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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TFUZZ.2014.2315675, IEEE Transactions on Fuzzy Systems

IEEE TRANSACTIONS ON FUZZY SYSTEMS VOL. X, NO. X, MONTH 2013 1

An Improved Direct Adaptive Fuzzy Controller ofUncertain PMSM for Web-Based E-Service Systems

Chunjie Zhou, Duc-Cuong Quach, Naixue Xiong, Senior Member, IEEE, Shuang Huang, Qi Zhang, andQuan Yin

Abstract—Web-based systems have enjoyed a tremendousgrowth and exhibited a wealth at both theory and applica-tions, and they are highly visible and influential realizations ofuser-oriented technology supporting numerous human pursuitsrealized across the e-service. In this paper, we focus on web-based e-service systems for the Permanent Magnet SynchronousMotor (PMSM) remote control. They can provide web services forupdating factors and the fuzzy law of T-S fuzzy, when the PMSMdevices are required. This paper designs the controller of PMSMwith uncertain inertia, friction factors, and working under loadnoise in Web-based e-service systems. This controller is basedon Rotor Field Oriented Control (RFOC) structures, InternalModel Control (IMC), and Improved Direct Adaptive Fuzzy(IDAF). In order to enhance the transient quality for the case ofuncertain inertia and friction factors, we use the IDAF algorithmfor outer-loop (speed-loop). The IDAF is designed based on theDirect Adaptive Fuzzy (DAF) algorithm combining with the G-Fuzzy system for adjusting online updating adaption factors.The essence of IDAF is a self-learning and self-adaption systemwith enhancing adaptive ability through the G-Fuzzy system. Forinner-loop (current-loop), an improved IMC (IIMC) structure isproposed to reduce the effect of load-noise. The IIMC combinesthe tradition IMC and a speed feedback loop to enhance theanti-load noise ability of the system. The difference between ourcontrol structure and the traditional control structure is thatthe system could automatically realize anti-load noise in inner-loop before adjusting the speed in outer-loop. This will createreally high performances for PMSM control systems. Especially,we also demonstrate the effect of this control algorithm to thePMSM-RFOC system control. The extensive simulation resultsdemonstrate that the current response satisfies the conditionof ability and settling time. Especially, anti-load noise abilityand transient quality of the system are controlled independently.Thus, it’s a solid foundation to develop a high quality PMSMelectric drive in the e-service.

Index Terms—Adaptive control, E-service, Fuzzy set technol-ogy, PMSM, Web-based.

I. INTRODUCTION

The use of Web-based concepts in industrial automa-tion is increasingly spreading. Nowadays, Web-based

solutions and e-services are available for a wide range of

C. Zhou, D. Quach, S. Huang, Q. Zhang and Q. Yin are withthe School of Automation, Huazhong University of Science andTechnology, Wuhan, 430074, P.R. China e-mail: [email protected],[email protected], [email protected], [email protected] [email protected].

N. Xiong is with School of Computer Science, Colorado Technical Univer-sity, USA, e-mail: [email protected].

The work was supported by the National Science Foundation of Chinaunder Grant 61074145.

Manuscript received July 31, 2013; revised xx xx, 2013; accepted March11, 2014. Date of publication xx xx, 2014; date of current version xx xx,2014.

applications, for examples, in remote monitoring, diagnosisand maintenance of industrial control system [1]–[3], or inremote experiment and engineering tools [4], [5]. Web-basedapplications in control system have been reported in manypublications [6], [7]. Web-based development technology andsystem architecture of these applications have been rathermature. However, the controller in these web-based controlsystems is still a hot topic, and how to design and optimize ofcontroller combined the advantage of web-based e-service isstill an important and difficult aspect of these web-based ap-plications [8]. As one of the most popular motor types, PMSMis widely used in many different industrial applications suchas electric motor drive coupling in CNC(Computer NumericalControl) machines and robot, etc. Because of the advantagesof PMSM(high power, low inertia, high efficiency and reliableworking) [9]–[13], there are many studies on PMSM controltechnique in order to enhance transient and steady qualityof PMSM applied electric drive system [14]–[16]. Almostmodern PMSM power electronic and drive (PMSM-PEDs) arebased on RFOC or DTC principle which include current-loopand speed-loop and they are synthesized in rotating coordinatesystem [17]. In general, the sampling frequency of current-loop and speed-loop are different [18], [19]. Because thefeature and required quality of these two control loops aredifferent. First, the electric inertia of current-loop is very smalland it has required fast electromagnetic torque response (Risetime of this torque response is about 1ms) [20]. Therefore,its sampling frequency fi is very high about from 2.5 to 5kHz (So, the current control loop algorithm must be simplestas Proportion Integral(PI), Proportion Integral Derivative(PID)to fast calculate). Second, for speed-loop, its mechanic inertiais greater than current-loop′s. In addition, its algorithms arevery diverse and abundant which demand long calculating timesuch as Adaptive, Fuzzy, Robust, Neural algorithms, etc [21]–[26]. Especially, if these algorithms are installed in mediumspeed embedded systems such as systems which use dsPICor AVR microcontroller, this problem must be more attentive[27]. Hence, its sampling frequency fω must be smaller thancurrent-loop′s. In practice, fω = fi/n with n is a positiveinteger greater than one. In normal RFOC structure, anti-load noise ability of the systems complete depends on speedcontroller [28]. Because not only load noise is out-off currentcontrol-loop but also sampling frequency of speed-loop is low(smaller than 1 kHz) [20], thus anti-load noise ability of thesystem is significant damping.

