D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 616 – 622, 2006. © Springer-Verlag Berlin Heidelberg 2006

Vector Controlled PMSM Drive Based on Adaptive Neuro-fuzzy Speed Controller

Xianqing Cao and Liping Fan

Shenyang Institute of Chemical Technology, Shenyang, China caoxianqing2005@163.com

Abstract. This paper presents the implementation of adaptive fuzzy neural net-work controller (FNNC) for accurate speed control of a permanent magnet syn-chronous motor (PMSM). FNNC includes neural network controller (NC) and fuzzy logic controller (FC). It combines the capability of fuzzy reasoning in handling uncertain information and the capability of neural network in learning from processes. The initial weights and biases of the artificial neural network (ANN) are obtained by offline training method. Using the output of the fuzzy controller (FC), online training is carried out to update the weights and biases of the ANN. Several results of simulation and experiment are provided to demon-strate the effectiveness of the proposed FNNC under the occurrence of parame-ter variations and external disturbance.

1 Introduction

For a high-performance drive system, not only a fast response is required, but also the ability of quick recovery of the speed from any disturbances and insensitivity to pa-rameter variation is essential [1, 2, 3, 4, 5].The speed controller used in PMSM drive system plays an important role to meet all the requires mentioned above. Parameter-fixed, conventional controllers such as PI controller have been widely used. For a long-run drive system, their performances are unsatisfactory. Because of the unknown load dynamics, and other factors such as noise, temperature or parameters variation, etc. It is difficulty to choose the optimal parameters of the PI controller for the PMSM drive.

To solve this problem, some adaptive controllers have been applied in both ac and dc motor drive. Such as model reference adaptive controller (MRAC) [6] and sliding model controller (SMC) [7], etc. all the types of controllers can improve the perform-ance of the motor drive. However, they are usually based on the parameters and struc-ture of the system model. It will lead to complex computation when the system model is uncertainty. Other persons replace PI speed controller with NC to meet the system’s dynamic characteristics. Generally, in order to get the error to tune the weights of the ANN, they all adopt an other controller (such as MRAC). Inevitably, it will lead to the complex computation again, To overcome this difficulty, this paper present an approach of designing adaptive FNNC which adopts the fuzzy logic to the artificial-neural-network. FNNC combines the capability of fuzzy reasoning in handling uncer-tain information and the capability of ANN in learning from processes.

Vector Controlled PMSM Drive Based on Adaptive Neuro-fuzzy Speed Controller 617

The proposed control scheme has been testified by simulation and experiment, the results indicate the proposed PMSM drive will have the ability of quick recovery of the speed from any disturbances and parameters variation. Accordingly, the PMSM drive will have better dynamic performances and robustness.

2 Vector Control Model of the PMSM

An efficient control strategy of the vector control technique is to make the d-axis current id zero so that the torque becomes dependent only on q-axis current. With this control strategy, the motor model of the PMSM becomes simpler as can be described by the following equations [4]

( ) qrbqsqq LKiRvpi /ω−−= . (1)

( ) JBTTp rLer /ωω −−= . (2)

Where vq is the q-axis stator voltage, iq is q-axis stator current, Lq is q-axis stator in-ductance,�r is rotor speed, Rs is stator resistance, p is differential operator, Kb=P�m, J is the rotor inertia, B is the damping coefficient, Te, TL are the electromagnetic torque and the load torque, and can be represented by [4].

rrLe BJpTT ωω ++= . (3)

322

1 KKKT rrL ++= ωω . (4)

Where K1, K2 and K3 are constants. Combining (1)-(4), the q-axis current can be ex-pressed by [4]

εϑδωγωβωωεαω /]nnnnB

CnBniAni rrrrrqq −−−−−−−+−+−= )2()()2()1()()([)1()( 221

11 . (5)

Where 111 C,B,A,,,,,, ϑεδγβα are given in Appendix A. Equation (5) reveals the non-linear function between iq and r. The purpose of the ANN is to map the non-linear relationship between iq and r.

