791} - 2010 RESEARCH OF NONLINEAR CONTROLLER STRUC lURE FOR LINEAR PERMANENT MAGNET EXCITED SYNCHRONOUS MOTOR REFER TO 2 NONLINEAR CONTROLLER DESIGNS NGHIEN CU'U C A u TRUC DIEU KHIEN
Trang 1JOURNAL OF SCIENC E & IEC HNOLOGY * No 791} - 2010
RESEARCH OF NONLINEAR CONTROLLER STRUC lURE
FOR LINEAR PERMANENT MAGNET EXCITED SYNCHRONOUS MOTOR
REFER TO 2 NONLINEAR CONTROLLER DESIGNS NGHIEN CU'U C A u TRUC DIEU KHIEN PHI fUYEN CllO D O N G CO TUYEN fiNIl DONCi BO
KICH THICH VINH CUU DUA TREN 1 CilAI PHAP DIEU KHUN PHI TUYEN
Nguyen Phung Quang, Dao Phuong Nam
Hanoi Univcrsit}' of Science and Technology
ABSTRACT
Today, linear motions are almost realized indirectly by rotation motors, which cause some inherent weakness The use of motors which have the aibility of direct linear motion making (linear motors) can reject these weakness Because of the nonlinear property in this motor, its controller need
to be refered to a class of nonlinear control method This paper presents 2 nonlinear controller design methods for permanent magnet linear synchronous motor refer to flatness based structure have ability
of dealing with parameter errors and exact linearization structure makes the demand of the separation between two components (Propulsion force and Flux) By using these design solutions, physical quantities reach the reference trajectory and all of currents in the primary section are mobilized to make the propulsion force of this linear motor The simulation results in Matlab - Simulink - Plecs softwares show the good quality, advantage and disadvantage of these two design solutions
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List of Symbols
^sd' ^sq d^ _ ^'^is inductance ( / / )
ifi^ R Mass, Resistance of primary section
[kg,n)
u i Vector of primary section current and
voltage {V,A)
v,v^,w^ Mechanical, Electrical Speed [m/s)
,Electrical Velocity (Rad/s)
F^ , F^ Electromagnetic, load force (TV)
/ ,/ ,u , d,q components of the primary
Current, Voltage ( ^ , K )
p_^ lp Number of Poles, Vector of Pole Flux
(Wb) Xp,d Pole position (m,7?ac/)
I INTRODUCTION
The Linear Permanent Magnet Excited synchronous motor (LPMSM) have operating principles of electromagnetic phenomenon [1,2,3] The use of exact linearizafion method has been presented in [2,3] The task of this paper are introduction of flatness based control method and analyse, compare to exact linearizaton method has been used
Trang 2II FLATNESS BASED CONTROL
METHOD AND IIIE USE I O K DESKiN
OF LINEAR PERMANENT MACJNET
E \ ( IIED SN N( MRONOUS M O I O R
In [4,5], the Hat svslem definition has
been proposed in l')')2 by flics M., Levinc J.,
Martin P., Rouchon P with the following
content:
The nonlinear svstem — = /(vji)
dt
with State variables v € ;•?." Input variables
//G i'*^'" This svstcm is called fiat system if
there exist the V = (.V|,l', r,„) satisfy all
follow ing conditions:
F satisfy ,cj is Unite (I)
There exist
du
v - f
1 unction
d'u
X.U.-dt X.U.-dt"
There exist function P,Q satisfy
dv d'u^
P
u = Q
• dt dt'
dv d'v
V ' ,
and
,r is finite (2)
• >" = (j^p.V:' -'^m) is differential
independence in the mean of no H
function existence satislv
H \',-dv d' v
dt dl'
finite number (3)
= 0 , A^ is a big enough
If the system satisfy three conditions (I),
(2), (3) then this system is called fiat system
and (v'p>'-., ,.!„,) is called fiat output
In [4,5], the mathematical model of
LPMSM is represented in (4) and LPMSM is
the fiat output with the flat variable
y = [0,l^j,F ) has been proposed.:
