A Shaft Sensorless Control for PMSM Using Direct Neural Network Adaptive Observer

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

Southern Taiwan University

Department of Electrical Engineering

2

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

3

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.

4

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.

5

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.

Total input Xj : i

ijij WYX

6

Multi-Layer Feedforward NN and Backpropagation Method

A sigmoidal nonlinearity function is applied to the unit j to obtain Yj :

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 :

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.

)1(1

jxj eY

2)(2

1jojo dYE

7

Multi-Layer Feedforward NN and Backpropagation Method

Learning rule for adjusting the weights :

Some steps for calculating local error : Calculate changing rate of an output unit when its activation is

changed.

Calculate changing rate when the input sum of a node in output layer changes.

Calculate the changing rate of preceding layer unit error when a unit in preceding layer is changed.

joijiji YEkWkW 1error local

rate learning

oE

jojojo

oj dYY

EE

`j

j

jjj X

Y

Y

E

X

EEX

ijj

ji

j

j jii WEX

Y

X

X

E

Y

EEO

8

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.

sppss UJnnkRIIL

L

dt

d

1

0exp

0

0

LpT

sp T

HH

C

H

BJnI

H

nk

dt

d 1

1

0exp

dt

d

• 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.

Tsss iiI , Tsss UUU ,

01

10J

9

Direct Neural Model Reference Adaptive Control

Motor Model of PMSM

The typical control design approach is transforming the motor dynamics into the rotor frame.

sps

p

ps vL

L

LKni

LRn

nLR

dt

di

10

01

10

H

T

H

C

H

B

H

KNi

dt

d LTs

sgn1

0

dt

d

sps

sps

VJnv

IJni

exp

exp

10

Direct Neural Model Reference Adaptive Control

Motor Model of PMSM

In order to implement in computer, the equations are put into discrete time.

kTvL

L

LkTJnkiTJnki

LRT

LRTki spspss

/10

0/1

/1

0

10

01

/10

0/11

kTH

Tk

H

TCki

H

TKnk

H

BTk L

Tp

sgn

1

011

kTkk 1

11

Direct Neural Model Reference Adaptive Control

Neural Adaptive Observer

Considering any discrete nonlinear plant, it can be described by :

If xk is estimated value, then the standard form of the observer is :

Here, and . 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.

kkk

kkk

uxhy

uxfx

,

,1

kkk Uxfx ,ˆˆ 1

,,ix Vu

12

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.

13

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 :

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.

1ˆ1 kikie ss

14

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 : . Input of current observer :

In order to reduce the memory space and running times, a three layer structure of the NNs is used.

kik ˆ,̂

kvkik ,ˆ,̂

15

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.

16

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.

17

Simulation Results

A DSP TMS320C30 is used as coprocessor. Sampling time of adaptive observer : 100us. Sampling time of speed controller : 1ms.

18

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.

19

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.

20

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.

21

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.