In this paper, a general web-based e-service system forPMSM is proposed firstly. And then, we design a high




performance PMSM-PEDs which can reduce effect of loadnoise and has good speed transient response under conditionof uncertain mechanic inertia and friction for a web-basede-service system. These systems are widely and commonlyused in robots and manipulator, etc [29], [30]. Furthermore,we also present control structure, which is applied for PMSM-PEDs as below. For the inner-loop, we propose an improvedrobust IMC (Internal Model Control) structure, which is calledIIMC (Improved IMC). It is combining IMC and a speedfeedback loop in order to reduce effect of load noise inworking. The parameters of this control loop are calculatedfrom requirement of transient quality, steady error and anti-load noise ability of current-loop. In speed-loop, we suggestan Improved Direct Adaptive Fuzzy (IDAF) algorithm which isbased on Direct Adaptive Fuzzy of L.X.Wang and the G-Fuzzysystem in order to adjust the updating adaption factor of DAFonline [31]–[33]. The control structure with self-regulatingfuzzy parameters is considered the self-learning system [34],[35]. We can see in [31], [36]–[38], it is clearly that in themath field, DAF is completely similar direct adaptive FuzzyNeural Network (FNN). In the IDAF controller, main purposeof the G-Fuzzy is to enhance adaption ability of the system.This above IDAF structure will significantly enhance transient-steady quality and stability of the system under changing ofsome parameter such as inertia and friction in the system.After the parameters of control algorithm are optimized inthe simulation server, they will be downloaded to the PMSMsystem to configure the real controller through the web service.

The rest of this paper is organized as follows. In Section II,we begin with a general web-based e-service system for thePMSM, mathematical model of PMSM and RFOC structurefor PMSM-PEDs. Section III analyzes and designs a currentcontroller based on requirements for reducing the effect of loadnoise. In Section IV, we design an improved DAF algorithmfor controlling speed loop. Section V proposes the systemconfiguration for simulation. In Section VI simulation resultand analysis are proposed. Finally, we have a conclusion andpropose the future works in Section VII.

II. WEB-BASED E-SERVICE SYSTEM AND PMSMMODELING

A. Web-Based E-Service System for PMSM

Web-based e-service system for PMSM control is shownin Fig. 1. The system consists of a Simulation Server, aWeb Server, a PMSM system, and some Clients. The WebServer provides a browser-based interface for the users’ loginand access to consoles. The Simulation Server connected tothe Internet has such task as conducting the IDAF controlalgorithm simulation, which is the key part of the web-basede-service system. The PMSM system is also connected to theInternet. Clients access the simulation server through the webserver that hosts the website for configuring the fuzzy rulesand parameters, and they can also direct access the PMSMsystem to configuring the fuzzy rules and parameters.

In the Simulation Server, the components are shown inFig. 1. Before simulation, the fuzzy rules and PMSM knowl-edge can be configured by a client through the Web Server

toolbox and Data Management (two components in Matlabenvironment). In the simulation, PMSM knowledge is em-ployed to conduct PMSM model, and the fuzzy rules are usedin the control decision. After simulation, the fuzzy rules andPMSM knowledge, which are optimized in the simulation,will be updated. The optimized factor and fuzzy rules canbe accessed by the Clients; and it also can be down to thePMSM system through the Internet, if the PMSM systemneeds. Essentially, the PMSM system is a real-time multi-tasksystem. In this system, the updating of system parameters isachieved by the communication task. To avoid negative impactto the stability of the control system, the specified priority ofthe communication task is lower than these of all other controlapplication tasks.

Fig. 1. System architecture of web-based e-service systems for PMSM.

B. PMSM Modeling

From [10]–[12], [20], [39], the model of PMSM in rotarycoordinate frame is described by a set of formulas as below

The current dynamic equations

diddt

= −Rs

Ldid + ωe

Lq

Ldiq +

1

Ldud. (1)

diqdt

= −ωeLd

Lqid −

Rs

Lqiq +

1

Lquq − ωe

ψp

Lq. (2)

Electromagnetic torque equation

TE =3

2np [ψpiq + idiq (Ld − Lq)] . (3)

Mechanic dynamic equation

dω

dt=

1

J(TE −Kfω − TL) , (4)

where ud, uq , id and iq are stator voltages, currents in d-q axes, respectively. Ld, Lq , Rs are stator inductances andresistance. ψp, ωe, ω and np are rotor flux, electrical speed,speed of rotor and number of pole pairs. J , TE , TL are systeminertia, electromagnetic torque and load torque. For PMSM,the electrical speed ωe = npω.

C. RFOC Structure for PMSM

The PMSM-RFOC structure is presented in two stages thatinclude current part and dynamic part. Particularly, currentpart shows the process of creating electric torque through twocurrents which are id and iq . For PMSM works in normal




operating range (slower than normal speed), value of id iscontrolled so that it becomes equal to zero, aiming to eliminateidiq(Ld − Lq) components in (3). Then the electromagnetictorque of PMSM motor is proportional to iq current compo-nent. Consequently, electromagnetic torque characteristics ofPMSM motor will be similar to those of DC motor. This isthe basic principle of RFOC technique for PMSM [40].

In general, current controller of RFOC structure consistsof two PI with feedforward decoupling or IMC control struc-ture [41], [42]. In case, the motor parameters are exact andinvariant, we can complete to design above controllers suchthat closed-loop of current loop approach desired 1-st ordersystem. These systems are robust stability, no-overshoot andtheir settling time rely on the desired pole. We can see generalRFOC structure for PMSM in Fig. 2.

Fig. 2. The traditional RFOC structure for PMSM.

III. ANALYSIS AND DESIGN CURRENT CONTROL-LOOP

A. The Traditional IMC Control Structure for Current Loop

From (1) and (2), we set a new voltage as uq = uq−ωeψp.The current equation can be rewritten in Laplace transform asfollows

Ud (s) = (Rs + sLd) Id (s)− ωeLqIq (s)

Uq (s) = (Rs + sLq) Iq (s) + ωeLdId (s).(5)

Set U(s) = [Ud(s), Uq(s)]T and Ic(s) = [Id(s), Iq(s)]T , itis easy to have the transfer function of current stage Gi(s)and invert transfer function G−1i (s) of PMSM as below

Gi (s) =Ic (s)

U (s)=

1

∆P (s)

[sLq +Rs ωeLq

−ωeLd sLd +Rs

], (6)

G−1i (s) =U (s)

Ic (s)=

[sLd +Rs −ωeLq

ωeLd sLq +Rs

], (7)

where ∆P (s) = LdLqs2+Rs(Ld+Lq)s+R2

s+ω2eLdLq . The

convention of IMC structure for PMSM is shown in Fig. 3,where Gi(s) is an internal model and P(s) is IMC controller.Matrix T = [1.5npiq(Ld − Lq), 1.5npψp]. L(s) is the desiredclosed-loop transfer function of current-loop.

