1/18

2007年2月22日

鄒 應 嶼 教 授

國立交通大學 電機與控制工程研究所

PID Control of a DC Position Servo Drive

LAB808NCTU

Lab808: 電力電子系統與晶片實驗室Power Electronic Systems & Chips, NCTU, TAIWAN

台灣新竹•交通大學•電機與控制工程研究所

台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、單晶片DSP/FPGA控制

http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan

2/18

Position Control of a DC Servo Drive for a Motion Table

Encoder feedback

Servo drive

Y

X

Positioncommand

How to synthesize the PID control law for a DC position servo drive? Block Diagram Construction and Modeling Parameterization Control Architecture or Controller Configuration Control Laws or Control Equations Determination of Control Parameters Controller Realization

3/18

Block Diagram of PID Control of a DC Position Servo

位置命令脈寬調變

產生器

解碼器

Controller

dcVT1

T2

T3

T4

va

全橋式脈寬調變電壓放大器

光電編碼器

直流伺服馬達

T 1 T 2 T 3 T 4

功率晶體

驅動電路開關式

電源供應器

EMI Filter

4/18

Block Diagram of a Practical DC Position Servo Drive

dcVT1

T2

T3

T4

va

電流控制速度控制位置控制位置命令

全橋式脈寬調變電壓放大器

光電編碼器

直流伺服馬達

T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

開關式

電源供應器

速度估測

解碼器

濾波器

EMI Filter

5/18

Block Diagram of a Practical BLDC Servo Drive

dcV

T5

T6

電流控制

&

換相控制

速度控制位置控制位置命令

三相橋式脈寬調變電壓放大器

光電編碼器

無刷直流伺服馬達

T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

開關式

電源供應器

速度估測

解碼器

濾波器

T3

T4

T1

T2

T 5 T 6濾波器

6/18

Motion Profile of a Position Servo System

(c)

(a)

(b)

t

t

t

s1

s1)( sa )( s )( s

a(t) : angular acceleration (t) : angular velocity(t) : angular position

s1

s1)( sa )( s )(s

pK

The proportional control of an double integrator plant is inherently unstable!

7/18

Multi-Loop Control Architecture

PositionController

VelocityController

Velocity Feedback

Position Feedback

Machine TableCurrent

ControllerPower

Amplifier

Current Feedback

Motor

MotionPlanning

PositionCommand

VelocityCommand

The purpose of the control loop is to eliminate the loop dynamics. Cascaded control loop design is inherent robust for practical

applications. Inner loop must be designed with higher bandwidth than outer loop. The loop controllers design should be designed from inside out. Each controller can be design with a PID controller with possibile

necessary phase leading compensation.

8/18

PID Control of a DC Position Servo

Ref: Benjamin C. Kuo and Farid Golnaraghi, Automatic Control Systems, Wiley Text Books, 8th Ed., Aug. 2002. pp. 402-436.

mm BsJ 1

TK

EK

2K

rCommand

preamp Power amplifierwith current FB DC motorGeartrain load

Tachometer

Sensory

Position of control surface

r e )(sKp

Sensor preamp

sLR as 1aE aI mT N

Gearratio

s1

m

m y

1K

Current feedback

Tachometer velocity feedback

)(sKv )(sKc vK

9/18

Modeling of a DC Position Servo Drive

mm BsJ 1

dT

Te m

aa RsL 1av

ai

TK

EK

s1 m

emfvs

K ivPWMK

*ai

sKK icpc

pvK

*m

pvK)1(

PLCK*m

Current loop

Velocity loopPosition

loop

Ra 4 7. (ohm )

KT 0 4511. ( Nm / A )

J m 0 00098. ( Kg m )

Bm 0 0015. Nm / ( rad / s)

K I 0 4. ) (V / A (H)La 0 011.

