vector controlled permanent magnet synchronous motor. To overcome these drawbacks, various adaptive. (PMSM) drive. In the proposed scheme, a direct fuzzy ...
IEEE PEDS 2005
Hybrid Model Reference Adaptive Speed Control for Vector Controlled Permanent Magnet Synchronous Motor Drive M. Nour, I. Aris, N.Mariun, and S. Mahmoud Department of Electrical and Electronic Engineering University Putra Malaysia 43400 Serdang, Selangor, Malaysia mutassim.nour(Znottinjfham.edu.my; ishakgeng.upm.edu.my Abstrad-This paper investigates new form of a hybrid model reference adaptive speed control (HIMRASC) for vector controlled permanent magnet synchronous motor (PMSM) drive. In the proposed scheme, a direct fuzzy logic controller (FLC) is employed as the main controller, and model reference based proportional integral (PI) controller as the adaptation controller. The design and optimlzation of the FLC and the adaptation mechanism prsne. T Thhe efficiency fiiec and n prfrac areare~~ Of th the presented. performance of HMRASC is examined, by simulation at different operat..g conditions. Th
operatingcondtionsstudi
operatinglu contions.p Thee commandsfromstanditions stu includevarious step speed commands from standstill with
nominal and changes in motor parameters and load torque. The results obtained are evaluated and compared the results o over direct F1C especially for load disturbances and lloade direct inertia variations.
achireve sChowt chMRanis achiesecal fhor suapertior duperisrbanHMRAnd
Keywords-PMSM drive; fuzzy logic; speed cotrol; model reference; adapive control.
I. INTRODUCTION Recent development in the field orientation control (FOC) method and electric drive technology, permanent magnet synchronous motors are becoming very popular in high performance motor drives applications compared to other types of motors. Some of PMSM advantages features including high efficiency, small volume, high power density, fast dynamics, large torque to inertia ratio, and low maintenance costs. Their applications can be found in machine tools, servo and robots, in aerials, in x-y tables, in computer equipment, in textile machines, electric vehicle, and ship propulsion [1]. Fast and accurate speed responses, quick recovery of speedrom load disturbances and insensitivity to parameter variation are some of the important criteria of high performance drive system. The conventional PI and proportional integral derivative (PID) contollers have been broadly used as speed controllers in PMSM drives. However, the conventional fixed gain PI and PID controllers have
0-7803-9296-5/05/$20.0O © 2005 IEEE
difficulties in dealing with dynamic speed tracking, parameter variations and load disturbances [1-3]. To overcome these drawbacks, various adaptive controllers have been demonstrated [1]. Fuzzy Logic (FL) is used as an altemative for conventional control theory to control nonlinear complex plants where accurate mathematical modeling is difficult. The design of FLC does not require the knlowledge of the mathematical model of the plant. FLC
provides a systematic way to incorporate human experience in the system modeling and design of the controller. The use of
FLC as a better alternative to PI and PID, to overcome the limitations, has been thoroughly demonstrated [1-4]. However, the current FLC employ large number of rules (7x7), which require powerful processors and large memories for implementation. Also, up to date, studies of FLC have not
addressed the performance ofthe controller over a wide speed range (especially at low speeds). In addition, direct FLC cannot adapt themselves to changes in the operating conditions. They can adjust their behavior from one rule to another, but the rules themselves do not change. Therefore in order to get the desired system performance despite changes in the operating conditions, some form of adaptation is required. This paper investigates new form of hybrid model reference adaptive speed control (HMRASC) for vector controlled PMSM drive. The HMRASC consists of two functional blocks. The first one is direct FLC whose inputs are the error and change of error measured between the actual motor speed and the desired speed, and its output is the command current (torque command). The second one demonstrates the model reference and PI controller as the adaptive scheme. In the proposed system, the output speed of the reference model is compared with the actual speed of the motor. The resulted speed error is applied to a simple PI controller. The PI output signal is added to the direct FLC output to compensate for any deviations of the motor speed from the reference speed. The performance and effectiveness of the HMRASC is evaluated by simulation for various operating condition using the real parameters of 400W PMSM drive system.
618
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3hr
controller form the adaptation mechanism, which serves as the
adaptive auxiliary regulator to adapt performance deviations. ibThe adaptation mechanism presented is based on signal adaptation approach in which the controller output signal is modified. Detailed explanations and design of the two controllers are explained in the following section.