In the IMC theory [12], [20], [43], [44], P(s) is definedL(s)G−1i (s) so that the closed-loop transfer function of the

Fig. 3. The traditional IMC control structure for PMSM.

system is the desired transfer function L(s) in case of Gi(s) =Gi(s). Normally, L(s) may be selected as follows

L (s) =ρi

s+ ρiI. (8)

In the (8), ρi is the desired pole of closed-loop currenttransfer function. It is selected base on requirement of transientquality. With P(s) = L(s)G−1i (s), from Fig. 3 we have F(s)controller.

F (s) =[I−P (s) Gi (s)

]−1P (s) . (9)

F (s) =[I− L (s) G−1i (s) Gi (s)

]−1L (s) G−1i (s) . (10)

In the control system which has a plant identification stage,the Gi(s) is an identification plant. For the system that doesnot use identification stage, the parameters of Gi(s) are setby rated parameters (the parameters in catalog of productionhouse). Therefore, Gi(s) is replaced by Gi(s).

F (s) = [I− L (s)]−1

L (s) G−1i (s) . (11)

F (s) =

[I− ρi

s+ ρiI

]ρi

s+ ρiIG−1i (s) . (12)

Insert (7) into (12), we obtain

F (s) = ρi

[Ld +Rs/s −(ωeLq)/s(ωeLd)/s Lq +Rs/s

]. (13)

The voltage vector is given by[Ud (s)

Uq (s)

]= ρi

[Ld +Rs/s −(ωeLq)/s(ωeLd)/s Lq +Rs/s

] [Ed (s)Eq (s)

],

(14)

where [Ed, Eq]T is error vector of current. The [Ed, Eq]T

= [I∗d − Id, I∗q − Iq]T . With controller F(s), electromagnetictorque is defined as follows

TE (s) =1.5npρis+ ρi

[I∗d (s)I∗q (s)

] [iq (Ld − Lq) ψp

]. (15)

In the RFOC structure for PMSM, I∗d is controlled to zerowhen PMSM run in normal speed range. Therefore we canconsider the electromagnetic torque TE(s) only relies on theIq(s) element. If idiq(Ld−Lq) 6= 0, then this value is regardas the noise of current-loop. From above analysis, the plant ofspeed loop is shown as below.

Gω (s) =ω (s)

u (s)=

45npψpρi/π

(s+ ρi) (Js+Kf )≈ 45npψp/π

Js+Kf. (16)

Next, we consider effect of load-noise in the system. Inpractice, rise time of current loop is very small about 1 ms.




Fig. 4. The traditional RFOC structure for PMSM.

The time constant of L(s) is small, hence L(s) is regarded asan amplifiers stage in order to simply consider effect of load-noise. From Fig. 4, it is easy to see that, current-loop has notthe anti-load noise ability. Because TL is out-of current controlloop, when the speed controller is the tradition PI controllerGc(s) = Kp +Ki/s, the transfer function of load-noise is asfollows

GL (s) =ω (s)

TL (s)=

30s

πJs2 + (πKf + 45npψpKpKω) s+ 45npψpKiKω.

(17)

From (17), we can see that transfer function of load noisedepend on Kp and Ki of speed-loop. This problem is not reallygood for designing. If speed-controller is designed to meetexpected transient quality, it can not meet the requirement ofanti-load noise. To overcome this challenge, we will realizeanti-load noise problem in current-loop. At the moment, taskof speed-loop is only controlling speed and enhancing thetransient quality of the system.

B. The Improved IMC Control Structure for Current Loop

In order to reduce influence of load-noise on the systemresponse, we propose the IIMC structure. The IIMC combinestraditional IMC and a speed feedback loop, this structure isshown in Fig. 5. In the structure, the anti-load noise abilitycompletely depends on the process of current loop. This ishigh sampling frequency loop, this leads to fast response ofelectromagnetic torque and less errors when the system undervariant load-noise. From IIMC structure in Fig. 5, we obtainthe load-noise transfer function as follows

Fig. 5. The improved IMC structure for reducing influence of load-noise.

GL (s) =ω (s)

TL (s)=

30

πJs+ πKf + 45npψpHω. (18)

Taking z-transform of (18) using Tustin’s rule with samplingtime τi of current loop.

GL (z)

=30τi (z + 1)

2πJ (z − 1) + τi (z + 1) (πKf + 45npψpHω).

(19)

The anti-load noise ability of IIMC structure

Υ = limz→1

GL (z) =30

πKf + 45npψpHω. (20)

The speed feedback factor Hω of current-loop

Hω =30− πKfΥ

45npψpΥ. (21)

In practice, the anti-load noise ability of the system rely onboth current-loop and speed-loop. However, for anti-load noiseproblem, current-loop plays the conclusive role. In normalRFOC structure, controller of outer-loop is designed basedon requirement of stability, transient quality and steady error.Thus, anti-load noise ability Υ completely depends on theouter-loop controller which is not designed for anti-load noiseproblem. The IIMC structure is proposed in order to annuleffect of load noise in inner-loop, before realizing controlspeed algorithm in outer-loop. This method allows to createhigh performance in the system.

