Southern Taiwan University
Department of Electrical Engineering
A Shaft Sensorless Control for PMSM
Using Direct Neural Network Adaptive
Observer
Authors: Guo Qingding
Luo Ruifu
Wang Limei
IEEE IECON 22nd International Conference,
Vol.3, 5-10 August 1996
Student: Sergiu Berinde,
M972B206
Outline

Abstract

Introduction

Multi-Layer Feedforward NN and Backpropagation
Method

Direct Neural Model Reference Adaptive Control

Structure and Training of NN Observer

Simulation Results

Conclusions
2
Abstract




Traditional rotor position detection method is based on resolver, absolute
encoder, etc.
A position and velocity sensorless control algorithm based on direct neural
model reference adaptive observer is proposed.
Two neural networks are trained to learn electrical and mechanical model
respectively, adaptation is realized by online training using current prediction
error.
Advantages of this method are shown by simulation results.
3
Introduction

PMSMs are highly efficient and widely used in servo drive applications.

Drawbacks of using encoders or resolvers :




Expensive
Environmental factors limit the accuracy of the sensor
Additional static and dynamic friction reduce the ruggedness of the drive
Some sensorless methods :


Sensing of the zero crosing of the back EMF -> not very accurate
Observer theory -> improved approach, not well developed for nonlinear systems

NN offer a promising way for the control and identification of systems with
nonlinear dynamics.

A neural network based adaptive observer is proposed to estimate currents,
rotor velocity and rotor position.
4
Multi-Layer Feedforward NN and
Backpropagation Method


After initial weight and training data are given, the unit in the latter layer
firstly receive input activation from preceding layer.
X j   YiWij
Total input Xj :
i
5
Multi-Layer Feedforward NN and
Backpropagation Method

A sigmoidal nonlinearity function is applied to the unit j to obtain Yj :
Yj  1


(1  e
x j
)
The activation of any node will feedforward to the output layer.
When all nodes of the NN are certified, the error of NN can be obtained, in
the form of an energy function :
1
E   (Y jo  d jo ) 2
2


The backpropagation learning algorithm is virtually an inverse process of
the feedforward calculation.
The output error is propagated backwards recursively to each lower layer
and the weights are adjusted according to the error of each node.
6
Multi-Layer Feedforward NN and
Backpropagation Method

Learning rule for adjusting the weights :
W ji k 1  W ji k   EoiY j

  learning rate
Eo  local error
Some steps for calculating local error :



Calculate changing rate of an output unit when its activation is changed.
E
Eoj 
 Y jo  d jo
Y jo
Calculate changing rate when the input sum of a node in output layer changes.
E
E Y j
EX j 


`
X j Y j X j
Calculate the changing rate of preceding layer unit error when a unit in
preceding layer is changed.
EOi 
E
E X j


  EX jWij
Yi
Yi
j X j
j
7
Direct Neural Model Reference Adaptive
Control
Motor Model of PMSM

The variables involved in motor dynamics are represented as space
vectors in the stator reference frame and described in matrix notation.
0 
d L 0 


I


RI

k

n


exp
Jn

s
s
p
p
1  U s
dt  0 L
 
•
•
•
0  B
d k  n p T
C  1

I s exp Jn p        TL
dt
H
H  H
1 H
•
d

dt
•
•
•
•
•
I s  is , is 
T
U s  Us ,U s 
T
0  1
J 

1 0 
L - stator phase inductance
R - stator phase resistance
np - no. of pole pairs
ω - rotor speed
Θ - rotor position
k - magnet constant
H – inertia
C - Coulomb friction coeff.
B – viscous damping coeff.
8
Direct Neural Model Reference Adaptive
Control
Motor Model of PMSM

The typical control design approach is transforming the motor dynamics into
the rotor frame.
dis   R L

dt  n p

n p 
 0   1L
i  Kn p  1   
R  s
 L   0
L
0 
v
1  s
L
d
B C
TL
T KN 0


 is


sgn


dt
H 1 H H
H
d

dt
is  exp  Jn p I s
vs  exp  Jn p Vs
9
Direct Neural Model Reference Adaptive
Control
Motor Model of PMSM