+ i. a
X0,
Spud
T,'
dq
T
COWrollW Curml
Figure 1. Vector controlled PMSM drive II. PMSM CONTROL DRIVE STRUCTuRE Fig. I demonstrates the basic building blocks of a vector controlled PMSM drive used in this work. The drive consists of the speed controller, current controller, PWM generator, incremental encoder, 3-phase inverter, and diode bridge rectifier. The PMSM drive blocks are designed built and simulated using Simulink from Mathwork [5]. A. Mathematical model ofPMSM The mathematical model of the PMSM in the synchronously rotating reference frame can be represented by the following equations.
dl=q
vq
w-m L
d
R+L
R+Ld -r dt j j +
PdpLd
qLi L"m'f
l
(I)
T = 1.5 P [2f iq + (Ld - Lq )'qd)]
(2)
Te =Jm dw-
(3)
+Bm.om +TL
Where vd and vq are the dq axis voltages, id and iq are the dq axis currents, Ld and Lq are the dq axis inductances, R is the per phase stator resistance, P is the number of pole pairs, Xf is the rotor permanent magnet flux linkage, Te is the electromagnetic torque, TL is the load torque Jm is the rotor inertial constant, and Bm is the rotor frictional coefficient.
Sie te d
permanent magnet on the rotor and no flux weakening is included, id is set to zero. This makes the vector controlled PMSM task easier and the electromagnetic torque can be simplified as Te=1.5PXfIq. III. HMRASC BASED PMSM DRIVE Fig. 2 shows the proposed HMRASC based PMSM drive, The direct fuzzy logic controller, which is the main controller processes the error between the motor speed and the reference speed, and generates the necessary torque current to meet the required speed performance. The reference model and the PI
A. Design of the directffuzzy logic controller The inputs to the direct FLC are the scaled speed error E(KT) and the scaled change in the speed error CE(KT), where KT is the sampling instant and T is the sampling time. The gains are adjusted to normalize the universe of discourse to [-1, 1]. The use of normalized universe of discourse is an advantage for practical implantation specially when using a fixed-point digital signal processor (DSP) [6]. The normalized error and change in error at a sampling instant KT can be
expressed in equation (4)
E(KT)=w:(KT )CE (KT)
=
(KT)
E (KT) E (KT T
T)
(4)
Where E(KT) is the speed error, co,(KT) is the reference speed, 4o(KT) is the actual speed, CE(KT) is the change in the speed error and T is the sampling time. The direct FLC consist of four stages; fuzzifications,
knowledge base, fuzzy sets and rule base, rules evaluations
(inference engine), and difuzzification. Fuzzification is the process of mapping the crisp variables E(KT) and CE(KT) into fuzzy sets with a degree of fulfillment determined by the associated membership function (MF). MFs can be triangle, trapezoidal, bell, Gaussian, or any other polynomial- based curves [6]. However, the choice ofthe MFs shape and distribution in the universe of discourse is an iterative process. In this work various MFs shapes were studied and evaluated by simulations. However, to simplify mathematical computation and practical implementation, the shape of the MFs used in this work are triangle and trapezoidal. The MFs and their distribution for E(KT), CE(KT) and L4(KT) are shown in Fig. 3. E(KT) consists of seven MFs, CE(KT) consists of three MFs and the output current Iq have seven MFs as follows: Negative (N), Positive (P), Zero (ZE), Negative Large (NL), Negative Medium (NM), Negative Small (NS), Positive Small (PS), Positive Medium (PM), and Positive Large (PL). The membership functions are distributed as shown in Fig. 3 to achieve fast transient response and low steady state error. The shape and distribution of the MFs for the input and output are optimized based on the experience and intensive simulation study using the Matlab Fuzzy Logic Toolbox and Simulink from the Mathwork [5,7]. The choice of the gains GE, Gc, and Gu, indicated in Fig. 2 play a crucial role for the performance of the direct FLC [1,2]. In this paper, the gain values are selected by iteration
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controller
Direct FLC
Figure 2. MRAC based PMSM drive
and taken as GE =1, GC =10, and GU =5. However, in order to gravity of the fulzzy set 'q on the interval ;=1 to i=N. The obtain the best performance for different operating conditions general expression for COM method of deffuzzification, is these values should be adjusted and tuned. On the other hand given in (5) N all the three gains are-set to unity for HIMRASC. lm(F processed by the control The fuzzy inputs E and CE are mN(CE)}. E qI,Zqa) 'p02 a~~C (5) Output 1x - =y. rules evaluation stage. Rule evaluation process is a kind of m (I qji) , THEN.... which is based onE conditional statements like IF.......... the fulzzy sets. It uses the suitable rules in the knowledge basei=z Wee' stemmesi fteiptadmI)i h to make the appropriate decision. The formation of the conltrol rule isbase onthe nowedgeof he PSM riveandthe output corresponding to the membership of Input. experience of the motor drive engineer. Table 1 shows the fuzzy control rule base used in this paper. Each rule is N-M PEiM'ot_ 1 NL expressed as follows: Rule x: IF E is NL AND CE is N THEN 0.8t 'q is NL. The fiuzzy operator used for the fulzzy rules is AND 1 08 11 -E0.8 (no). The AND operator can be interpreted as intersection or algebraic product. Therefore for Rx, mNL,.N = min{mNL(E) , ,}0 La|a 0 TIhe formation of these rules can be understood as 1 follows. For example ifwe consider the rule IF E is NL AND CE is N THEN 'q is NLEN e.P The condition E is NL (negative large) impl-ies that he £ actual motor speed is much higher than the desired speed, and 0. g still is that motor speed CE is N (negative) implies the the n g r e accelerating above the reference speed. In other words 0i controller at the previous step is driving the motor speed g 0.2 upward. Therefore, as a control action, we set the motor crent yq to in (negative large) to turn the speed in the