IV. IMPROVED QUALITY OF SPEED RESPONSE WITH IDAFALGORITHM CONTROLLER

In this section, we present the IDAF control algorithmapplied to control speed of PMSM. This controller includestwo fuzzy systems C-Fuzzy and G-Fuzzy. The C-fuzzy is aconventional DAF controller proposed by L.X.Wang [31]. TheDAF controller consists of a fuzzy system and an adaptivecontrol rule. This adaptive is designed by Lyapunov approachwhich can online estimate the parameters of the fuzzy systemaiming to generate an optimal control law for controllinguncertain nonlinear plants. The G-Fuzzy is a fuzzy systemwhich is used to online change the updating factor. [31]–[33], [36] show that the quality of system rely much onthe updating factor of adaptive rule. In order to enhance thetransient quality of the system, we use the G-Fuzzy systemfor online adjustment of the updating factor. The diagram ofthe system is shown in Fig. 6.

Fig. 6. The IDAF structure for controlling PMSM speed.




A. The Plant of Speed-Loop

From Fig. 5, the plant of speed-loop is constructed following

Gω (s) =ω (s)

u (s)

=45npψpρi/π

Js2 + (ρiJ +Kf ) s+ ρiKf + 45npψpρiHω/π.

(22)

Model (22) is described in state equation form asx = a1x+ a2x+ buy = x

. (23)

where x = [x, x]T = [ω, ω]T is state vector, y = ω andu = i∗q + ωHω are output and input signals. The parametersof the plant a1 = −(ρiJ + Kf )/J , a2 = −(ρiKf +45npψpρiHω/π)/J and b = (45npψpρi)/(Jπ).

B. Direct Adaptive Fuzzy Algorithm for SISO Uncertain Plant

In this research, the DAF controller is designed to controlthe speed of PMSM-RFOC system under uncertain of inertiaJ and friction factor Kf . Therefore parameters a1, a2, andb are regarded as unknown.From (23), we have the optimalcontrol law as below

u∗ =1

b(x− f(x)) , (24)

where the function f(x) = a1x + a2x. The tracking errore = yr − y is the difference between the reference speedyr and the actual speed y of the PMSM motor. We furtherdefine an error vector e = [e, e]T . The 2-nd order differentialequation of error is given by

e = yr − x. (25)

The differential equation to represent the control object isin 2-nd order, thus the 2-nd derivative of its error holds.

e+ k1e+ k2e = 0. (26)

Based on (26), the characteristic equation of error is

s2 + k1s+ k2 = 0. (27)

If k1 and k2 take the appropriate value which makes the realpart of all numerical solutions of (27) negative, the system isstable (limt→∞ e(t) = 0). From (25) and (26), we have 2-ndderivative of x.

x = yr + k1e+ k2e. (28)

By substituting x in (28) for (24), (24) is rewritten by

u∗ =1

b(yr + k1e+ k2e− f(x)) . (29)

In (29), f(x) and b are unknown, leading to the fact that u∗

can not be implemented. However, we can design a Takagi-Sugeno (T-S) fuzzy system in which the output u is toapproximate the optimal control law u∗ [31], [32]. The T-Sfuzzy is described by a collection fuzzy rule as follows [31]–[33], [36], [45]–[47]

If x1 is SPi and x2 is ACj then uij = θij .

where SPi (1 ≤ i ≤ n) and ACj (1 ≤ j ≤ m) are thefuzzy variables characterized by the membership functions µs

i

and µaj of variables x1 and x2 (x1 = x and x2 = x). When

the product inference and the center of gravity defuzzificationsingle method are used, the output u(x|θ) of the T-S fuzzysystem is as follows

u (x|θ) =

∑ni=1

∑mj=1 θijµ

si (x1)µa

j (x2)∑ni=1

∑mj=1 µ

si (x1)µa

j (x2). (30)

The (30) equation can be written by multiplication of twovectors as bellow

u (x|θ) = θT ξ (x) , (31)

where

θ =[θ1 θ2 · · · θ(i−1)m+j · · · θn×m

]T,

θ(i−1)m+j = θij ,

ξ(x) =

[ ξ1(x) ξ2(x) · · · ξ(i−1)m+j(x) · · · ξn×m (x)]T ,

ξ(i−1)m+j (x) =µsi (x1)µa

j (x2)∑ni=1

∑mj=1 µ

si (x1)µa

j (x2).

Here, θ is an adjustable parameter vector and ξ(x) is a vectorof fuzzy basis function. u(x|θ) can approach u∗. Now, we willspecify θ so that u(x|θ) ≈ u∗. From model of plant in (23),we have

x = f (x) + bu (x|θ) + bu∗ − bu∗. (32)

From (29)

x = f (x) + bu (x|θ) + yr + k1e+ k2e− f (x)− bu∗. (33)

Consequently

yr − x = KTe + b (u∗ − u (x|θ)), (34)

where KT = [−k2 − k1]. From (34), the differential equationof error is described

e = Ae + B [b (u∗ − u (x|θ))], (35)

where, A = [0 1;−k2 − k1] and B = [0; 1]. Next, studyingthe stability of the error (35) aims to develop an adaptivelaw to adjust the parameter vector θ of the T-S fuzzy system.Definition optimal parameter vector θ∗ is optimal parametersto u(x|θ∗) approximate the optimal control value u∗ of (29).And optimal minimum approximation error is

ε = u (x|θ∗)− u∗ ≈ 0. (36)

Substituting (36) in to (35)

e = Ae + B [b (u (x|θ∗)− u (x|θ))]−Bbε. (37)

Base on (31), we also have

e = Ae + B[b(θ∗T ξ (x)− θT ξ (x)

)]−Bbε. (38)

Define Γ = θ∗ − θ

e = Ae + BbΓT ξ (x)−Bbε. (39)

Select Lyapunov function as follows

V =1

2eTPe +

b

2γΓTΓ. (40)




In (40) γ is a positive constant called updating coefficient. P isan symmetric positive definite matrix. When we find derivativeof the V function, note that PT = P, ΓT ξ(x) is a 1× 1 sizematrix. From (40), we have derivative of the V function

V =1

2eT[ATP + PA

]e

+b

γΓT[γeTPBξ (x) + Γ

]− eT bPBε.

