor. This is the Amplitude

Invariant form of the Clarke Transform

)()(31

32 tctbtat +-a

tctbt -3

1b


2-Phase Stationary Frame Current Regulators

+

-

+

-

PI

PI

Reference current waveforms synchronized to rotor position

2-phase to 3-phase

transform

-- 3-phase to

2-phase transform

i B iα

iβ

i C

i A

Phase α

Phase β

Va

Vb Vc

Vα Vβ

q


Stationary Frame Tracking


Synchronous Frame Tracking


ai

bi

A

B

C

si

q

i q

i d

Jump up on the rotating reference frame, whose x-axis is the rotor flux axis.


ba

ba

qq

qq

cossin

sincos

iii

iii

q

d

+-

+a b

This is called the Park Transform


and are handled independently. Since the comparison is

performed in the synchronous frame, motor AC frequency is not

seen. Thus, they are DC quantities!

i d i q

i d +

-

errord (t)

+

-

errorq (t)

(commanded)

i d(measured)

i q

i q (commanded)

(measured)

Since id is directly aligned with the rotor flux, it can be used to

control the effect of the rotor flux on the stator coils.

iq controls the amount of torque generated by the motor

Under normal conditions, we have all the flux we need supplied by the permanent magnets on the rotor. So commanded id is set to zero.

This is how much torque we want!



Commanded Id Kb

Error

Measured Id

Ka

PI Controller (d-axis)

+

-

+

+

Vd

Commanded Iq Kb

∫

Error

Measured Iq

Ka

PI Controller (q-axis)

+

-

+

+

Vq

3. (Finally!) Amplify the error signals to generate correction voltages.

LRKb sec)/(radBandwidthCurrentLKa

Motor Rd Rq Ld LqPMSM Rs Rs Ls Ls

ACIM Rs Rs+Rr

IPM Rs Rs Ls_d Ls_q

-

sr

ms

LL

LL

2

1

-

sr

ms

LL

LL

2

1

,

∫


Voltage vector

av

bv

Part A. Transfer the voltage vectors back to the stationary rectangular coordinate system.

q

A

B

C

vd

vq

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.

vd (t)

vq(t)

a b

b

a

qq

qq

cossin

sincos

qd

qd

vvv

vvv

+

-


av

bv

A

B

C

va

vc

vb

Part B. Next, we transform the voltage vectors from the rectangular coordinate system to three phase vectors.

Reverse Clarke Transformation


Voltage Vector

a b A B C

ba

ba

a

2

3

21

2

3

21

--

+-

C

B

A


Phase A - top

Phase B - top

Phase B - bottom

Phase C - top

Phase C - bottom

Phase A - bottom


Over time, under steady-state conditions, the correction voltagesva, vb, and vc will be sine waves phase shifted by 120o.


FOC in a Nutshell

+

-

+

-

PI

PI

Wilson

Reverse Clarke-Park Transforms

-- Forward

Clarke-Park Transforms

i B iq

id

i C

i A

Torque Current

Flux Current

Desired Torque

Desired Flux

VqVd

Va

Vb Vc

q

q

q


Dave WilsonOwnerKappa Electronicswww.kappaiq.com


-Vth


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!

General equivalent circuit showing arbitrary value of referral ratio “a” (a=1 corresponds to a turns ratio of Ns/Nr, which yields the conventional circuit.)

sr ms aLLj -

maLj

mr aLLaj -2

S

ra r

2

ACIM Circuit Representation with Arbitrary Turns Ratio “a”


Rotor leakage inductor is gone!

Source: Vector Control and Dynamics of AC Drives, by Don Novotny and Tom Lipo, Oxford University Press, 2000

Rotor Fluxcurrent

Torque current

id

iq

Stator current

This implies that a reference frame exists where the stator current can be resolved into torque current and flux current.

ACIM Circuit Representation with Turns Ratio a=Lm/Lr


dmr iL

disi

qi

P equals the number of poles

Stator current is resolved into flux producing and torque producing components.

Rotor flux is NOT fixed w.r.t. rotor. It is “asynchronous” to rotor position.

qd

r

mq

r

mdme ii

L

LPi

L

LiL

PT

2

4

3

4

3

rotor flux

Torque Production in an ACIM

Both id and iq produce torque.So why is torque usually set by iq only?

Hint: There are two reasons.


dr

dsi

qsiqri

qsiqs

r

mqr i

L

Li -

dr

dsi

qsiqri

Torque instantaneously changed.

dsi

dri

dr

Torque slowly changed.

Step change in iq Step change in id

Dynamic Response of Rotor-Referenced Field Orientation


Encoder

+

+

r

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.