opposite direction. is reverse process of fuzzification. Defuezification the The input for the defuzzification block is the aggegate output fulzzy set (ombined output of each rule) and he output is a single number (the crisp curenit command Iq*). Various
. G 0.8 . o
defuzzification methods can be used to produce a crisp output value [8,9]. However, te choice of the proper metodT is a compromise between accuracy and computational burden. is Here,iThe commonly used center of mass (COM) method D b q [1]. This used to defo aiffthe current command defhzzification metiod finds a point representing te center of
620
.41 0 0.5 (a) Speed error E P ZE
-0.5
o
05
qi
(b) Change in speed error CE
NL
PL
NM NSZEPS P
j
i
c
0.8 M 04 0 . 0
m
NM
L
l
|
0 -0.5 (c) Current command 11 Figure 3. Membership finction.
-0.5
The adaptation mechanism, shown in Fig. 2, is based on the model reference principle where the desired performance is achieved the reference model that provides the desired output to thebycommand signal. The speed response produced by the reference model is compared with the actual motor speed. The resulted error term Ec is an indication of the performance of the direct FLC. If Ec is zero, this means that
TABLE 1. FUZZY LOGIC CONTROL RULE BASE Eror U PL PM PS ZE NS NM NL E PL PL PM ZE NM NL NL .5 - - ____ ZE PL PL PM ZE NM NL NL N PL
U
PL
PM
ZE
NM
the required
NL
NL
The reference model The reference model is selected to specify the desired performance that satisfies the design criteria such as rise time, overshoot, settling time and steady state error. In addition, it should be a stable and robust model under various operating conditions. If a PMSM is vector controlled and fed from an ideal current controller, very fast torque response and superior speed control can be obtained. In this work, a vector controlled PMSM drive is used as reference model. The reference model which can be expressed by a second order system is shown in Fig 4. The desired response of the reference model is verified using simulations and the results are shown in Fig. 5, which are very much satisfactory for high performance PMSM drives. C. The adaptation mechanism Different adaptive control techniques have been proposed in the recent years [1,10,11,12,13]. The proposed algorithms, which include self-tuning controllers, model reference adaptive control, backstepping control, sliding mode control .. etc, have obtained good results. However, the design and development of these adaptive control techniques are based on the mathematical model of the plant. Therefore their design and implementation are not an easy task due to the required intensive computation.
B.
response
achieved
Otherwise Ec is fed into the PI controller and the resulted correction term Iqc is added to the FLC output Iqf to form the command torque current I* to be supplied to the vector controlled PMSM drive. As a result, the FLC output is modified so that the actual motor speed tracks the output of the ueference model. output
is
by
the
direct
FLC.
IV. SIMULATION RESULTS
The performance and efficieny of the proposed adaptive mechanism have been tested and verified using numerous simulations. The simulation has been carried out using Matlab/Simulink and Fuzzy Logic Toolbox. The system prameters used in the simulation test are shown in the appendix. Speed and current command transient responses to repetitive step changes in the speed command have been obtained for both no load and full load operating conditions at nominal inertia and 5 times the nominal inertia. The responses obtained have been evaluated for two different repetitive step speed commands; high speed (500 rad/s) and low speed (30
)
Figs. 6 and 7 show the step response for no load conditions at nominal inertia and 5 times the nominal inertia for 500 to 500 rad/s speed command. Fig. 8 shows the step response for full load conditions and 5 times the nominal inertia for 500 to -500 rad/s repetitive speed command. As shown in Figs. 7 and 8, the direct FLC response becomes slow when the moment of inertia increases. On the other hand, the adaptive FLC tracks closely the reference model for increased moment of inertia. T0=ONm, J=Jm, 500 rad0s
Iq +
K
T1
I
.I
01
__
JS+B__
______________________________________ _-4 n A
-200_
Figure 4. PMSM reference model -6 00
0
0.05
0.1
0.15
0.2
Time (s)
450 0.02
0.04 0.06
0.08
0.1
0.12
0.14 0.16 0.18
time (s) Figure 5. Speed response of the reference model
0.2 1
°°05;1:o.
