a neural network approach to position sensor less

8/4/2019 A Neural Network Approach to Position Sensor Less

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A Neural Network Approach to Position SensorlessControl of Brushless DC Motors

Fengtai Huang Dapeng TienMachine Laboratory Neural Network CentreDepartment of Electrical EngineeringNgee Ann Polytechnic, Singapore

Email: [email protected] [email protected]: To control brushless dc motors without usingposition sensors has been a challenging task for sometime. This paper presents a new approach to the prob-lem based on neural network methods. Instead of us-ing position sensors, neural networks are used to iden-tify the rotating angles of the rotor. Neural networksare trained to associate between the measured phasevoltages and currents and the rotor positions. Oncethis association is established, the networks performindependently to identify the rotor positions based onthe measured voltages and currents. The background,theoretical analysis and the results obtained are de-scribed in this paper.

the stator phase current vector. The 6 and i are givenby: .i,= v ,e i~ vbej1200 + v c e j 2 4 ~ 0- 0 (2)(3)a e j OD + be j l20" + C ,j24Oo

where U,, 216, v, are stator phase voltages and i,, i b , i,are stator phase currents. For a balanced 3-phase mo-tor, the phase voltages add up to zero and so do thephase currents, i.e.:

V a $. V b + vc = 0ia + b + i, = 0 (4)(5 )

substitute (4 ) into ( 2 ) and (5 ) into (3),

A brushless dc motor requires a rotor position sensorfor commutation and current control. Resolvers andabsolute encoders are used as position sensors, Thesesensors increase the cost and size of the motor andrestrict the industrial drive applications. Because ofthis, many efforts have been made to eliminate themechanical sensors [l , , 3 , 4, 51.

Several methods have been proposed to detect therotor position signal of a brushless dc motor: com-paring the motor source voltages with phase voltages[l];solving the state equations of the motor; andmore recently, identifying the conducting state of free-wheeling diodes [3] and obtaining the position of themotor by detecting the switching signals of the slidingmode observer [4]. This paper presents a new posi-tion sensorless control for brushless dc motors basedon neural network techniques.

- 3 J 3 .i = -i, + - ( 2 , + 2 i b )2 2 (7)The 'stator phase back emf vector 2 in (1) s determinedby,

where 3 is the sta tor phase flux linkage vector. Thisflux vector 4 an be defined in the following form:d = LF - ( e ) (9)where L = L, - M , L, is the self inductance of thestator windings, M is the mutual inductance of thestator windings and i ( 0 ) is the magnet flux linkagevector which is a function of rotor position 8. Thei ( 8 ) is given by,

X(O) = A a ( s ) e j o o + & ( e ) ej120 + ~ , ( , 9 ) ~ j 2 4 0 " (10)where .Aa(8),A b ( e ) , & ( e ) are the magnetic fluxes link-ing the stator phase windings and can be describedby:11. The Mathematical Model

The mathematical model of a brushless dc motor canbe described in space vector form as:

x , p ) = cos(qA, (B) = A , cos(e+ 1200) (11)b ( 8 ) = Am Cos(8 - 2 0 ' )e^=ij-Ri ( l )

where e is the stator phase back emf vector, 6 is thestator phase vector, R is the stator resistance and iswhere A , is the amplitude of the flux linkage estab-lished by the permanent magnet as viewed from thestator windings.

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Substitute (6), (7) and (8) into (1) and integrateboth sides, equation (1) becomes,'$a = / 32 ( v a - ~ ~ a ) + j - [ ( v a + 2 v b ) - . t t o ) l ) d 7

0 2(12)where 6, s the actual flux. Substitute (7), (10) and

(11) into (9 ) yields:3 & 3cos(8)]+ j[-(iu +2ib) - m - in(8)](13)2 2e= - Awhere 4e is the estimated flux. By directly measur-

ing the motor phase voltages and phase currents, theactual flux linkage vector can be estimated as shownin (12). The estimation of rotor position based on theflux linkage as shown in (13) is achieved by applyingneural network algorithms.

111. Neural Network AlgorithmEquation (12) and (13) are used as two independentobservers to estimate the flux linkage vector. One in-volves the measured voltages and currents only (12),and the other provides the reference for the estimationof the rotor position (13).

The integration of (12) is evaluated using a numer-ical technique at discrete time intervals. By applyingthe r ec t anguh rule:

where AT is the sampling interval. The initial valueof flux da(0)can be found by bringing the rotor to aknown position before starting.

The estimation of the rotor position (13) is also car-ried out at discrete time intervals,

32(k) = - [ i a ( k ) - m cosqk)]

The aim of the neural networks is to minimize thesum of the squared error function between the esti-mated value deand the actual value $,

P

p = l

where P is the number of training patterns, and Jp(e)is the total squared error for the p th pattern, i.e.

q= 1

where N I is the number of nodes in the output layer,~ 1 , ~s the output of the qth node in layer I , xp is thepth training sample and dq(cp) s the desired responseof the qth output node for the pth training sample.

