IASTED MIC 2000

1Automatic Control Lab. YNU, Korea

Precise Motion Control of Linear Pulse Motor based on Disturbance

Compensation using Neural Network

2000. 2. 14.

Young Gun Kwon, Jung-il Park

School of Electrical and Electronic Engineering,Yeungnam University, Korea

IASTED MIC 2000

2Automatic Control Lab. YNU, Korea

Purpose

• Propose a neural network-based learning controller

– Finding the current commands to reduce the ripple of error occurred when we control a linear pulse motor

IASTED MIC 2000

3Automatic Control Lab. YNU, Korea

Introduction

• Importance of a linear motor

• What is a linear motor?

• What is a linear pulse motor(LPM)?

– Merits of LPM

– Difficulties in controlling LPM using conventional control algorithm

IASTED MIC 2000

4Automatic Control Lab. YNU, Korea

• Excitation methods of LPM– Micro-step control to reduce force ripple

• Force ripple – Due to nonlinear factor or unmodeled

dynamics

• Studies for reducing force ripple – Finding the accurate model via either

experiments or theoretical studies for dynamics of a LPM

IASTED MIC 2000

5Automatic Control Lab. YNU, Korea

• Purpose of this paper :

– Getting a better performance by finding the current commands considering nonlinear factor and unmodeled dynamics

– Introducing the neural network-based current controller considering these factors at a time

• Validity of the proposed controller

– confirmed by motion control experiments

IASTED MIC 2000

6Automatic Control Lab. YNU, Korea

Principle of Hybrid type LPM

N S

Permanent magnet

Electromagnet

N S

Permanent magnet

Electromagnet

N S

Permanent magnet

Electromagnet

N S

Permanent magnet

Electromagnet

(a) (b)

(c) (d)

IASTED MIC 2000

7Automatic Control Lab. YNU, Korea

Neural network-based current controller

• Linear motor model

• Generating force

eL FFdtdxB

dtxdM =++2

2

(1)

( )

+

−= BABAe ix

pix

pKxiiF ππ 2cos2sin,, (2)

IASTED MIC 2000

8Automatic Control Lab. YNU, Korea

• Current commands

– If we use the current commands in equation (3), the force ripple is generated by unmodeled dynamics.

– Propose a neural network-based current control scheme

=

−= x

pix

pi BA

ππ 2cos,2sin(3)

IASTED MIC 2000

9Automatic Control Lab. YNU, Korea

• Structures of neural network applied in control fields

– Feedback error learning type

– Direct inverse model learning type

– Indirect model learning type

IASTED MIC 2000

10Automatic Control Lab. YNU, Korea

Structure of proposed controller

setpoint y

OutputPlantT H K

2HRM0205-1020L

err MotorDriver

xia

ib

++ A, /A

B, /B

PIDcontroller

CurrentCommand

+

-

++

NeuralNetwork1

++

uPID

uNN1

uIN

NeuralNetwork2

ibia

IASTED MIC 2000

11Automatic Control Lab. YNU, Korea

Structure of used neural networksetpoint(t)

output(t)

out_velocity(t)

velocity(t)

LPF

uNN1

(a) Neural network 1

IASTED MIC 2000

12Automatic Control Lab. YNU, Korea

setpoint(t)

setpoint(t-1)

Output(t)

Output(t-1)

IA

IB

IB

IA

(b) Neural network 2

IASTED MIC 2000

13Automatic Control Lab. YNU, Korea

Specifications of neural network

– Bipolar sigmoid activation function

– Momentum term

– Standard back-propagation algorithm

IASTED MIC 2000

14Automatic Control Lab. YNU, Korea

• The j-th hidden layer output

( ) ∑=

===N

kkjkjjj Qjxvgh

0,,2,1;; Lψψ (4)

• i-th output of output layer

( ) ∑=

===Q

jjijiii Mihwfy

0,,2,1;; Lψψ (5)

• Cost function

( )∑=

=M

iPIDUE

1

2

21 (6)

IASTED MIC 2000

15Automatic Control Lab. YNU, Korea

( ) ( )

( ) ( ) ( )nhnnwwEnwnw

jyiij

ijijij

ηδ

η

+=

∂∂

−=+1(7)

( ) ( )i

iPIDyi

fUwhereψψδ

∂∂

=,

( ) ( )

( ) ( ) ( )nxnnvvEnvnv

khjjk

jkjkjk

ηδ

η

+=

∂∂

−=+1(8)