ACIM Flux Angle Calculation

s^

qd^

Slip Calculator

Commanded id

Commanded iq

1

1 + Strtr

N

D


Center

A

B

C

dq


i d

I

P+

+

+-

error(t)

I

P+

+

+-

error(t)

iq and id are still regulated independently. However, we now need a non-zero id value, since the rotor doesn’t produce any flux on its own (i.e., it doesn’t have a permanent magnet)

(commanded)

i d(measured)

i q

i q (commanded)

(measured)

vd

vq

controls rotor flux magnitude.

controls amount of torque generated by motor

i d

i q

Synchronous Frame Regulation


+

-

Commanded

Rotor

Speed

P

I ∫

+

+

Actual Rotor Speed

Vb

Vc

Va

Control Diagram of a Variable Speed Control System Utilizing Field Oriented Control.

Commanded id

+

-

P

I ∫

+

+

+

-

P

I ∫

+

+

Commanded iq Reverse

Clarke-Park

Transform

Forward

Clarke-Park

Transform

id iq

ia

ib

ic

∫Commanded id

Commanded iq

Slip

Calculator

Slip

Frequency +

+

θd

θd

θd

Vd

Vq

(flux)

(torque) Dave’sMotor Control

Center

-

-


Motor D-Q Coupling

1/Ld

1/Lq


Stator Voltage Differential Equations

sqsqsqssdsqssq

sdsdsdssqsdssd

LidtirV

KLidtirV

--

++-

sqdtd

sqssdsqssq

sddtd

sdssqsdssd

iLirV

iLirV

--

+-

0

0

-+--

-+-

sqdtd

sqssdsdsqssq

sddtd

sdssqsqsdssd

iLKLiirV

iLiLirV

Taking the derivative of both sides:

Substituting for flux terms and rearranging:

Voltage equations from the block diagram:

d-axis

q-axis

d-axis

q-axis

d-axis

q-axis


Current Regulator Decoupling

+

-

+

-

Commanded iq

id

iq

Vd

Vq

Ka

Kb ∫

+

+

Ka

Kb ∫

+

+

Commanded id

+

-

Ls

++

KE

+

Permanent Magnet Motors

Vd compensation

Vq compensation


Current Regulator DecouplingAC Induction Motors

+

-

+

+

LmL

R

r

r

rm LL /

rr LR /

iq

r

ms

L

LL

2

-

+

-

id

r

ms

L

LL

2

-

rm LL /

Vd compensation

Vq compensation


Cross-coupling Effect with FOC Current Regulators

400ms 420ms 440ms 460ms 480ms 500ms 520ms 540ms 560ms 580ms 600ms 620ms 640ms 660ms 680ms

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


Dave WilsonOwnerKappa Electronicswww.kappaiq.com


-Vth


Reluctance Torque

N

S

i

The magnet exerts force on the knife

in an effort to minimize the

reluctance of the flux path.

Flux is “reluctant” to jump through air because air has high permeability.

Torque


qsdsqsdsqsdr IILLIP

Torque -+ 22

3

Reaction Torque Reluctance Torque

Permanent Magnet Rotor

Total Motor Torque

Iqs

Ids

†

†Torque expression based on amplitude invariant form of Clarke Transform.


Buried Magnets Create NEW Torque

Buried rotor magnets produce different inductances on the d-q axes.

This results in a NEW torque component proportional to the difference in these inductances.


Torque vs. Angle

To

rqu

e

0o 45o 90o 135o 180o

Reaction Torque (magnet to magnet)

CC

WC

W

Reluctance Torque (magnet to metal)

The magnets exerts force on the rotor in an effort to minimize the resistance

(reluctance) of the flux path.

Locked Rotor

Stable UnstableStable

Unstable Unstable

D

Q

-D

-Q

D

Q

-D

-Q


Effect of Saliency on Optimum Torque Angle

Positive Ids Negative Ids


+

-

Commanded

Speed

Actual

SpeedVb

Vc

Va

Commanded id

+

-

+

-

Commanded iq

Reverse

Clarke-Park

Transform

Forward

Clarke-Park

Transform

id iq

ia

ib

ic

θd

θd

Vd

Vq

IPM

d/dt

MTPA Control of IPM Motors

id

Current Controller

Current Controller

iTLimit

Rotor Flux Angle

22

dTTq iiisigni -

+

-+

-- 2

2

2

84

1T

qd

r

qd

rd i

LLLLi

id

-

-


Center

Dave Wilson Co-Owner Kappa Electronics Field... · 2018-04-04 · Keeping your motors spinning....

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Transcript of Dave Wilson Co-Owner Kappa Electronics Field... · 2018-04-04 · Keeping your motors spinning....