3 Structure of the FNNC for PMSM Drive

3.1 Structure of the ANN

The inverse dynamics of PMSM as described in equation (5) indicates the inputs and output of the ANN used in the control system. The proposed architecture of three-layer ANN includes M=4 input nodes, N=3 hidden-layer neurons, and Q=1 output nodes. W1, b1 are the weights matrix and biases vector between the input layer neurons and hidden layer neurons, W2, b2 are the weights matrices and biases vector between the hidden-layer neurons and output-layer neuron. The transfer function used in the hidden layer and output layer neuron are tan-sigmoid

( )x

h

exf −−

=1

1 and pure-linear ( ) xxf o = , respectively. Once the structure of the ANN is

618 X. Cao and L. Fan

done, the initial weights and biases are obtained through the off-line training. BP algorithm is used in this work. To get the satisfactory weights and biases, the train-ing data should slid over the entire speeds and q-axis currents. Supposing the load torque is a constant (TL=0N·m), two sets of data are obtained. The input matrix is the size of 4�960. while the output vector is the size of 1�960. After the off-line training is well performed, the weights and biases are considered as the initial pa-rameter set of the neural network controller. To tune the weights and biases, the neural network error gradient must be evaluated online. So the system output error between desired output (iq

*) and actual output (iq) is necessary. In fact, the desired output (iq

*) is unknown. So we can adopt the fuzzy logic to the ANN. using the desired speed and actual speed, we can get the q-axis current increment �iq to tune the weights and biases online.

3.2 Structure of the FC

In this work, the output of the FC is the q-axis current increment �iq, the number of the input variables is 2, giving

es1=�r(n)*-�r(n) . (6)

es2=�r(n-1)-�r(n) .(7)

The universe of all input and output variables are normalized to [-1 1] and the three fuzzy variables are divided into 7 fuzzy subsets with the linguistic values {NB NM NS ZO PS PM PB}. The fuzzy membership functions are shown in Fig. 1.

Fig. 1. Fuzzy membership functions of the input and output variables

In this work, using the reference speed and the actual speed, we can calculate es1

and es2. Once the actual speed can not track the reference speed. We can tune the weights and biases of the ANN with the output of the FC.

3.2 Online Weights and Biases Updating

The error function is given by

)(2

1)( 2 nine q∆= . (8)

Vector Controlled PMSM Drive Based on Adaptive Neuro-fuzzy Speed Controller 619

Using the error, we can update the weights and biases as follows [5].

)()()()1( nXnnWnW ihj

hij

hij ηδ+=+ . (9)

)()()1( nnBnB hj

hj

hj ηδ+=+ . (10)

)()()()1( nOnnWnW hj

ok

ojk

ojk ηδ+=+ . (11)

)()()1( nnBnB ok

ok

ok ηδ+=+ . (12)

Where xi is the output of the ith neuron of the input layer, hijW is the weight between

ith neuron of the input layer and jth neuron of the hidden layer, hjB is the bias of the

jth neuron, ojkW is the weight between jth neuron of the hidden layer and kth neuron

of the output layer, okB is the bias of the kth neuron, is the learning rate, h

jδ and

okδ are the local gradient, respectively. In real time implementation, error is

derived from the fuzzy controller at each instant. When the actual speed can track the reference speed, the output of the fuzzy controller is zero. Otherwise, the weights and biases will be updated online as described above. And the structure of the FNNC is shown in Fig. 2.

Fig. 2. Block diagram of the structure of the fuzzy neural network controller (FNNC)

4 Results of Simulation and Experiment

A block diagram of the proposed PMSM drive is shown in Fig. 3. The parameters of the PMSM are given in Table. 1. The simulation conditions are given:

r/min1000m,N52:1Case *r =⋅=×= ωLT,JJ ; mN5:2Case ⋅== LT,JJ .Where J is

the changed rotor inertia. For all the simulation conditions, the results of the reference speed �r

*, actual speed�r and the output of the NC ( iq) are given by Fig. 4, Fig. 5.

Table 1. Parameters of the PMSM

Rated power PN 3kW Rotor inertia J 7.25e-3kg.m2

Stator resistance Rs 2.875 Damping coefficient B 0.8e-3(N.m)/rad/sec Magnetic flux m 0.175Wb d-axis stator inductance Ld 8.5e-3H

Number of poles 4 q-axis stator inductance Lq 8.5e-3H

620 X. Cao and L. Fan

Fig. 3. Block diagram of PMSM drive with the proposed FNNC

Fig. 4. Simulation results of the proposed PMSM drive at case 1:(a) Track response (b) Control effort

Fig. 4 shows the simulation results of the load change (TL=0N�m�TL=5N�m) and the machine parameter change (J=7.25e-3kg.m2

�J=2*7.25e-3kg.m2). Because of these changes, the motor speed changes slightly, but the motor speed approximately tracks the reference speed after that.