(41)

With B = [0; 1], PB = p2. The p2 is the last column of P.If we select vector Γ as follow

Γ = −γeTp2ξ (x), (42)

and setATP + PA = −Q, (43)

where Q is a positive definite matrix, then

V = −1

2eTQe− eT bp2ε. (44)

Based on the universal approximation theorem, if the num-ber of control law is enough, the error ε will be very small[31], [33], leading to |eT bp2ε| < eTQe/2 . Hence, V < 0according to Lyapunov stability theory, shows that controlsystem is in certainly stability. From Γ = θ∗ − θ, we notethat θ∗ is an expected optimal parameter, and it is a constantvector. From (42), θ vector is updated by (45) [31], [33]

θ = γeTp2ξ (x) . (45)

In the digital control systems, the time derivative is just thesampling time. For speed-loop of electric drive system, thisvalue is normal selected a few milliseconds. In system config-uration part, the value of this time is selected 1 millisecond.

C. An Improved DAF

Reference [31] shows that, the quality of system relies toomuch on the updating factor γ and fuzzy law number of T-S fuzzy system. In the term of the updating factor, the (45)indicates that, when γ is large, the updated value of it is moresensitive to the error, so the effect of the updating law to thesystem is stronger. However, when the error is small, if γ isstill too large, the output response oscillates largely aroundthe reference point [33]. Therefore, it is necessary for us toadjust online appropriately the value of the updating factorusing the G-Fuzzy controller. In order to realize the G-Fuzzy,we observe in Fig. 7. This picture shows the time response ofsystem track reference input. The error between the referencesignal and the system response always exists, we describe thisrelationship in 4 regions.

Area I (from t0 to t1): both of error and differential error areall positive values. The trend of this region requires increasingcontrol signal system to pull fast system time to responseto reference input asymptotic. In this region, as can be seeneTp2 > 0, in order to increase control signal value we canincrease θ through increasing updates coefficient γ value.

Area II (from t1 to t2): In this area, the error is positive andthe differential error is negative. Time response in this regiontends asymptotically to reference input. Hence the updating

Fig. 7. Analysis of updating coefficient in error areas.

factor tends to decrease gradually to avoid overshooting.This downward trend will be determined by the sign of thecomponent which is shown by qualitative way in Table I.

Area III (from t2 to t3): Both of the error and the differentialerror are negative values. In this region, we must decreasecontrol signal. As can be seen, in this area eTp2 is negative.So, in order to cut control signal we need to increase theupdating factor value.

TABLE IANALYSIS - ADJUSTING UPDATING FACTOR

Errorareas Signoferrorvector eTp2 UpdatingfactorI e > 0, e > 0 Positive BigII e > 0, e < 0 Positive MeanII e > 0, e < 0 Negative SmallIII e < 0, e < 0 Negative BigIV e < 0, e > 0 Negative MeanIV e < 0, e > 0 Positive Small

TABLE IIFUZZY LAWS OF THE G-FUZZY SYSTEM

e - de/dt NBd NSd ZOd PSd PBdNBe VB VB M M MNSe VB B M S VSZOe VS S S S VSPSe VS S M B VBPBe M M M VB VB

Area IV (from t3 to t4): The error is negative and the dif-ferential error is positive. Time response tends asymptoticallydecrease to reference input-error. Based on the sign of eTp2

to change value of γ, if eTp2 < 0 the γ value is stable inaverage level. However, if eTp2 > 0, the time response tendsasymptotically to reference input. Also, it tends asymptoticallyfaster with reference input. This is the time to decline the γvalue.

Based on the above analyses, we can describe a trendstable setting to adjust the updating factor which is shown inTable I. We will use the G-Fuzzy system to adjust the valueof updating factor. The G-Fuzzy system includes two variableinputs, error e and differential error e. They are fuzzifiedby five triangles fuzzy sets NBe,NSe, ZOe, PSe, PBefor e and NBd,NSd, ZOd, PSd, PBd for e. Its out-put ∆γ value is also fuzzified by five triangles fuzzy setswith V S, S,M,B, V B. We use isosceles triangles form




for membership functions of all input/output, because whenapplied to an embedded system it is very simple to calculate,and it saves time for calculation on chip.

According analyzed results in Table I, fuzzy laws of G-Fuzzy are presented in Table II. Fuzzy inference of G-Fuzzyis selected MAX-PRODUCT form, centre-average defuzzifi-cation method is used to de-fuzzy. Finally, the updating factoris calculated by (46) (γ0 is the initialization value of γ).

γ = γ0 + ∆γ (46)

Based on [31], we can conclude that the system is com-pletely stable when we use the G-Fuzzy to adjust the positiveupdating coefficient γ online. But simulation shows that ifthe sampling period of G-Fuzzy and C-Fuzzy are similar, thequality of the system is not good. This may be caused bythe sensitive γ when regulating speed of γ is too fast. In thefollowing simulation part, we solve this problem by increasingthe sampling period of G-Fuzzy to several times than the C-Fuzzy system.

V. SYSTEM CONFIGURATION

The numerical simulations of the PMSM-RFOC controlare given to illustrate the effectiveness of the PMSM-PEDsdesign. The simulations in discrete form are carried out inthe MATLAB-SIMULINK environment, as shown in Fig. 8,it consists of several parts. The PMSM and IGBT model arefrom SimPowerSystems library, and the IDAF speed controllerand IMC current controller form the controller part, whoseoutput voltage and angle signal product the IGBT drivepulses through a discrete SVPWM (Space Vector Pulse WidthModulation) generator.

A. The Parameter of Plant

The normal parameters of PMSM for simulation are shownin Table III.

TABLE IIIPARAMETERS OF PMSM MOTOR

Parameters V alue Parameters V alueRated power 2.2kW DC voltage 300VRated speed 4250rpm Rated torque 2.8NmRated current 3.53A Resistance Rs 1.6ΩInductance Ld 6.365mH Inductance Lq 7.105mHInertia J 0.0001854Kgm-2 Rotor flux ψp 0.1852WbFriction Kf 0.00005396Nms/rad Pole pairs np 2

The two-level SVPWM voltage source inverter is used tofeed electric energy for PMSM. Feature of the inverter are 340VDC supply voltage, 10 kHz switching frequency, maximumof amplitude modulation is 170 V and does not use powerfilter.

