Sensorless Rotor Position Estimation for Switch Reluctance Motor: A Review

Sensorless Rotor Position Estimation for Switch Reluctance Motor: A Review

T. M. Shubham, Pramod Pal

1. ech Scholar, Department of Electrical Engineering, Maulana Azad National Institute of Technology Bhopal

   Abstract- Rotor position information in SRM is important for steady state operation because nature of torque depends entirely on inductance profile of machine. Inductance at any instant depends on rotor pole position with respect to stator pole of energized phase. So, it is necessary that information of rotor position should be specific throughout operation right from starting of motor. Easiest way of collecting rotor position information is using position sensors but it reduces reliability and putting further mechanical constraints. Efforts being made to replace position sensors and proper position estimation techniques are being applied called as sensorless techniques. In this paper, different sensorless position estimation techniques are discussed with their shortcomings.

   Amit Ojha

   Assistant Professor, Department of Electrical Engineering,

   Maulana Azad National Institute of Technology Bhopal

   Inductance

   at any instant of operation as shown in figure 1. The nature of starting torque will depend on position of rotor accordingly it can move forward or backward. Sensorless operation in running condition cant be implemented without proper starting technique. Proper algorithm is desired which will give better estimation of position during running. There should be proper technique to start motor conveniently. In this paper different sensorless techniques both for starting and steady state running are discussed.

   Keywords- AC- DC convertor, Asymmetric H-bridge, Reluctance torque, State observer, SRM

   1. INTRODUCTION

      Nowadays Switched Reluctance Motors (SRM) is becoming popular in the field of automation industry due to its several advantages. It has simple structure and has good mechanical strength due absence of rotor winding and permanent magnet rotor. SRM does not contain conductors which permits it to achieve high efficiency especially in high speed region for prolonged operation. Also the copper losses are less in SRM then any motor. The main agenda in motor drives is to obtain a low cost, high performance motor drive but both are contradictory parameter, therefore main focus of researchers is to obtain an optimal solution. Now the problem faced during operation of SRM is torque ripple, accuracy in position estimation and stored reactive power.

      torque

      (a)

      (b)

      (c)

      Rotor position (in deg)

      Rotor position

      Rotor position (in deg)

      current

      Torque ripple can be minimized by increasing the number of stator phase but consequently it increases the cost. Stored reactive power is handled by using capacitors.

      This paper is focused on rotor position estimation. Position of rotor is defined in terms of the position of rotor poles with respect to stator poles. It can be done either by use of sensors (like encoder, hall sensors) or by use of mathematical modeling (sensorless) for position estimation. Obviously sensorless techniques are cost effective but accuracy is an issue. Due to non linear magnetic structure, it exhibit variable inductance. Torque will also be variable in nature as it is proportional to the rate at which inductance is varying so it may be positive, negative or zero (positive torque is the torque which drive rotor in required direction)

      Fig 1(a) inductance variation v/s rotor position (b) torque variation v/s rotor position (c) current v/s rotor position

   2. BASIC MODELLING OF SRM

      SRM is an electric machine that operates due reluctance torque. In SRM, both stator and rotor have salient-poles, which contributes to produce a reluctance torque

      The basic principle of SRM operation is that when a stator phase is excited, the rotor of the SRM always rotates to the nearest position of minimum reluctance (when stator and rotor poles aligned). To minimize reluctance of flux path rotor poles tend to align with stator poles by producing reluctance torque. When stator pole becomes nearly aligned

      with rotor pole, the excitation of active coils is removed because after that rotor will move further and there is decrease in inductance. As the rate of change of inductance will become negative the torque will produce in negative direction. And hence opposes the normal motion of machine. Therefore the adjacent winding will be energized and the previous winding will be de-energized and same process goes on further. By selectively exciting the stator pole pair continuous synchronous motion can be produced. The number of poles on SRM stator is usually unequal to number of poles on rotor to avoid the possibility of zero initial torque.

      The fundamental equations of an SRM can be generated in terms of phase voltage and torque as follows

      V = R. i + L rms , i di + i dl(rms ,i) rms (1)

   3. STARTING OF SRM

      Different methods are discussed for starting of motor without using sensors.

      1. Feed Forward Open Loop Method

         The motor is controlled feed-forward in open loop as a stepper motor. In this method a train of pulses of fixed frequency is applied to each phase of motor in a sequence. Each phase pulse train is phase shifted by 22.5 degree. Now frequency is increased linearly in order to increase the rotor speed.

         Shortcomings- It is neither efficient nor optimal, but it permits a reliable start even under load.