cit
,ll
"1
(It
R
' , ; , ' •
••' /
/ •
+
'271
T
f27r 1
V
V
/.^,
'2TT
V'
T
u
+ •
(4)
''.K'}'
/ • • / • •
civ niT eld
"'di~'2^'Jl'
However the description of this motor model as input variables is calculated from flat output is complicated, makes some difficulties
of control design
lo reduce these difilculties, wc can design control structure reler to LPMSM Model separation become 03 subsvstems and each of all satisfies the flatness property [5]
Hence, a detail structure is proposed
(figure I) refer to 03 Controllers: Current ( R^),
Speed (/?,,), Position {R,) Controller The
detail results are pointed out in [5]
III ANALYSIS AM) COMPARISON OF THE USING Ql ALITN OF 2 NONLINEAR CONTROLLERS
The main difference between these two controller is pointed out in current loop because [2,3] show that the direct separation method is
used in "Subsystem - Current There are soine
control methods for speed and position Controller and [2.3] point out the design method refer to optimal standard
I 0 compare accuralciv between the two nonlinear controller, the speed and posiuon loops of these two controller are the same result and from (4) we have the load force is estimated bv;
sq
dt ^ '
The analysis, comparafion between 2 controllers under 2 contents: Current error Processing and treatment of limitation of primary voltage (w,^,w^J
Trang 3JOURNAL OF SCIENCE & TECHNOLOGY * No 79B - 2010
iiJs + -j<',ii
v_Fq
Figure I The control structure of LP MS.\f refer to flatness based Control Method
2.1 Current error Processing
In the exact linearization Controller [2,3],
State feedback (Figure 3) has been realized
easiK refer to sums
" l
'/,
-ll
= f'su
T '
'1
0
+
0
— K^^
T
(^„-v,+v'v)
1
^'l 11',
I f ;
(6)
However this structure is highly sensitive to
motor parametter errors iL^j,L,.^,R,.,'ippj
For this reason, it makes bad influences in
02 current Controllers R^^j, R,^^
For this problem, flatness based Controller
have some following treatments (Figure 3):
The "Calculate (ul^, u]^ \ " makes the reach
trend of {l,dJsq) i" principle If there exist
current errors because of motor parametters
errors or disturbance influence then error
processing will realize by Feedforward
Method (figure 2) and R^d^K, ^^e PI
controllers, help /, reachs I,, as the PTl
\_
Besides, this process controller can be also realized by exact linearization method to inject influence of other channel in motor
model (figure 2)
Figure 2 The design of current errors
b.Treatment of limitation of primary voltage
The treatment of Controller when the primary voltage (w,^/,w,,J is bigger than limitation value has been represented in [6] In the flatness based control structure, there is need of changing the reference f/*^ {^)J7C, (^))
become (Cr (^)'C'-(^)) ^"^ ^^^ limitation is
switched off Hence, we get these results (8), (9):
«,, {k) = «.v (^) - -5", (^); V {k) = «.„ [k)- K , (*),
sd,g
Trang 4>4HI^>
10
' 1 ~ '
i
•1 l l l " 1 \
4 i
;«•()
; I '
»-/r,
/<„
—
S l i i l c
I c i ' i l h ' U ' k
Figure 3 The control structure of l./'MSM refer to exact linearization Control Method
^KAI<) =
''"Ak)+~\{k)l.^f,ijk)
1 ]
•'•' + R^
[T, j
/•
"' + R,
T +
[ • » / ( ]
T
hc^\k)- — v[k)t.Ju,Xk) [l, \
^ + R
[T J
fi.,-^-^R ]
[T J
-1-['^f
I r 1
By this idea, the treatment to exact
linearization Structure (figure 3) can be
realized refer to current errors correction to
switch off the i:i!crgrc:l p::r: in (.'^,^,, .'•?,^J
This Technique has been realized in [3]
under digital PI controller with output
limitation and anti - windup