For the simulation results approach to actual value, theresolutions of current sensor and speed sensor are configured5 mA and 0.2 rpm.

B. The Current Controller

The current loop uses IIMC control structure with samplingtime τi = 200µs. Selecting the expected settling time ofcurrent loop is 1 ms (expected pole of current closed-loopρi = −4000) and Tustin’s rule for converting from continuousto discrete form. From (13) and parameters of PMSM are inTable III, we obtain a discrete F(z) controller as follows

F (z) =10−2

z − 1

[2610z − 2482 −0.28z − 0.280.25z + 0.25 2906z − 2778

]. (47)

The ud and uq voltage elements for vector modulation inSVPWM inverter as

Ud (z) =26.10z − 24.82

z − 1Ed (z)− 0.0028

z + 1

z − 1Eq (z) . (48)

Uq (z) = 0.0025z + 1

z − 1Ed (z)+

29.06z − 27.78

z − 1Eq (z)+ωeψp.

(49)The speed feedback factor Hω for anti-load noise is calculat-

ed by (21). We select the expected Υ = 15 rpm/Nm, thereforethe speed feedback factor of current-loop is Hω = 0.12

C. The Speed Controller

The DAF controller is designed to control the PMSM speedin the range from -4250 to 4250 rpm. The discrete DAFalgorithm is described in sequel.

1) Fuzzy logic controller design: Takagi-Sugeno fuzzy sys-tem is used to design the controller. This fuzzy system includestwo inputs of speed, acceleration and one output. The outputvalue of fuzzy system is the control signal, i.e. PWM value.The speed is x1, x1 ∈ [−4500, 4500] rpm, and it is fuzzifiedusing SPi fuzzy sets with i = 1, 2, . . . , 7 and the membershipfunctions are normalized [0, 450]. The acceleration variableis x2. In fact, rise time of some system can be obtained0.01 s with amplitude 1000 rpm so that x2 can be set inthe range of [−100000, 100000] rpm/s. However, when wesetup up the actual digital system, we can replace x2 withfirst order difference of the variable x1. Because samplingtime of speed-loop is 1 ms, thus x2 variable will be normalizein the range of [-100, 100]. The acceleration is fuzzified usingACj fuzzy sets with j = 1, 2, . . . , 7 and the membershipfunctions of acceleration are normalized [0, 100]. The outputu of fuzzy system is referred to us value from [0, 170]V. Themembership function of u is singleton fuzzy sets θ(i−1)m+j .Hence, fuzzy logic controller has 49 fuzzy rules, which areshown in Table IV. From (30) u is calculated by (50).

TABLE IVFUZZY LAWS OF THE C-FUZZY SYSTEM

x1 / x2 AC1 AC2 AC3 AC4 AC5 AC6 AC7

SP1 θ1 θ2 θ3 θ4 θ5 θ6 θ7SP2 θ8 θ9 θ10 θ11 θ12 θ13 θ14SP3 θ15 θ16 θ17 θ18 θ19 θ20 θ21SP4 θ22 θ23 θ24 θ25 θ26 θ27 θ28SP5 θ29 θ30 θ31 θ32 θ33 θ34 θ35SP6 θ36 θ37 θ38 θ39 θ40 θ41 θ42SP7 θ43 θ44 θ45 θ46 θ47 θ48 θ49




Fig. 8. Simulation diagram of PMSM-RFOC system.

u (x (k) |θ (k))

=∑7

i=1

∑7

j=1θ(i−1)m+j (k) ξ(i−1)m+j (x (k)).

(50)

Fig. 9. The time response of ia, ib, ic, id and iq in the first case.

2) Adaptive rule for Fuzzy controller: The task of adaptiverule is to update the θ(i−1)m+j parameter in (31). The discreteequation of (45) can be written by

∆θ(i−1)m+j (k) = γe(k)Tp2ξ(i−1)m+j (x (k))

θ(i−1)m+j (k + 1) = θ(i−1)m+j (k) + ∆θ(i−1)m+j (k).

(51)We set the updating constant γ = 1 and select k1 = 10,k2 = 50, Q = [100 0; 0 100], resulting in P = [265 1; 1 5.1],and thus p2 = [1; 5.1].

(a) Time response of id current.

(b) Time response of iq current.

Fig. 10. The time response of id and iq in the first case: (a) is the timeresponse of id current, (b) is the time response of iq current.

D. G-Fuzzy for Online Adjusting Updating Factor γ

G-Fuzzy controller is designed to adjust the updating factorγ online to obtain better adaptive performance. The parametersof G-Fuzzy is setup as follows: γ0 = 0.5, ∆γmin = 0 and∆γmax = 5.

VI. SIMULATION RESULTS AND ANALYSIS

The our control structure is compared with traditionalRFOC control structure which uses the desired PI algorithmfor certain PMSM modeling and current-loop has no speed




(a) Time response of iq current without speed feedback loop.

(b) Time response of iq current with speed feed loop.

Fig. 11. The iq response with some difference Υ: (a) is the time response ofiq current without speed feedback loop, (b) is the time response of iq currentwith speed feed loop.

(a) Time response of id current when Rs, Ld and Lq vary.

(b) Time response of iq current when Rs,Ld and Lq vary.

Fig. 12. The responses of id and iq with changing the parameters of PMSM:(a) is the time response of id current when Rs, Ld and Lq vary, (b) is thetime response of iq current when Rs,Ld and Lq vary.

feedback loop. The speed controller of traditional RFOC isgiven by

G∗c (s) =πρω

45npψp× Js+Kf + 45npψpHω/π

s, (52)

where ρω is designed closed-loop pole, with settling time isselected 0.1 s then ρω = 40. The discrete transfer function ofG∗c with sampling time 1 ms as below

G∗c(z) = 9599z + 1

z − 1. (53)

Fig. 13. The speed response at high range.