The weights of the network are determined itera-tively according to the following equation:

where p is the learning rateIt can be seen from (18) that the estimation of

the gradient is the sum of all pattern samples, i.e.This is quite difficult in a- real train-ing situation , because the network weights have to be

updated before all the patte rns pass through the train-ing phase. In practice, the estimat ion of the gradientis based on a single sample. i.e. (18) becomes:

BJ,8EP--1 awl ,J , , '

where ( k mod P ) is the index of the pattern used toestimate the gradient at the kth itetation.

This crude estimation works well because the er-rors occurring are often reduced to an arbitrarily smallnumber through the repeated iterations.

The sigmoid function, fs = (1 + exp(-py))-', isused as the nonlinear activation at the output. Thesensitivity of Jp(B) to the output of node ulj can bewritten:

(22)The results in (20) to (22) are substituted in (19)

to form the gradient search algorithm. Equation (21)is called the hidden layer error, and (22) the outputerror.

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The networks work in the following manner: duringthe training phase, measured voltages and currents, U,,V b i, i b , are provided to the networks. The networkoutput, 13,is used to generate the estimated flux link-age (13). The error between the actual flux linkage4, 12 ) and the estimated flux linkage is calculated.This error is then used to modify the network weightmatrices, which are used to generate the new angle8. This process is repeated until the error is within apre-set value.

Once the training is finished, the neural networksestablish the relationship between the input volt-ages/currents and the rotor angles, hence can be usedas a sensorress rotor angles identifier.

R = 2.1RIce = 0.13V/rad/sJ = 147gcm2

IV. Simulations and Results

L = 2mHpoles = 8P = 29QW

To verify the proposed approach of the position es-timation, digital simulations were carried out . Therequired phase voltages and currents were measureddirectly from an existing brushless dc motor drive sys-tem. This system consists of a brushless dc motor,an incremental encoder, a PI controller and a PWMcurrent controller. The rotor position required by thecurrent control and corpmutation is provided by anup-down counter. The input of the counter is fromthe encoder. The parameters of the brushless dc m dtor are listed in Table 1. The three phase windings ofthe motor are delta connectedsexternally, so that thephase current can be accessed. Standard voltage andcurrent transducers were used together with a 14-bitAD/DA card as a part of a data acquisition system.

Table 1: The brushless dc motor parameters.

The rotor positions were estima$ed under two dif-ferent speeds: 3000 rpm and 6000 rpm. The simula-tion results at 3000 rp m are given in Figure 1. Fig-ure l(a) shows the measured motor phase voltage andcurrent. Figure l(b) and Figure l(c) present the mea-sured and estimated rotor positions. Figure 2 showsthe simulation results at 6000 rpm. The measuredmotor phase voltage and current are presented in Fig-ure 2(a). The measured and estimated rotor positionsare given is Figure 2(b) and (c). Note that the rotorpositions stand for the electrical rotor position. Th eactual physical position of the rotor should be scaleddown by a factor of 4 ince the motor has 8 poles.

V. ConclusionsA neural network approach to rotor position estima-tion of a brushless dc motor was proposed. The sim-ulation result shows that stator voltages and currentscan be used to est imate the rotor position. The newapproach is based on flux linkage estimation, whichmay pave the way to intelligently controlling a brush-less dc motor in real time.

. . .. .. _ . .~ . .. . .. . .. . . .

. . . .time (Wd i v )Q

0 5 10 IS 20

time (ns)(4Fig1Simulationresult Z?X 3ONi rpm.(a): m d otor p k oltag~ nd current,CO). measured rotor position;(c ) .estimited rotor po-'til on.

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References[l] T. Endo. Microcomputer-controlled brushless mo-

tor without a shaft-mounted position sensor. InProceedings of the 1983 International Power Elec-tronics Conference, pages 1477 - 1488, The Insti-tute of Electrical Engineers of Japan , Japan , 1983.

[2] K. Lizuka, H. Uzuhashi, M. Kano, T. Endo, andK. Mohri. Microcomputer control for sensorlessbrushless motor. IEEE Transactions on IndustryApplications, 19:595 - 601, 1989.m e 2ddiv) [3] Satoshi Ogasawara and Hirofumi Akagi. An ap-proach to position sensorless drive for brushless dcmotors. I E E E Transactzons on Industry Applzca-tzons, 27(5):928 - 933, September 1991.

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[4]Takeshi Furuhashi, Somboon Sangwongwanich,and Shigeru Okuma. A position-and-velocity sen-sorless control for brushless dc motors using anadaptive sliding mode observer. IEEE Transac-tzons on Industry Electronics, 39(2):595 - 601,April 1992.

time (2mddiv)@I[5] T. H. Liu and C. P. Cheng. Controller design

for a sensorless permanent-magnet synchronousdrive system. IEE Proceedings-B, 140(6):369- 78,November 1993.

0 5 10 I5 20

Fig2 Simulation result at 6000 rpm.(a). measured motor phasevoltage and me n t ;@). mcasurd rotor position;(c).estimated rotor position.

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a neural network approach to position sensor less

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