IV V E R I F I C A T I O N BY S I M l LATION
All the system will be simulated refer to
these 02 methods by X\\Q figure 1.3 in Matlab
Simulink/ Plecs software with the sample
Period 7] = 100/i.v and the rctcrcncc trajecttMV
of position is: xj!, = 0 5 ( c o s ( 7 r / ) - i V m ) (10)
From (4) (5), (10) and//^'//rt' 7 wc have:
V* =-0,5.7r.sin(7c/);w'^, 371V
T L f:M
«/ i / ( ' ,
dv -^
in +h
r it
(\2)
^ + Ri :KV ' - " - ^
Simulation parametters are from the LSI IK 1004 I.SMIO.vx(Baumueller):
Nominal Current 0.8 A Number of poles 4 Pole pitch 72 mm
Resistance of primary section 8.5 Q
d _ axis inductance 47 mH
(/ _ axis inductance 88%
Flux 0.8Wb
\ C O N C L U S I O N The results of speed Position, Current,
estimated force behaviour (figure 4.5) show
good qualifv of these two methods The Current behaviour of flatness based Controller is better than of exact linearization Controller because of
the effect of "Current error Processing" (figuf^
I) and the ability to inject influence of other channel in motor model (figure 2) However,
the advantage of exact linearization Controllei
is the ignorance of differential operator On thf other hand, the existance of differentia
46
Trang 5JOURNAL OF SCIENCE & TECHNOLOGY * No 79B - 2010
operators (12), (13) in flatness based Controller
cause the resuhs is only good for the small
enough sample Period T
; \
; \
; ;
* * ! 1
^ ^ V ;
; ^v
;
Time (s)|
, 504
5.02
O
L^r : J
/ ^ • • •
^^^ JJ-LJAJJIJ/ILJIILIAIJIIUJIIU
i i
-.rxc .'
l^c i
1 I
0 0 0 5 0 1 0 15 0 2 0 2 5 0 3 0 35 0 4 0 45
m
Figure 4 The Simulation results refer to
flatness based Control (a Position behaviour;
b Speed behaviour; c Current behaviour; d
Load force estimation) •
0
.0 05
-0 1
.0 15
_ 0 2
c
5 <I25
C
^ 03
4)35
.04
4)45
1 ^ x U'-^''/'
;• [ - - > ^ - - - ; - - ^ ^ ^
r \ r • •
-
^r'r-\ :
Time(s)
0 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45
(O)
0 0 2
• " -0 4
E
QJ
CL
J~
.08
.1.2
- 1 6
^ 1 1 1 1 1
i- j ; ;
\ v i ^ V
I > \
1 ^ \
1
:
: Ti|ne(sJ~~~—
8
••fa
: F : i 1 i
- - - • , - ^ , ^ ; —- 1 1
:
i- -> y-i- -L
y^ \ ' ; ;
'• ' • 'A '^ •
^
-i^^F i
; : Tirjie (s)
0 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45
(d)
Figure 5 The Simulation results refer to exact linearization Control (a Position behaviour; b
Speed behaviour; c Current behaviour; d
Load force estimation)
Trang 61 .lacck F.Ciircas /bigiiew I.Pieeh; Synehronous motor transportation and automation systems; CRC Press 2000
2 Dao Phuong Nam, Nguven Phung (,)uaiig; ( oiilrol Structure with direct decoupling for linear permanent magnet excited synehronous motor; louriial of Science and fechnology Vol 75,
2010
3 Dao Phuong Nam; Design, assembly and operating linear drive svslem under synchronous motor: Master Ihesis Ha Ni)i Dnivcrsilv ol" I echnology, 2007
4 F.mmamicl Delaleau, Alcksandar M.Slankovie; I lalness based hierarchical control of the I'.M synchronous motor; Proceeding of the 2004 American Control Reference 2f)04
5 Le Ngoc Hung Ninh Van Cuong; Research of flatness svsiem theory and control structure for permanent magnet linear svnchronous motor; (iradualc I hesis Ill 1 2f)IO
6 Nguven Phung Ouang .lorg Aiidrcsas Dittricli; Vector Control of ['hrcc - Phase AC Machines-Svstem Development in the Praeliee, S|)iinger, 2008
Author s aclclres.s: Dao Phuong Nam •I'el.:( f ,S I )9S3565 1 17; email: namdp-autolab a mail.hut.edu.vn
Centre for Research and Development of 1 ligh I echnologv Hanoi University of Science and 1 eelmoh)gv
No 1 Dai Co Viel Str., Ha Noi, Viet Nam