Fig. 14. The speed response at low range.

A. The First Case: Current Characteristic

In this case, PMSM runs under no-load at 1000 rpm speed,at t = 0.15s add 2.8 Nm rated load torque, then at t = 0.2s theload torque reduces to 1.4 Nm. The time response of currentsis shown in Figs.9-10.

From Figs.9-10, we can see that time response of id isstable in zero area. When step form of 2.8 Nm rated load-noise appears, overshoot and settling time of id are 0.015 Aand 0.01 s, respectively. For iq , overshoot and settling time are24% and 0.0015 s, respectively. Besides, when the load torqueis reduces to half, the steady-state value of iq also decreasesto half. These phenomena indicate that the electromagnetictorque is only controlled by iq and the RFOC control structurehas achieved its purpose. At start process current responses arestrong oscillation because the desired pole of current closed-loop is big, and the inertia of the system is damped. Dueto the system usually has sensitivity with change of inputsignal. Moreover, current value at no-load start process issmall, voltage vector for modulation SVPWM inverter hassmall amplitude due to high-order current harmonics are high.

Fig. 11 shows the difference of transient quality of iq withsome different Υ, in which fig.a illustrates that if current-loophas speed feedback loop, settling time of iq is very short,




Fig. 15. The anti-load noise ability with PI, DAF and IDAF.

Fig. 16. The anti-load noise ability with with some difference of Υ.

which is about 0.015 s, and oppositely, if current-loop has nospeed feedback loop, the settling time of iq is about 0.185 s,large overshoot, strong oscillation. It shows that the anti-loadnoise ability of system is significantly enhanced when usingspeed feedback loop. Fig.11(b) is the partial enlarged view ofFig.11(a), this picture shows that by reducing Υ value withinlimits, we can improve anti-load disturbance ability of system.

Next, we consider id and iq response with difference ofresistance, inductance of PMSM. The parameters of PMSM1:Rs1 = Rs, Ld1 = Ld and Lq1 = Lq . The parameters ofPMSM2: Rs2 = 1.4Rs, Ld2 = 1.7Ld and Lq2 = 1.2Lq .The parameters of PMSM3: Rs3 = 1.7Rs, Ld3 = 1.3Ld andLq3 = 1.1Lq The system is configured as follows: Υ = 15rpm/Nm, 1000 rpm speed set-point and step form of 2.8 Nmrated load. Fig. 12 is shows id and iq responses. It clearlyshows that there is no obvious difference of iq between thethree situations above. For id, the difference between the threesituations are relatively significant. However, the values of idare very small (0.01, 0.03 and 0.06 A), hence their influence ontime response of electromagnetic torque TE is not significant.

B. The Second Case: Step Response

The PMSM starts at no-load. The reference input is in theform of step. The speed response of high speed range (2500rmp) with tradition PI, DAF and IDAF controller is shown inFig. 13. The speed response of low speed range (a few rpm) isshown in Fig. 14. The settling time of DAF and IDAF are 0.05s and 0.025 s at high range, 0.03 s and 0.01 s at low range,respectively. The steady-state error of PI, DAF and IDAF areall closed to resolution of speed sensor (±0.2 rpm). From thetwo pictures above, we can see that the transient quality ofPMSM-RFOC using DAF and IDAF are completely able toapproach the transient quality of the system which uses theperfect PI algorithms. The difference between DAF and IDAFis that the reaction rate of IDAF is faster than DAF. When thesystem starts (at t = 0), the error of the system is very large, and∆γ is increaseed by the G-Fuzzy, thus control signal becomeslarger. Therefore, the settling time of system is reduced. At thelow speed range, IDAF has the best performance, however atthe high speed range time response of the system is stronglyoscillated. Hence, IDAF is suitable for controlling at mediumand low speed range.

C. The Third Case: Characteristic of the System under Load-noise

In Fig. 15, the system is configured with anti-load noiseability of Υ = 20 rpm/Nm. The PMSM runs with no-load atthe speed of 1000 rpm. At t = 0.2 s there is a sudden 1 Nmload noise and this load lasts 0.1 s. Fig. 15 shows anti-loadnoise ability of the system with difference speed controllers(PI, DAF and IDAF). It is clear that overshoot values ofresponse speed does not all dependent on speed controllertype. The problem of anti-load noise is completely realizedby inner loop which has a very high sampling frequency.The difference between the three speed controllers are rateof convergence to balance state. For IDAF settling time is thesmallest, about 0.025 s. Settling time of DAF and PI are 0.04s and 0.08 s, respectively. It can be seen from this that theanti-load noise ability of IIMC-IDAF structure is the best.

Next, we observe Fig. 16, this picture shows the anti-loadnoise ability of IIMC-IDAF control structure with Υ = 15, 20and 30 rpm/Nm. The PMSM runs at the speed of 1000 rpmwith no-load. At t = 0.1 s there is a sudden 1 Nm load noiseand this load torque lasts 0.13 s. The simulation results showthat correspondence overshoot of speed responses are 17, 22and 27 rpm, and they are all close to the pre-set Υ value.With above simulation results, we can complete design thePMSM-PEDs with requirement of anti-load noise ability inwithin limits.

D. The Fourth Case: The System under Uncertain J and Kf

In the fourth case, we will investigate the control abilityof IDAF with different inertia J and friction factor Kf .Resistance and inductance parameters of all three situations arethe same: Rs = Rs, Ld = Ld and Lq = Lq . Only parametersJ and Kf are changing as in Table V.

The system is configured with anti-load noise ability Υ =15 rpm/Nm. The input signal of the system is in the step form




Fig. 17. The speed response with some difference of J and Kf .

