8/11/2019 Double Closed-loop Brushless DC Motor Control Based on Variable Structure

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I. INTRODUCTION

The brushless DC motor, which emerged as thedevelopment of technology of electronics, is a new kind of DCmotor, and it is also the important part of modern industry [1].Because of its reliability of operation, brushless DC motor has

been widely used in many special areas, such as aerospace andmining.

At present, the common control technology of BLDCM isthe classical PI control theory [2]. As the BLDCM is ahigh-order and nonlinear system, the PI control which is linearcan not reach the control requirements.

The Variable Structure Sliding Mode Control (VSSMC)is nonlinear, and it is widely used in DC motor controlsystems because of its better robustness. Deal with the specialconfiguration of BLDCM, this paper offers a new kind ofcontrol system, the double closed-loop BLDCM controlsystem based on variable structure sliding mode, andsimulation experiment are used to verify the validity of thesystem.

II. THE BLDCM MODEL

The dynamic balance equation of the BLDCM isdescribed as

au a a a

diu k i R Ldt

= + + (1)

where,

a L , a R , uk and denote the armature inductance,armature resistance, motor constant and the motor shaftangular speed.

The mechanical equation is described as

em t a l d

T k i T B J dt

= = + + (2)

where,

l T is the external load and t k is the torque constant. B and J denote the viscous friction coefficient and inertiaconstant of the motor, respectively.

10

10

a u

aa a a a

l t

R k i ui L L L

T k B J J J

= +

(3)

Choosing ai and as the state variables, the followingstate equation is obtained.

Using Laplace transform in (3), and assuming that(0) 0ai = , (0) 0 = , we can get the equation as following,

( ) ( )( )

( ) ( )( )

ua

a a

t a l

k s U s I s

L s R

k I s T s s

Js B

+= +

=

+

(4)

According to (4), the block schematic of brushless DCmotor is given by Fig.1.

1

a a L s R

+

1

Js B

+t k

uk

Ua

a

l T

Fig.1 the block schematic of brushless DC motor

III. THE VARIABLE STRUCTURE SLIDING MODE CONTROLLER

The design of variable structure sliding mode controllermay go through two stages, first, the switching function,which makes the motion equations work satisfactorily, andsecond, the approach law, which meets the arrive condition ofthe sliding mode.

A The controller of the speed loopThe sliding surface of the speed loop is designed as follow,

( *) s ce c = =

5

where, c is a positive constant.We choose the approach law as follow, and it meets the

arrive condition of the sliding mode.( ) 0 s sign s = , >

6 According to (6), we have,

( )( ) 0

t l

a

K T B s ce c i J J J

sign s

= = = , >

7

assuming that c J = , we can get,

( ) , 0t a l s ce K i B T

sign s

= =

= >

8

list systematically

Double Closed-loop Brushless DC Motor Control Based on Variable StructureSliding Mode

Yuanfeng Huang , Haifeng Wang Guobiao Gu1Institute of Electrical Engineering in Chinese Academy of Sciences, Beijing

2Graduate University of Chinese Academy of Science, BeijingE-mail: huangyuanfeng08@mail.iee.ac.cn

8/11/2019 Double Closed-loop Brushless DC Motor Control Based on Variable Structure

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0

0

l

t t t a

l

t t t

T B s

K K K i

T B s

K K K

+ , >

= + + , <

9

The dc motor has the following parameters,20.009 , 0.554, 5, 0.08t u J kg m K K B = = = = =

Substituting the parameters into the equation (9), we can getthe control low of the speed loop as follow,

0.144 1.8 9 0

0.144 1.8 9 0l

al

T si

T s

+ , >=

+ + , > 10

B The controller of the circuit loopThe sliding surface of the circuit loop is designed as

follow,*( )i a a s ce c i i= =

11

where, c is a positive constant.According to (6), we have,

( ) 0

a ui a

a a a

cR cK cu s ce i L L L

sign s

= = +

= >

12

assuming that 1c = , we can get,

( ), 0

a ua a

a a a

R K u s ci i

L L L

sign s

= = +

= > 13

list systematically

0

0

a a u a

a a u a

R i K L su

R i K L s

+ , >=

+ + , >

14

The dc motor has the following parameters,0.83 , 0.003 , 0.554, 50a a u R L H K = = = =

Substituting the parameters into the equation (9), we can getthe control law of the circuit loop as follow,

0.83 0.554 0.15 0

0.83 0.554 0.15 0a

a

i su

i s

+ , >=

+ + , > 15

IV. SIMLATION AND DISCUSSION

Based on the control laws of the speed loop and circuitloop, simulation studies have been carried out by MATLAB.The variable structure control system of the speed loop isgiven by Fig.2, and the control system of the circuit loop isgiven by Fig.3.

Fig.2 the control system of the speed loop(VSC1)

Fig.3 the control system of the circuit loop (VSC2)

Using two contrrol modules to show the control systemsmentioned in Fig.2 and Fig.3, and adding the mathematicalmodel of BLDCM into the system, we can get the total controlscheme of the system in Fig.4.

Fig.4 the total control scheme of the systemThrough the MATLAB/Simulink simulation, the result isgiven by Fig.5.

Fig.5 the simulation curses of the speed and circuitFrom Fig.5, we can see that the VSC can improve the

system response speed. When applied load suddenly, thespeed of motor has a modest decrease, but it recovers rapidly.

Meanwhile, the circuit tends to increase in equal increments asthe load increase.

V. CONCLUSION In this paper, a new way has been shown to control

Brushless DC motor. Experiment and simulation resultsdemonstrate the VSC, compared with the traditional PIcontrol, can improve dynamic quality effectively, and thesystem achieves excellent tracking performance. It illustrates agood prospect of application and extension.

VI. R EFERENCES[1] Zhen Yuan , Haifeng Wang, Jie Yang, and Guobiao Gu, Research on

Torque Balance of Permanent-Magnet Brushless DC motor , Proceedings of ICEMS , 2007, pp. 786-788.

[2] S Edward Lyshevski, Control of High-performance Permanent-Magnet.Synchronous Motors For Underwater Vehicls. Proceedings of TheAmerican Control Conference, Chicago, Illinois June 2000