In order to implement in computer, the equations are put into discrete time.
0
1  RT / L

1 0
 0  1 / L 0 






is k  1  
i
k

TJn
i
k

TJn

k
p
p
s
s
1 / L   0 1 / LTvs k 
0
1

RT
/
L
0
1





 



 k  1  1 
TKn p T 0 TC
BT 
T
i k   
sgn  k   TL k 
 k  
H 
H
H
1 H
 k 1   k   Tk 
10
Direct Neural Model Reference Adaptive
Control
Neural Adaptive Observer

Considering any discrete nonlinear plant, it can be described by :
xk 1  f xk , uk 
yk  hxk , uk 

If xk is estimated value, then the standard form of the observer is :
xˆk 1  f xˆk ,U k 


Here, x  i, ,  and u  V .
As there exist some parameter uncertainty and condition uncertainty in
motor system, the open-loop estimates may seriously deviate from the
real ones => error feedback loop should be added to the observer.
11
Direct Neural Model Reference Adaptive
Control
Neural Adaptive Observer


A direct neural adaptive observer is adopted to compensate the
uncertainties.
The two NN are trained offline to learn the dynamics, then the observer is
trained online to compensate the effect of parameter variations.
12
Direct Neural Model Reference Adaptive
Control
Correction of Neural Observer


State feedback correction is important to maintain high precision of the
estimated value.
In this paper, the adaptive correction of ω(k) is accomplished by means of
the output current error e :
e  is k  1  iˆs k  1


Reason: the electrical variable i responds faster to the noise than the
mechanical variable ω => good adaptability.
The output error is backpropagated to the two NN independently and the
weights are adjusted => online training.
13
Structure and Training of NN Observer
Structure Selection of NN Observer



If the structure is selected correctly, the NN can map any nonlinear
function, given a set of input-output sample pairs.
Using the discrete equations for speed and current, the NNs learn the
electrical and mechanical model of the motor.
Input vector of speed observer :
̂ k , iˆk , vk 

̂ k , iˆk  . Input of current observer :
In order to reduce the memory space and running times, a three layer
structure of the NNs is used.
14
Structure and Training of NN Observer
Training of NN Observer


The training is divided into offline training (learn dynamics) and online
training (corrective procedure).
At time step k, the input components are applied to the NNs and the
output is compared with the desired response. The error is then used to
adjust the weights.
15
Structure and Training of NN Observer
Training of NN Observer



Learning rate is set to 0.5 and the criteria used to stop training is 0.003.
Training patterns selected cover all operating regions including starting,
acceleration and breaking.
Online training is just the corrective procedure.
16
Simulation Results



A DSP TMS320C30 is used as coprocessor.
Sampling time of adaptive observer : 100us.
Sampling time of speed controller : 1ms.
17
Simulation Results



The motor under control is a 2.5kW surface mounted PM motor.
For testing the adaptive capability and the robustness of the proposed
observer, 10% noise is added to the measured variables.
To ensure stability, the correction process of the observer is not carried
out in every sample period.
18
Simulation Results


After starting, there is an error between estimated and the actual speed,
but it decreases during stable operation.
Although there exists error and dead time, the estimated speed can satisfy
the requirement of the system.
19
Simulation Results


At a constant speed of 500rpm, the estimated rotor position can track the
actual signal well.
A random variation of the load torque from 0Nm to 0.2Nm is added =>
the estimated waveform contains a little ripple and delay.
20
Conclusions


A new sensorless method is proposed. A NN based observer is adopted to
estimate velocity and rotor position.
Some advantages compared to other methods:





Nonlinear observe ability
Learning and adaptive ability
Robustness to noise
Simulations were carried out and the results show that the proposed
method exhibits good estimating performance.
The prediction errors are kept within a small region.
21