Fig. 18. The speed response tracks signal of a model transfer function.

of 1200 rpm amplitude. Fig. 17 shows the speed response ofthe system with IDAF controller. We can see that the systemis stable in all the three situations, and settling times are all0.03 s. However rise time and overshoot of the three casesare different. J in case 1 is the smallest. Hence the timeresponse of the system is the shortest. For case 3, J is thelargest, therefore time response of the system is the longest.The problem shows physics essence of the system. In practice,the input signal of the system is normal signal of modeltransfer function so that time response of the system is robust,and oscillator is avoided. Using set-point value from modeltransfer function not only enhances system’s transient qualitybut also can reduce starting current of motor. Fig. 18 showsthe time responses of the system trace the signal of model

TABLE VPARAMETERS OF THE SIMULATION OF FOURTH CASE

InCase − Parameters J Kf

Case 1 J Kf

Case 2 1.5J 5Kf

Case 3 3J 1.3Kf

transfer function which is given as follows

G(s) =11300

s2 + 140s+ 11300. (54)

From Fig. 18 we can see that, in the three cases, the timeresponses of the system all track the signal of model transferfunction well. In cases 2 and 3, the inertia J or frictionfactor Kf increases several times compared to case 1, but thetracking errors are almost the same. This also indicates thatthe IDAF speed controller is able to compensate the system’sparameter uncertainty to some degree.

VII. CONCLUSION

This paper introduces a web-based e-service system foruncertain PMSM controllers based on intelligent support sys-tems using fuzzy set system, and proposes the design ofhigh performance PMSM-RFOC base on IIMC and IDAFcontrollers. The web-based e-service system provides an easyway to optimize and update the parameters and fuzzy rulesof the fuzzy controller. Especially, IIMC is designed fromthe requirement of enhancing anti-load noise ability. Thesimulation results demonstrate that IIMC structure control canreduce the influence of load noise within limits. Advance ofprocessing load-noise in inner-loop is able to create the fasttorque response in inner-loop. Thus anti-load noise ability ofthe system does not rely too much on outer-loop. For thespeed control problem, we suggest using the IDAF algorithm.Although the IDAF is designed with unknown parameters ofsystem, but the control results show the fast time responseand the good anti-load noise ability. Especially, in the lowspeed range, the settling time of the system with IDAF controlstructure can reach 0.01s and overshoot is 0 %. In fact, thecombination between IIMC and IDAF in the PMSM-RFOCsystem creates the system, which permits to independentlycontrol anti-load noise ability and transient quality. Further-more, with the IDAF controller of outer-loop (The essenceof IDAF is self-learning and self-adaption system), it is veryflexible to be applied, because if we know the order of object,we can design a control algorithm. Hence we can completelydesign the general speed controller, which can apply to manydifferent types of PMSM motors.

To accommodate more PMSM objects, the PMSM knowl-edge base will be improved in the future. And we should makethe system more conveniently. Also, the performance of theproposed control algorithm could be promoted further, andmore control algorithms need be complemented in the future.

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Chunjie Zhou (Hubei,1965) received the MS andPhD degrees in control theory and control engi-neering from Huazhong University of Science andTechnology, Wuhan, China, in 1991 and 2001, re-spectively. He is currently a professor at School ofAutomation, Huazhong University of Science andTechnology. His research interests include industri-al communication, artificial intelligent, theory andapplication of networked control system.

Duc-Cuong Quach was born in Namdinh, Vietnam,in 1979. He received the B.S. degree in ElectricalMachines and Power Electronics from Hanoi U-niversity of Science and Technology in 2002 andM.S. degree in Automation Engineering from HoChi Minh City University of Transport, Vietnam,in 2008. Form 2010 to 2013, he was a doctoralcandidate at the School of Automation, HuazhongUniversity of Science and Technology, Wuhan, PRChina. Now, he is currently working in Faculty ofElectrical Engineering Technology, Hanoi University

of Industry, Vietnam. His research interests include Wireless control system,Intelligent control theory and Embedded systems apply to Power electronic-Electrical drives and industrial applications.

Naixue Xiong (M’08-SM’12) is current a full Pro-fessor at School of Computer Science, ColoradoTechnical University, Colorado Spring, CO, USA.He received his both PhD degrees in Wuhan Uni-versity (about software engineering), and Japan Ad-vanced Institute of Science and Technology (aboutdependable networks), respectively. Before he at-tends Colorado Technical University, he worked inWentworth Technology Institution, Georgia StateUniversity for many years. His research interests in-clude Cloud Computing, Security and Dependability,

Parallel and Distributed Computing, Networks, and Optimization Theory.He has been a General Chair, Program Chair, Publicity Chair, PC member

and OC member of over 100 international conferences, and as a reviewerof about 100 international journals, including IEEE JSAC, IEEE SMC (Park:A/B/C), IEEE Transactions on Communications, IEEE Transactions on MobileComputing, IEEE Trans. on Parallel and Distributed Systems. He is serving asan Editor-in-Chief, Associate editor or Editor member for over 10 internationaljournals (including Associate Editor for IEEE Tran. on Systems, Man &Cybernetics: Systems, and Editor-in-Chief for Journal of Parallel & CloudComputing (PCC)), and a guest editor for over 10 international journals,including Sensor Journal, WINET and MONET.

Shuang Huang Shuang Huang received the B.S.degree in Automation from Huazhong University ofScience and Technology, Wuhan, China, in 2009.He is currently working toward the PhD degree incontrol science and control engineering at School ofAutomation, Huazhong University of Science andTechnology, China. His interests are in industrialcommunication and industrial control system withspecial focus on security.

Qi Zhang (Liaoning, 1987-) received the BSc de-gree in Automation from Huazhong University ofScience and Technology, Wuhan, China, in 2011.He is currently working toward the PhD degree incontrol theory and control engineering from Schoolof Automation at Huazhong University of Scienceand Technology under the supervision of ChunjieZhou. His research interests include distributed sys-tems/networks and industrial ethernet.

Quan Yin (Jiangsu, 1968-) received the M.S. andPh.D. degrees in Control Theory and Control Engi-neering from Huazhong University of Science andTechnology, Wuhan, China, in 1995 and 2001, re-spectively. He is currently an associate professorat School of Automation, Huazhong University ofScience and Technology. His research interests in-clude servo control system, intelligent control andautomation equipments.

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