total sliding mode position control of a linear variable ... · a linear variable reluctance motor....

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Ruchao Pupadubsin Industrial and Control Automation (ICA) Laboratory

NECTEC

NECTEC ACE 2010 Pathumthani, Thailand

September 23-24, 2010

Total Sliding Mode Position Control of

a Linear Variable Reluctance Motor

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Contents

� Introduction

� Structure and Principle of Linear

Variable Reluctance (LVR) Motor

� Position Control

� Experimental Results

� Conclusions/Future work

“Total Sliding Mode Position Control of a Linear Variable Reluctance Motor”

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�� Applications of linear motion

automation process

Transportation

Elavator

Material handling

Assembly Payload

Applications

Introduction


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Introduction

�Technologies for linear motion

– Rotary motors with mechanical transmissions

Lead screw

Tooth belt Disadvantages

Mechanical transmission losses, high

maintenance, mechanical limitations on

acceleration and velocity, limited accuracy

Advantages

Simplicity for implementation, lower

cost, more widely use


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Introduction

�Technologies for linear motion

– Linear motors (direct drive): permanent magnet, reluctance, induction, DC

Advantages

Less friction, higher accuracy, no

backlash, low maintenance, longer

lifetime

Disadvantages

Higher cost, high maintenance (LPM)


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Introduction

�Goals of paper

2.2. Implement the developed position

control, which is based on a simplified

sinusoidal flux model for LVR motor

1.1. Develop a simple position control

with good performance for LVR motor


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Structure and Principle of LVR Motor

� Two E-cores moving along the stator

� Motor windings are installed on each side of the E-cores

� Strong magnetic coupling between phases

� Symmetric structure with zero normal force when balanced


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Advantages:

Simple structure, compactness, low cost (no

permanent magnet)


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� Phase voltage equations of the LVR motor in the dq0

domain

� Force function of the LVR motor


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� Mechanical dynamic equation of the LVR motor

M : Moving mass

B : Viscous friction coefficient

FL : External force


LF Mx Bx F= + +��

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Position Control

� Design for high precision position control

for manufacturing automation applications

� Use the dq0 theory of classical synchronous

reluctance motors

– Sinusoidal reluctance/inductance

approximation


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� Control block diagram

1 2 3


Current

command

generation

LVR

motor( )di j jk i i−

ji

x

x�

Udji ju

dx

dx�

dx��

Velocity

calculation

+-

+-

Curbing

Control

e

e�

cU

S-profile

command

generation

BMCUBaseline

Model Control

ρ

Total Sliding Mode Control

Force Control

++

Position Control

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Position Control

�� S-curve profile command1

Ref. [15]


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� Total Sliding Mode Control2

1 2

1- ,n n

BC C

M M= =


LF Mx Bx F= + +��

1 2( ) ( ) ( ) ( )n nx t C x t C U t W t= + +��

( ) lumped uncertainty

U F

W t

=

=

Position Control

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� Total Sliding Mode Control2

UBMC

: Baseline model control

Uc

: Curbing control

Position Control


BMC cU U U= +

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� Total Sliding Mode Control

:Baseline model control

2

1st term to compensate nonlinear effects

2nd term to determine system performance

Position Control


1 12 1 2BMC n n n p d

U C C x C x k e k e− − = − + + +

� ��

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� Total Sliding Mode Control

:Curbing control

2

To eliminate the perturbation and uncertainty effects

Position Control


12( ) ( ) sgn( ( ))c nU t t C S tρ−= −

( )W t ρ<

The selection of ρ affects the chattering phenomena

and system stability performance

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Position Control

� Desired phase current command3

� Constant parameters

Ref. [7]


1 1 1

2 2 2

3 33

cos sin1

cos sinsgn( )

cos sin

dd

dd

d

i x xF

i x xF

x xiγ

− = − −

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Position Control

� Current control3

- Desired phase voltage

ki= Current control parameter


( )dj i j ju k i i= −

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Position Control� Experimental setup

- dSPACE controller board

- Three phase power inverter

- 14kg payload

- Two desired trajectories for experimental test

- Short-distance profile: 400 µm

- Long-distance profile: 10 cm

- Two controllers for experimental test

- Input-output linearization control [8]

- Total sliding mode control


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Position Control� Experimental setup


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Experimental Results

Position and position error responses for short-distance profile: 400 µm

Max dynamic error

≈ 61.9 µm

Steady state error

≈ 27.5 µm


Previous [8]

Control

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Positio

n [µm

]P

ositio

n e

rror [µ

m]


Position and position error responses for short-distance profile: 400 µm

Max dynamic error

≈ 31.7 µm

Steady state error

≈ 10 µm


Total Sliding

Mode Control

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Position and position error responses for long-distance profile: 10 cm

Max dynamic error

≈ 331.4 µm

Steady state error

≈ 22 µm


Previous [8]

Control

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Position and position error responses for long-distance profile: 10 cm

Max dynamic error

≈ 264 µm

Steady state error

≈ 15 µm


Total Sliding

Mode Control

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Conclusions/Future work

�Advantages

- Simple and computationally efficient for

implementation

- System robustness to parameter variations

� Disadvantages

- Chattering phenomena problem

- Future work to reduce chattering phenomena to achieve higher accuracy for high-precision application


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Thank You


total sliding mode position control of a linear variable ... · a linear variable reluctance motor....

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