      2. Locking the rotor along a particular phase axis

         dt

         Tm = 1 i2 dl (rms ,i)

         drms

         (2)

         In this method one phase is excited for sufficient time so

         2 drms

         where, R : resistor of phase winding, rms : rotor position,

         rms : rotor speed,

         L (rms , i) : inductance is linearly varying with rotor position for a given current

         Now in equation (2) it clearly observed that motor torque is directly proportional to rate of change of inductance. As the rotor pole approach to the stator pole, inductance increases and slope is positive and hence the torque. But as rotor pole get completely aligned with stator pole and starts moving away from stator pole its inductance starts decreasing and slope become negative thus making torque negative.

         So firstly we have to find the position of rotor at standstill and should apply the supply in such a way so that positive torque is produced

         WhereRn , In , vn and are the resistance, current, and voltage of the nth phase respectively. It is assumed that each phase is magnetically decoupled from every other phase. The rotor angular position and velocity are denoted by and , respectively. TL is the load torque.

         that rotor may experiences a force and rotor poles get aligned to one of stator poles. Once the rotor poles get aligned to any stator poles the position of all the phases with respect to rotor can be obtained and with suitable switching logic motor can be started.

         Shortcomings- The inductance profile of SRM is such that there is no- torque zone near aligned and non-aligned region in which even if we excite rotor winding, motor will not experience any torque. So if rotor is positioned in that region then motor cannot be started.

      3. Flux Computation Technique

         In this method, voltage pulse is injected in any phase and flux linkage is computed. Using the value of current and flux, position of rotor in starting can be obtained by using flux linkage characteristics same as in running condition. Theoretically, in this method excitation of one phase ay not give the accurate result, so two phases will be excited at a time to get a better and accurate result. Besides if particular phase is in the no-torque zone then estimated position will be error prone.

         Shortcomings- Before the actual start, rotor may move backward and hence hesitation is observed.

         Torque

      4. Three Phase Excitation Method

      Base speed

      Speed

      Constant power T1/

      T1/2

      This method is most reliable for estimation of rotor position for starting of SRM. In this method test signals are given to excite all the phases simultaneously. By exciting all the phases up to a moderate value of flux and current such that there will be no appreciable rotor movement. Now during excitation current of all the phases are measured. The phase will have maximum inductance with which rotor poles are aligned. So that phase will have minimum current among all phase.

      Shortcomings- Extra care has to be taken while choosing the time duration for excitation of phases because if we excite the motor for long time the rotor will experience a force, which may be negative or positive so again there will

      Fig 2 Speed Torque characteristics of SRM

      be change in rotor position.

   4. SENSORLESS METHOD FOR RUNNING

      Running of SRM requires a DC source, power convertor like asymmetric H-bridge. DC source can be obtained by using any AC- DC convertor. There are many power convertors which are used for driving SRM. Controllers are used to control timing and width of switching pulses given to power switches of power convertor. Due to its non linearity SRM produce all three types of torques i.e. zero, positive and negative torque.

      Pulses should be given to power switches at the instants when rotor is in such position that machine can give positive torque to rotor. So basis of controller is position sensing. Now position sensing can be done by either using sensor or without sensor i.e. sensorless. In sensorless methods position of rotor is to be estimated. More accuracy in position sensing leads to good performance as accuracy increases machine performance also improves. Methods of

      This method is based on the comparison of the estimated flux linkage and the reference flux linkage in order to define turn-off (commutation) position. This is called on-off control method. In this method, actual flux linkage value is compared with reference value. When the estimated flux linkage is nearly equal to the reference flux linkage, it indicates that the switching position has been reached and the commutation can be performed .Gate pulse is removed, convertor switch is turned off and the following phase is turned on. Reference flux linkage is obtained from the magnetization characteristic as a function of phase current for the desired commutation position. The reference flux linkage is obtained from the flux linkage in the aligned position of the rotor. Flux linkage is calculated and it is compared with the reference level from the reference magnetization curve.

      (u-RI)dt

      position sensing are classified as follows:

      The sensorless methods of estimation can be classified into modern control-based and inductance-based estimation schemes.

      The inductance-based estimation methods exploit the inherent unique characteristic of the three-dimensional relationships among the flux linkages or inductance, current, and rotor position,. And the availability of the first two variables leads to resolution of the third unknown, i.e. rotor position. A number of methods does exist using inductance-

      uphase

      	RI
      Iphase

      cal

      +

      –

      ref

      Look up table with theta commutation values

      based estimation. They can be further divided into direct and indirect forms of inductance measurement. The salient difference between these methods lies in which either the inductance is measured directly or by monitoring other variables.