Fig. 5. Simulation results of the proposed PMSM drive at case 2:(a) Track response (b) Control effort

At case 2, the reference speed follows a profile of 1000r/min-0r/min-1000r/min-0r/min, as depicted in Fig. 5. This figure shows the proposed control scheme is oper-ated well even if at the instant of the reference speed changes.

To verify the proposed control scheme, the laboratory control board was con-structed (Fig. 6). This system is based on TMS320LF2407 DSP. The parameters of the PMSM are given in Table. 1. Offline training of the neural networks is completed in the MATLAB/SIMULINK. When the load torque TL=5N⋅m and the reference speed *

rω change from 500r/min to 1000r/min, the results are given in Fig. 7. From Fig. 7 we can see the proposed control system has better performances than the conventional drive, and can adapt the running conditions quickly. In this experiment, all the results are derived from TDS2014 oscillograph.

Vector Controlled PMSM Drive Based on Adaptive Neuro-fuzzy Speed Controller 621

Fig. 6. Configuration of the proposed control system

(d) Speed response(c) A phase current

(b) Speed response(a) A phase current

Fig. 7. Experimental results of the PMSM drive: (a) (b) response of the conventional control drive; (c) (d) response of the proposed control drive

5 Conclusion

In this paper, a vector control scheme with the fuzzy neural network controller (FNNC) for the PMSM has been presented. FNNC includes neural network controller (NC) and fuzzy logic controller (FC). It combines the capability of fuzzy reasoning in handling uncertain information and the capability of neural network in learning from processes. The initial weights and biases of the artificial neural network (ANN) are obtained by offline training method. Using the output of the fuzzy controller (FC), online training is carried out to update the weights and biases of the ANN. The results of simulation have shown that the PMSM drive with the proposed FNNC has the merits of simple structure, robustness, accurate tracking performance, and parameter learning algorithms.

622 X. Cao and L. Fan

References

1. Lin. F.J, Lin, C.H..: A Permanent-Magnet Synchronous Motor Servo Drive Using Self-Constructing Fuzzy Neural Network Controller. IEEE Transactions on Energy Conversion, Vol. 19,No. 1,(2004)66-72

2. Liu, J., Liu D., Wu, P.S., Bai, H.Y.: The Simulation Analysis of Permanent Magnet Syn-chronous Motor Based on the Strategy of Modulating the time of Voltage Vector�Proceedings of the CSEE, Vol. 24,No. 10,(2004)148-152

3. Ha, J.I., Sawa, Toshihiro, Sul, S. K.: Sensorless Rotor Position Estimation of an Interior Permanent-Magnet Motor From Initial States. IEEE Transactions on Industry Applications, Vol. 39, No. 3,(2003)761-767

4. Yang, Y., D. Mahinda Vilathgamuwa, Rahman, M. A.: Implementation of an Artificial-Neural-Network-Based Real-Time Adaptive Controller for an Interior Permanent-Magnet Motor Drive. IEEE Transactions on Energy Conversion, Vol. 39, No. 1,(2003)96-104

5. Rahman, M. A, St. John: On-line Adaptive Artificial Neural Network Based Vector Control of Permanent Magnet Synchronous Motor. IEEE Transactions on Energy Conversion, Vol. 13,No. 4,(1998)311-318

6. Naitoh, H., Tadakuma, S.: Microprocessor Based Adjustable Speed dc Motor Drives Using Model Reference Adaptive Control. IEEE Transactions on Industry Applications, Vol. 23,No. 2,(1987)313-318

7. Dote, Y., Hoft, R. G.: Microprocessor Based Sliding Mode Controller for dc Motor Drives. IEEE/IAS Annual Meeting (1980)641-645

Appendix A: Inverse Dynamic Constants

.L

TKC;

L

TB;

L

TRA

)LKBLJR(TJLD;.D/]TRK[;D/]TK[;D/)]TRL(TK[

D/]LTK[;;D/LqJ;D/)]LKKKBR(T)LKBLJR(TLqJ[

q

b

qq

s

qqsqsTsq

qqbTsqqs

∆∆∆∆∆ϑ∆ε∆∆γ

∆δβ∆∆α

−==−=

+++=−==+−=

=−=++−+++=

111

22

32

1

1222

1

2

Where T is the sampling interval.