(b)
Figure 6. (a) Speed response at high speed for no-load and nominal inertia, (b) Current command
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T-=Tl-ONmJ=SJm
-
600 co
-.
400
- -
-
200
*1-t
/
f -200
To further demonstrate the efficiency of the proposed
controller, both controllers have been examined for load
500 rad/s
11\
disturbance capabilities when full load is suddenly applied to the motor shaft. Initially the motor speed is 30 rad/s and rt l | / runing at no load. At 0.04 sec, full load torque is applied to 11; the motor shaft. At 0.08 sec the load is removed, and the
--
11'
motor runs at no load. At 0.1 sec the motor speed is increased load is applied to the motor shaft, then the load is removed at 0.17 sec. The speed response to step full load torque application and removal at both low speed and high speed are shown in Figs. 11 and 12. As noted in Figs. 11 and 12 the adaptive FLC has a lower dip in the
g - < -400t A,dageep:t ltePLF;c r60 0.02 0.04 0.06 0.08Tjg(Sm12 0.14 0.16 0.18 0.2 -801
(a)
30
Z 20-
'°
10
- - -
C
T
A
p-ve FLC
-. -
n3 20,-I-
-20
0.1
speed than the direct FLC. This shows that the adaptive FLC tis more robust than the direct FLC.
< 11
~~~
0.02 0.04 0.06 0.08
0
to 500 rad/s, at 0.13 sec full
0.12 0.14 0 .18 0.18
0.2
-
-E -0
-30
~
-...
p
(#I
TI=ON
-
J=5Jm, 30 rad/s -
-r 0l
-
s Time (s)~ ~ increased ~ ~ inertia, ~ ~ ~~~~~~~~~im Figure 7. (a) Speed response at high speed for no-load~ and 320-Adaptore LC L.~ r (b) Current command D4oirect PLC = = = 0
Fig. 9 shows the step response for no load and 5 times the nominal inertia for 30 to -30 rad/s repetitive speed command. At increased inertia the direct FLC response becomes slow when compared with the adaptive FLC. thFig. 10 shows the step response for full load and 5 times comm inertia for 30 to -30 rad/s nominal the repetitive adatien FLCaretrnieth rhesadponeiver the. dietFCZ 2m1speedd command. Again similar results have been obtained here, at increasedinertiathesimulationresults showthesuperiority of
adaptiveFLCtansientresponseoverthedirectFLC.
.
1
s
TI=0h8Nm
2001i1
thenominal
,n500
and J-5Jm
1 1 1l
red/s
t- r --l
0daptive
0.5
d
~
50 0.020.04 30
4
4 10
Current command ~~~~~~~~~(a)
anI l=J
30re/ - dptive FLC
-30
t
-
200
(b)
0
0
,Time(s)
~~~~~~~~~~~~~~~~~(b)
ime (s
(b)
Tie(s)
(b) Currentcommanda(a)iCurentLcomand -22
F-nirgri
Fl r
0
row speed Figure 10. (a) Speed response atCurrenm d and increased inertia, (a) for noll-load
-400 -AdaptTiei(s)
20
FL
(a) Speed response at row speed for no-load and increased inertia,
8d
J=5Jm =0ee 8spnse and spee frSlad/sdicese nri 200 Trncm d
0.2
0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) (b)
T0
Time (5)
FigurT.(a
3-
TION
y of
v
-
-.1
repetitie L.2
0.12 0.14 0.18 0.18
-
Figure 9.
s the c
0.1
Time(a) - - rAdaptive -1 - - PL-C - l| DirectPLC -[ - - 'I -rc FLC T- -_s . - - -
---1
inertia fo 30 to |30 rads
inerti the simulation ress s incrased400~~~~~~~(a te
0.02 0.04 0.06 0.08
kA>
-
1622
31 - 30.5 30
-
and robustness of the proposed controller
- -
5 - -
29 -
28.5ZB
W 23OV, 400W, 2A, 600rad/sec, three-phase, star connected, 4 pole pairs, Ld = 4.8 mH, Lq =6 m R=3.1Q, X = 0.191 volts/rad/sec, Jm = 0.52 Kg.cm2 and B =0.00006 Nm/rad/sec. APPENDIX: MOTOR PARAMTERS
- 4 ------ -- - 1 @ tveO
27.5 r 27- 0.0394 0.0396 0.0398 0.04 0.0402 0.0404 0.0406 0.0408 33
32s532
3i
-3 29.5 _
-
2828.0.794 .9 _09
compared to direct
-FLC.
