dave wilson co-owner kappa electronics intro to sensorl… · dave wilson co-owner kappa...

2016 Kappa Electronics Motor Control Training Series © 2016 Kappa Electronics LLC

Dave WilsonCo-OwnerKappa Electronicswww.kappaiq.com

-Vth

Dave WilsonKeeping your motors spinning.

Dave’sMotor Control

Center

+

-

CommandedRotorSpeed

P

I ∫

+

+

Rotor Speed

Vb

Vc

Va

Commanded id = 0

+

-

P

I ∫

+

+

+

-

P

I ∫

+

+

Commanded iq ReverseClarke-ParkTransform

ForwardClarke-ParkTransform

id iq

Phase CCurrentCalculation

ia

ib

ic

θd

θd

Vd

Vq

(torque)

PMSM

Observer

θd Sp

eed

Shaft position sensors are VERY expensive ($1,500 in some cases).

Many applications cannot afford the cost of a shaft sensor.

Sensorless FOC


MathematicalModel of Process

Σ+

-

Measurement

Estimate

Error feedback

Process Σ

Noise

Model Based Filtering


nynynyny

nynynynyny

)1(ˆ)(ˆ

1

Better tracking is obtained when α and β are highBetter filtering is obtained when α and β are low

Σ

Σ Σ Σ

Z-1

Z-1

αβ

+

-

++

+ ++

1

ny

ny

ny

ny

y correctiony correction nerror

Integrator Integrator

+

^ ^

Tracking Filters


Delay Delay

Delay

+

+ +

X(n)

X(n-1)

Y(n+1)

Y(n)

Y(n-1)

Accumulator

+

1

2

The tracking filter is revealed to be a simple 2nd order IIR filter as shown below.

The Tracking Filter…Unmasked!


Σ

Σ Σ Σ

Z-1

Z-1

αβ

+

-

++

+ ++


+

MeasuredPosition

EstimatedPosition

EstimatedVelocity

EstimatedAcceleration

Error

This form of the filter reveals the derivatives of the tracked variable.

Cascaded Representation


Feedforward input fixes this problem

Tracking Filters have Phase Delay

CHICAGO


Observers literally recreate the desired signal mathematically (great noise decoupling).The “guess” is corrected by comparison with an observable signal.

Observers are used to “observe” a quantity which is difficult to measureby mathematically modeling the system.

Model of H(z)


αβ

Source: Motion Controller Employs DSP Technology,Robert van der Kruk and John Scannell,Phillips Centre for Manufacturing Technology,PCIM – September, 1988

By providing an additional feedforward input, the tracking filter can make better output estimates. It then takes the form of an OBSERVER.

Can be designed to have zero (or near

zero) estimation lag.

Parameter Estimation with Observers


Observer with PI Front-end

(Alpha)

(Beta)

PIController


Servo Performance with Velocity Directly from Encoder vs. Observer


Va

sL

sL

sR lsLmL

synEk V

Clarke

sR lsLmL

synEk V

PMSM

emf

emf

synEss ki

i

dt

dL

i

iR

v

v

cos

sin

Appliedvoltage

Resistancevoltage

Inductancevoltage

Back-EMFvoltage

Vb

Vc


+

-

Vin alpha

EMFalpha

+

-1/Ls

Rs

alphai

Current Estimator Block

+

-

Vin beta

EMFbeta

+

-

1/Ls

Rs

betai

Current Estimator Block

Phase Current Model


+

-

Vin alpha

EMFalpha

+

-1/Ls

Rs

alphaiCurrent Estimator Block

+

-

ialpha

(measured)

error

+

-

Vin beta

EMFbeta

+

-1/Ls

Rs

betaiCurrent Estimator Block

+

-

ibeta

(measured)

error

(0)

(0)

Compare to Actual Phase Current


+

-

Vin alpha

EMFalpha

+

-1/Ls

Rs

alphaiCurrent Estimator Block

+

-

ialpha

(measured)

error

+

-

Vin beta

EMFbeta

+

-1/Ls

Rs

betaiCurrent Estimator Block

+

-

ibeta

(measured)

error

PI

PI

Back-EMF Observer

Use observable parameter (current) to estimate unobservable parameter (back-EMF).


Actual Back-EMF

Estimated Back-EMF

LTSpice

Sampling frequency = 10 KHz


)(

)(tan 1

tEMF

tEMF

alpha

beta

Finding the Angle

Requires floating point math

Must take inverse tangent function

Singularity when EMFalpla(t) = 0

Takes a long time to calculate


Vin alpha

EMFalpha

alphai

CurrentEstimator

Block

+

-

ialpha

(measured)

error

Vin beta

EMFbeta

betai

ibeta

(measured)

PI

CurrentEstimator

Block

+

-

errorPI

x

+

-

x

sin

cos

k2

k1+

+

Angle Demodulator

)cos(synEk

)sin(synEk

sin()cos(est)-cos()sin(est) = sin( -est)

sin( -est)


Sliding Mode EMF Observer

+

-

Vα+

-

Zα

Rs/Ls

Iα

+

-

KslideSGN

ZαEMFα

Iα^

Iαerror+

-1/Ls

LPF

“A Position and Velocity Sensorless Control of Brushless DC Motors Using an Adaptive Sliding Observer”, Takeshi Furuashi, Somboon Sangwongwanich, Shigeru Okuma, 1990 IEEE Proceedings, 087942-600-4/90/1100-1188, pp. 1188-1192.


s

1P IL P FDemodulator

High Frequency Voltage Injection (about 500 Hz)

θerr

High Frequency Current Measurement n

L P F n

err

qdhf

mq

ZZ

ZVi

2sin

2

ZdZq

Z2

P I regulator results in steady state value servoing to zero

Zero-Speed Saliency Tracking Observer

Only works on motors with a strong saliency signal.

Saliency graph shifts when the motor is loaded.

Works at low speeds, but falls apart at high speeds.

Disadvantages:

err = 0

dave wilson co-owner kappa electronics intro to sensorl… · dave wilson co-owner kappa...

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