dave wilson co-owner kappa electronics intro to sensorl… · dave wilson co-owner kappa...
TRANSCRIPT
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
Dave WilsonKeeping your motors spinning.
MathematicalModel of Process
Σ+
-
Measurement
Estimate
Error feedback
Process Σ
Noise
Model Based Filtering
Dave WilsonKeeping your motors spinning.
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
Dave WilsonKeeping your motors spinning.
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!
Dave WilsonKeeping your motors spinning.
Σ
Σ Σ Σ
Z-1
Z-1
αβ
+
-
++
+ ++
Integrator Integrator
+
MeasuredPosition
EstimatedPosition
EstimatedVelocity
EstimatedAcceleration
Error
This form of the filter reveals the derivatives of the tracked variable.
Cascaded Representation
Dave WilsonKeeping your motors spinning.
Feedforward input fixes this problem
Tracking Filters have Phase Delay
CHICAGO
Dave WilsonKeeping your motors spinning.
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)
Integrator Integrator
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
Dave WilsonKeeping your motors spinning.
Observer with PI Front-end
(Alpha)
(Beta)
PIController
Dave WilsonKeeping your motors spinning.
Servo Performance with Velocity Directly from Encoder vs. Observer
Dave WilsonKeeping your motors spinning.
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
Dave WilsonKeeping your motors spinning.
+
-
Vin alpha
EMFalpha
+
-1/Ls
Rs
alphai
Current Estimator Block
+
-
Vin beta
EMFbeta
+
-
1/Ls
Rs
betai
Current Estimator Block
Phase Current Model
Dave WilsonKeeping your motors spinning.
+
-
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
Dave WilsonKeeping your motors spinning.
+
-
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).
Dave WilsonKeeping your motors spinning.
Dave WilsonKeeping your motors spinning.
Actual Back-EMF
Estimated Back-EMF
LTSpice
Sampling frequency = 10 KHz
Dave WilsonKeeping your motors spinning.
)(
)(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
Dave WilsonKeeping your motors spinning.
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)
Dave WilsonKeeping your motors spinning.
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.
Dave WilsonKeeping your motors spinning.
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