-
Time (s)
ACKNOWLEDGMENT
(a)
The authors would like to thank the Ministry of Science, Technology and Innovation, Malaysia, for providing the financial support for tie project.
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-
-
-
-
-
-
RREFERENCES [1] B. K Bose Modern power electronics and ac drives. Prentice Hall PTR, Upper Saddle River, 2002, ch. 2-11.
-
[2] M.N. Uddin and M.A. Rahman, "Fuzzy logic bsed speed control of an IPM Synchronous motor drive," IEEE Conference on Electrical and Computing Engineering, Canada, pp.1259-1264, May 1999. [3] B. Heber, L. Xu, and Y. Tang, "Fuzzy logic enhanced speed control of an indirect field oriented induction machine drive," IEEE Transaction on Power Electronics. v. 12, no. 5, pp. 772-778, September 1997. Figure 1 1. (a) Speed response to step full-load torque application at 30 rad/s, (b) Removal of the load [4] L. Baghi, H. Razik and A. Rezzouq, "Comparison between fuzzy and classical speed control within field oriented method for induction motors," 7" Euro. Conf Power Electronics & applications, EPE, l l 501 - _ -7_ i< lTrondheim, Norway, pp. 2.444-2.448, 1997. 50 1 [5] Matlab Simulink User Guide, The Math Works Inc, 2001. X499 1 1 tt 1 [6] "Implementation of a Speed Field Orientated Control of Three Phase AC 498 Induction Motor using TMS320F240," Literature Number: BPRA076; , 497.Texas Instruments Europe, 1998. f Fuzzy [7] Logic Toolbox User Guide, The Math Works Inc, 2001. 496 [8]J. M. Mendel, "Fuzzy logic systems for engineering: A tutorial," 495 lDirect FLC -Adaptive FLC Proceeding ofthe IEEE, vol. 83, no3, pp.345-377, 1995. 0.129 0.129 0.129 0.129 0.1 0.130 0130 0.130 0.130 0.13 0,131 [9] C. C. Lee, "Fuzzy logic in Control systems: fuzzy logic controller: Part I Time & II,' IEEE Trans. Syst. Man and Cybernetics, vol. 20, pp. 404-435, (a)(s) 1990. so1.5s| i [10] J.L Silva and H. Le-Huy, "An improved fuzzy learning algorithm for _ motion control application," Industrial Electronics Society. IECON '98. I" 501 Annual Conference of the IEEE, vol.1, pp.1 -5, 1998, -' - - - _ 500.5 - - - [11] M.Nasir Uddin, M. A. Abido, M Azizur Rahman, "Development and implementation of hybrid intelligent controller for interior permanent u l magnet synchronous motor drives," IEEE Transaction on Industry l 499.5 Application. vol. 40, No. 1, p-p 68-76, 2004. { FLC [12] K.Kouzi, L. Mokrani, M-S. Nait-said, "A fuzzy logic cortroller with -Adapive I9gl 1 1 1 IIap fuzzy adapted gains based on indirect vector control for induction motor 0.1697 0.1898 0.1699 0.17 0,1701 0.1702 0.1703 0.1704 drive," Joumal of Electrical Engineering, vol. 3, 2003. [13] Y. Tan, J. Chang H. Tan, "Adaptive backstepping control and friction (b) compensation for AC servo with inertia and load uncertainties," IEEE Transaction on Industrial Electronics, vol. 50, no. 5, p-p 944-952, 2003. Figure 12. (a) Speed response to step full-load torque application at 500 rad/s, (b) Removal of the load
0 = 0 = 0.08 0 0.0796-= 0.0798 0. ri 0802 Time (s)
-
F
-eFul
0.0804 0.0806 0.0808
1
i
5_1
499
V. CONCLUSION A new hybrid model reference adaptive speed controller for vector controlled PMSM drive with a PI signal based adaptation technique has been presented. In the proposed system, the correction signal produced by the adaptation loop is added to the output of the main controller so that the actual system output is forced to follow the reference model output. The performance of the system is evaluated by simulation studies. Simulation results obtained confirms the efficiency
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