KE 0 4511. V / (rad / s)K V

10 20000 04775

/.

rpmV / (rad / s)

SENSORS & AMP DC SERVO MOTOR

f kHzs 2

CURRENT SENSOR

PWM AMP

TACHOGENERATOR

CURRENT LOOPCONTROLLER

VELOCITY LOOPCONTROLLER

DUTY-RATIO LIMITER

G sc( )G sv( )

CUR. CMD LIMITER

Kz

c

0 62202

.Kpz

v

255 635

1

1

.

gain

180

80Dd

max %%

gain

18 0

8 0

max. .

.*vi

Table 1. Parameters of a 1HP dc position servo drive.

Vdc=150V

POSITION LOOPCONTROLLER

30PLCK

10/18

Simplification with Intrinsic Property

mm BsJ 1

dT

Te m

aa RsL 1av

ai

TK

EK

s1 m

emfvs

K ivPWMK

*ai

sKK icpc

pvK

*m

pvK)1(

PLCK*m

Current loop

Velocity loopPosition

loop

For study purpose, we can eliminate the current loop!

11/18

Position Servo Without Current Loop

mm BsJ 1

dT

Te m

aa RsL 1av

ai

TK

EK

s1 m

emfvs

K ivPWMK

pvK

*m

pvK)1(

PLCK*m

Position loop

Velocity loop

What about to eliminate the velocity loop?

12/18

Position Servo Without Velocity Loop

mm BsJ 1

dT

Te m

aa RsL 1av

ai

TK

EK

s1 m

emfv

PWMK

*m

PLCK

Position loop

Now, we have a very simple P-controller! What about its performance for practical applications?

13/18

Position Servo with Small Ra and Bm

mm BsJ 1

dT

Te m

aa RsL 1av

ai

TK

EK

s1 m

emfv

PWMK

*m

PLCK

In practical applications:The armature resistance is very smallThe friction constant is also very small

Neglect these parameters!

Position loop

14/18

A Pair of Complex Poles and a Pole at the Origin

sJ m

1

dT

Te m

asL1av

ai

TK

EK

s1 m

emfv

PWMK

*m

PLCK

Position

loop

m2

1sLJ

K

am

Tav

EK

s1 m

emfv

PWMK*m

PLCK

Position

loop

Under zero disturbance condition:

15/18

Deduction of the Motor Plant

22

2

22

2

2

11

1

)(o

o

am

ET

am

T

TEam

T

am

TE

am

T

m sK

LJKKs

LJK

KKsLJK

sLJKK

sLJK

sG

am

ETo LJ

KK

EKK 1

mavs1 m

PWMK*m

PLCK

Position loop

22

2

)(o

om s

KsG

16/18

Effect of Inner Current Loop

C. K. Taft and E. V. Slate, "Pulsewidth modulated DC control: a parameter variation study with current loop analysis," IEEE Trans. on IECI, vol. 26, no.4, pp. 218-226, Nov. 1979.

RE

IM

RE

IM

Kv s1

RLs 1

SJsKr

REF )(si )(s

PWM )(s

Ka

KsKp

REF

Kv s1

RLs 1

SJsKr

)(si )(s

PWM)(s

Kp

Ks

Ka

Ki

17/18

Model Reduction of a Current Controlled Drive

REF

Kv s1

RLs 1

SJsKr

)(si )(s

PWM)(s

Kp

Ks

Ka

Ki

Current loop

REF

s

1

c

c

i sK

1

SJsKr

)(si )(s )(s

Kp

Ks

The current control can be reduced to a first-order system with an equivalent bandwidth of cl. The back emf can be considered as an external disturbances within the current loop.

18/18

Extended Readings

Control System Design Guide, George Ellis, Academic Press, 3rd Ed., February 17, 2004.

Feedback Control of Computing Systems,Joseph L. Hellerstein, Yixin Diao, Sujay Parekh, Dawn M. Tilbury,Wiley-IEEE Press, August, 2004.

DC Motors, Speed Controls, Servo Systems, including Optical Encoders, (Chap. 6: Brushless DC Motors)An Engineering Handbook by Electro-Craft Corporation,Hopkins, MN, Fourth Edition, 1980.

Incremental Motion Control: DC Motors and Control Systems, B. C. Kuo and T. Jacob, 1978.