      Fig 3 Block Diagram for angle control method

      Lookup table with (i,phase)

      Voltage equations, neglecting the saturation and the induced voltage, can be expressed as follows:

      V = RI + L dI/dt (3)

      0

      The modem control methods are based on observer and intelligent control techniques. The observer-based methods

      = t V RI dt

      (4)

      use a state observer or a sliding mode observer, both of which essentially depend to an extent on the inductance slope for their convergence and functioning. The observers are computationally intensive and have the problem of

      Using equation (4) flux linkage (reference value and actual value) can be calculated

      convergence in terms of the time taken to converge to the correct estimates. The intelligent control methods encompass estimators based on artificial neural networks and fuzzy control. These methods are computationally less intensive compared to observer methods but due to their

      Reference

      speed

      Power supply

      PWM

      Desired

      Current

      AC/DC

      Power converter

      Desired current

      SRM

      learning capability provide adaptive control. The accuracy of the rotor position estimation is not sufficient for high- performance applications, such as a position servo control application, but is acceptable in many other industrial applications. Most of the sensorless methods require phase currents and applied voltages for their estimation.

      Speed error

      Speed regulator	s	peed

      voltage

      Angle calc

      current MUX

      regulator

      comparator

      voltage

      Calc flux

      Ref flux

      1. Inductance-based estimation method

         Machine has inherent property of variable inductance.

         Speed calc

         Commutation angle

         Inductance is a function of rotor position. Reluctance torque is a function of inductance and current but DC source is used in operation so torque is solely depends on rate of change of inductance.

         Here flux linkage is used for estimation of rotor position. Flux linkage is also proportional to inductance as current is constant so with the help of flux linkage also rate of change in inductance can be traced since inductance is not measured directly. This method can be called as indirect method

         Fig 4 Speed Control of SRM

      2. Sliding mode observer

         The magnetic nonlinearities of an SRM can be taken into account by appropriate modeling of the nonlinear flux- current- angle (-i- ) characteristics of the machine. The output electromagnetic torque of the machine can also be described by nonlinear torque-current-angle (T-i- ) data.

         The machine model may be described by

         = (I, ) (5)

         T = T (I, ) (6)

         The state-space differential equations of the SRM to be solved are

         To keep the system in the sliding regime, a proper equation must be defined for the sliding surface as a function of the system states, in this case the equation of sliding surface is e = 0.

         Slide Mode Controller (SMC) forces the system states to slide on e = 0 surface in the state space. If the states slide

         dn = R

         dt

         n In

         t + vn

         (7)

         on the desired surface that means that the system is under

         control. If the numerical value of e = 0 is equal to zero, than the system is on the sliding surface, otherwise, not. The

         d = (t) (8)

         dt

         numerical value of e = 0 is calculated by entering the actual values of the states. When (x) is greater than zero, this means that a control signal must be applied to decrease

         d = D t + 1 n Tn (,

         ) 1 TL (9)

         the value of e = 0. The opposite occurs when e = 0 is

         dt J J n J less than zro.

         Sliding mode observer or state observer depends up to an extent on the inductance slope for their convergence and

         the sliding-mode observer incorporates a state-space model of the SRM to estimate rotor position and velocity. The

         Inverter

         State Observer

         Controller

         sliding-mode observer estimates rotor position and velocity from phase current and terminal voltage measurements. An error correction term is computed based on the difference of the motor flux computed from the mathematical model and that derived from motor measurements.

         0

         n t = t[vn t In t Rn ]dt

         (10) v

         SRM

         i

         Consider a second-order sliding-mode observer for the SRM of the form

         = + ksgn(ef ) (11)

         = ksgn(ef ) (12)

         Where and are the estimated rotor position and velocity, respectively, and ef is an error function based on measured and estimated variables.

         e t = t (t) (13)

         e = t (t) (14)

         Differentiating both sides of (13) yields

         T

         SRM model Eqn(5)&(6)

         i

         Flux observer Eqn(10)

         v

         (a)

         Slide mode observer

         de = d d

         (15)

         (b)

         dt dt dt

         Substituting eq. (11) and eq. (13) in eq. (15) produces

         f

         de = t t k sgn(e )

         dt

         And using (12) yield the position error dynamics

         dt

         de = e k sgn (ef) (16)

         Similarly velocity error dynamics become

         f

         de = k (e ) (17)

         dt

         Thus, (16) and (17) describe the convergence properties of the observer. Once the sliding surface e = 0 is reached,

         Fig 5 (a) Block diagram of model based sensorless controller.