( )j

jM

iijyihj

gwwhere

ϕϕ

δδ∂

∂=∑

=1,

IASTED MIC 2000

16Automatic Control Lab. YNU, Korea

Experimental environments• Methods of experiments

– Using DSP board to implement control algorithm• TMS320C31

– Motion speed • High speed : 4.5mm/sec

• Low speed : 0.2mm/sec

IASTED MIC 2000

17Automatic Control Lab. YNU, Korea

• Specifications of experimental system

– LPM(2HRM0205-1020L) • Pitch length : 0.8mm

• Stroke : 1m

– PWM current driver

– Linear scale resolution : 20㎛

– DSP board : TMS320C31 • Sampling time : 2.5msec

IASTED MIC 2000

18Automatic Control Lab. YNU, Korea

Structure of experimental system

PCDSP

DAC

DAC

Counter

Driver LPM scale A B/A /B

IASTED MIC 2000

19Automatic Control Lab. YNU, Korea

Block diagram of current driver

LPMPWM

L298NStep

motor driver

LA25-NPCurrentdetector

inputIa, Ib

+

-

PI

IASTED MIC 2000

20Automatic Control Lab. YNU, Korea

Experiment results• Initial conditions of NN1 :

– learning rate =0.3

– momentum coefficients =0.9

• Initial conditions of NN2

– learning rate =0.1

– momentum coefficients =0.9

• Initial weights :– chosen as values from –0.1 to +0.1

IASTED MIC 2000

21Automatic Control Lab. YNU, Korea

Desired velocity profile

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

Velo

city

[mm

/sec

]Time [sec]

0 4 8 12 16 20 24 28 32 36 400.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 x10-3

Velo

city

[m/s

]

Time [sec]

Low speed High speed

IASTED MIC 2000

22Automatic Control Lab. YNU, Korea

Results at low speed

0 4 8 12 16 20 24 28 32 36 40-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10 x10-3

Erro

r [m

]

Time [sec]0 4 8 12 16 20 24 28 32 36 40

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10 x10-3

Erro

r [m

]

Time [sec]

Open loop controller only FF+PI controller

IASTED MIC 2000

23Automatic Control Lab. YNU, Korea

Results at low speed

0 4 8 12 16 20 24 28 32 36 40-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10 x10-3

Erro

r [m

]

Time [sec]0 4 8 12 16 20 24 28 32 36 40

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10 x10-3

Erro

r [m

]

Time [sec]

NN2+PI+FF controllerNN1+PI+FF controller

IASTED MIC 2000

24Automatic Control Lab. YNU, Korea

Results at low speed

0 5 10 15 200.00

0.02

0.04

0.06

0.08

0.10

0.12x10-3

MSE

Learning iteration

0.0050.050PI+FF+NN2

0.0100.075PI+FF+NN1

0.0200.075PI + FF

0.0400.095Open loop

Offset error

(mm)

Peak to peak

error(mm)Controller

Mean squared error, PI+FF+NN2 controller

Performance comparison of each controller at low speed

IASTED MIC 2000

25Automatic Control Lab. YNU, Korea

Results at high speed

0 1 2 3 4 5 6 7 8 9 10

-0.1

0.0

0.1

0.2

0.3 x10-3

Erro

r [m

]

Time [sec]0 1 2 3 4 5 6 7 8 9 10

-0.1

0.0

0.1

0.2

0.3 x10-3

Erro

r [m

]

Time [sec]

Open loop controller only PI+FF controller

IASTED MIC 2000

26Automatic Control Lab. YNU, Korea

Results at high speed

0 1 2 3 4 5 6 7 8 9 10

-0.1

0.0

0.1

0.2

0.3 x10-3

Erro

r [m

]

Time [sec]

PI+FF+NN2 controller

IASTED MIC 2000

27Automatic Control Lab. YNU, Korea

Performance comparison of each controller at high velocity

Controller

Peak to

peak

error(mm)

Offset

error(mm)

Open loop 0.17 0.100

PI+FF 0.13 0.030

PI+FF+NN2 0.10 0.025

IASTED MIC 2000

28Automatic Control Lab. YNU, Korea

Conclusions• Introduced neural network of feedback

error learning type changes a current command to improve position accuracy.

• Neural network works efficiently for reducing the position ripple error.

• We must develop better neural network to operate for periodic error.