         (b) Sliding mode observer theory based observer

   5. CONCLUSION

Of all the methods used to start SRM, three phase excitation method is most effective but care should taken while implementing because if we give keep supply for long time the rotor will change the position. In sensorless methods used for steady state operation, inductance based estimation method is more reliable because it easy to implement. While state observer are computationally intensive and have the problem of convergence in terms of the time taken to converge to the correct estimates. Still it has been studied extensively to tackle problems of the nonlinear dynamic control systems.

the error dynamics become

de = 0 dt

de = k e

dt k

REFERENCES

1. R. Krishnan, Switched Reluctance Motor Drives, CRC Press 1996

2. T.J.E. Miller, Switched Reluctance Motors and Their Control,

   Magna Physics Publishing and Clarendon Press, Oxford 1993

3. R. Krishnan, Switched Reluctance Motor Drives: Modeling, Simulation, Analysis, Design, and Applications, CRC Press (2001), pp. 351-384

4. A. K. Pradeep, J. P. Lyons, and S. R. MacMinn, Application of sliding mode observers for state estimation in rotating machines, in Proc. VARSCON91, June 1991, pp. 5764

5. R. Visinka 3-Phase Switched Reluctance (SR) Sensorless Motor Control Using a 56F80x, 56F8100 or 56F8300 Device, Freescale Semiconductor Application Note AN 1932, Rev 2/2005

6. L.Xu and J. Bu, Position Transducerless Control of a Switched Reluctance Motor Using Minimum Magnetizing Input, Proc. Of 32nd IEEE/IAS Ann. Meeting, 1997, pp. 533-539

7. S.R MacMinn, W.J Rzesos, P.M. Szczesny, and T.M.Jahns, Application of sensor integration techniques to switched reluctance motor drives, Conf. Rec. IEEE Industry Applications Society Annual Meeting, 1988, pp. 584-588.

8. D.A.Torrey and J.H.Lang, Modeling a nonlinear variable reluctance motor drive, IEE Proceedings., Pt. B, Vo1.137, No.5, pp.314.326, Sept., 1990

9. A. Brosse, G. Henneberger, M. Schniederneyer, R. D. Lorenz, and

   1. Nagel, Sensorless Control of a SRM at Low Speeds and Standstill Based on Signal Power Measurement, Proceedings of IEEEIECON 98 Conference,1998, pp. 1538-1543.

10. B. Fahimi and A. Emadi, Robust Position Sensorless Control of Switched Reluctance Motor Drives over the Entire Speed Range, Proceedings of Power Electronics Specialists Conference, 2002, vol.1, pp. 282 288

11. C.S. Dragu and R. Belmans, Sensorless control of switched reluctance motor, 15th International conference on electrical machines (ICEM), Brugge, Belgium, August 25-28, 2002

12. Subrata Saha, Kyoe Ochiai, Takashi Kosaka, Nobuyuki Matsui andYoji Takeda Developing a Sensorless Approach for Switched Reluctance Motors from a New Analytical Model, Proceedings of Thirty-Fourth IAS Annual Meeting, Conference Record of the 1999 IEEE, vol. 1, pp. 525-532.

13. M. Ehsani, I. Husain, K. R. Ramani, and James H. Galloway, Dual- Decay Converter for Switched Reluctance Motor Drives in Low Voltage Applications, IEEE Trans. On Power Electronics vol. 8, no. 2, April 1993.

14. Freescale, Apparatus and Method for Estimating the Coil Resistance in an Electric Motor", Chalupa, L.,Visinka, R., US Patent, 6,366,865,2002-04-02

15. A. Lumsdaine and J. H. Lang, State observers for variable reluctance motors, IEEE Trans. Ind. Electron., vol. 37, pp. 133 142, Apr. 1990

16. E. A. Misawa and J. K. Hedrik, Nonlinear observers: A state-of- the-art survey, ASME J. Dynam. Syst. Meas., vol. 111, no. 3, pp. 344352, 1979

17. J. J. Slotine, J. K. Hedrik, and E. A. Misawa, On sliding observers for nonlinear systems, ASME J. Dynam. Syst. Meas., vol. 109, pp. 245252, Sept. 1987

18. I. Husain, S. Sodhi, and M. Ehsani, A sliding mode observer based controller for switched reluctance motor drives, in Conf. Rec.

    IEEE-IAS Annu. Meeting, Denver, CO, 1994, pp. 635643

19. F. Blaabjerg, L. Christensen, S. Hansen, J. P. Kristofferson, and P.

    1. Rasmussen, Sensorless control of a switched reluctance motor with variable-structure observer, Electromotion, vol. 3, no. 3, pp. 141152, July 1996

20. Y. J. Zhan, C. C. Chan, and K. T. Chau, A novel sliding-mode observer for indirect position sensing of switched reluctance motor drives, IEEE Trans. Ind. Electron., vol. 46, pp. 390<397, Apr. 1999

21. McCann, R.A. Islam, M.S. Husain, I., "Application of a sliding mode observer for position and speed estimation in switched reluctance motor drives," Industry Applications, IEEE Transactions on , vol.37, no.1, pp.51,58, Jan/Feb 2001