APPLICATION OF A SLIDING MODE OBSERVER FOR SENSORLESS OPERATION OF SWITCHED RELUCTANCE MOTORS. Stefan Brock
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1 APPLICATION OF A SLIDING MODE OBSERVER FOR SENSORLESS OPERATION OF SWITCHED RELUCTANCE MOTORS Stefan Brock Poznań University of Technology, Institute of Control and Information Engineering Piotrowo 3a, Poznań, Poland, Stefan.Brock@put.poznan.pl Abstract Purpose The purpose of this work is to applicate a sling mode observer for sensorless control of switched reluctance motor (SRM) drive Design/methodology/approach This paper presents an evaluation of the sling-mode observer to estimate the SRM speed and rotor position. Non-linear model of a SRM is used and a computer simulation is developed based on data from an experimental motor system. The implication of sample rate was examined. Finngs A new concept of observer based on a simple but quite accurate model of SRM has been proposed. Research limitations/implications The presented paper describe now the simulation results. Practical implications Practical implementation should be presented in the future. Originality/value The presented observer based on non-linear model of SRM is orginaly developed. Keywords: switched reluctance motor, sling mode observer, real time implementation Paper type Research paper I. INTRODUCTION The points in favour of switched reluctance motor (SRM) are simple and economical construction, high maximal speed and the possible high reliability. Generally SRM requires a rotor position sensor for correct commutation. The use of inrect position sensing can eliminate the mechanical complexity, reduce cost and increase reliability. Various methods of sensorless position estimation have been investigated for SRM. First group of methods is based on principle of inductance measurement in one of the inactive phases. The drawbacks of
2 these methods are the generation of non-useful torque by injecting a test pulse and low resolution for high-speed operation. The second group of methods uses the state observer theory, which estimates the position of rotor by using measurements of phase voltages and currents. The sling mode observers are robust with regard to the parameter variations and load. Husain et al. [1 3] presented a sling mode observer (SMO) rotor position estimation scheme for SRM. This observer is based on linear magnetic model of SRM [1,2], and on algebraic modelling of saturation nonlinearity [3]. Similar work was presented by Park et al. [4]. Zhan et al. [5] proposed sling mode observer for SRM based on estimation of the phase currents. Although the magnetic circuit is linearized, the practical realisation of the observer algorithm requires a great amount of computation. In this paper method proposed in [1 3] is extended for non-linear model of a SRM. Model is based on data from an experimental motor system [7]. The implication of sample rate is examined. II. MODEL OF SWITCHED RELUCTANCE MOTOR In general, the nonlinear magnetics characteristics of a SRM can be appropritely modeled by 2D tables defing the nonlinear flux-current-angle and torque-flux-angle charakteristics. 2D look-up tables are hard to implement for real time application due to interpolation and memory size. In this paper, the flux equation for each phase, governing the SRM dynamics can be written as follows: ψ (, Lc + L ( )* sat( = (1) where components of phase inductance L c and L and non-linear saturation function sat( can be can be identified through measurements [7]. The results of the experimental identification are presented on fig. 1. Fig. 1. Inductivity L () and effective current sat( identification results
3 The derivative of eqq. 1 can be written as: where dψ (, ω = is the speed of the motor. Table value dl ( ) dsat = Lc + ω sat( + L ( ) (2) dsat experimental data L ( ) and sat(. Accorng to equation 3: ( ( dl ( ) and can be calculated based on dψ = u R i the state equation 4 for phase currents can be writen: dl ( ) u R i ω sat( = dsat ( ) ( Lc + L Based on derivative of coenergy, the torque T generated by every phase can be desribed as equation 5: i i dl ( ) T(, = ψ (, ι)dι = sat( ι)dι 0 0 i= const (3) (4) (5) i The integral sat( ι) dι can be also calculated from experimental data sat(. 0 The equations of mechanical part are (6): 1 ω& = Tph L J N (, T & = ω (6) From equation 1 to 6 the model of SRM can be build. The model is presented on fig. 2. III. PROPOSED OBSERVER ALGORITHM For an SRM described by equation (1)-(6) the sling mode observer SMO is implemented by the form (7) (9) as showed in fig. 3. The estimation error e est is chosen as fference between fluxes calculated from measured voltage u m and current i m and fluxes calculated from non-linear characteristic (1) with estimated position ˆ.
4 t e = est F m m, m 0 ( u ( τ ) i ( τ ) R) dτ ψˆ ( ˆ i ) The estimated position is sequencing to interval <-π/6,π/6> (for four phase 8/6 SRM). In this case the error function F() can be chose as the sum of flux error for each phase. The sign of estimation error is used as input for speed and position observer (8)-(9). & ˆ ω = K sgn ω ( ) e est & ˆ = ˆ ω + K sgn Fig. 2 Model of SRM ( ) e est (7) (8) (9) u m e ψ e est ψ(u, im + F - sgn() K ω ^ ψ(, K ω^ + + LPF ^ sequencer ± (π/6) Fig. 3. Block agram of the sling mode observer
5 Gain K ω is selected to be large enought to compensate the terms of speed equation (6). It can be shown that by appropriate selecting of gain K ω and K convergence properties and the desired dynamics of the observer can be achieved. Because the estimated speed contains the chattering component, the low pass filter (LPF) should be used. IV. TEST RESULTS The simulation results using the proposed SMO are shown in Fig. 4. The left column is for system with position feedback, the middle column is for system with fast, semi-continuous observer (sampling time 1 µs) and the right is for screet time observer (sampling time 50 µs). For observer there is the initial position error =π/12. The step change of reference speed from still stand to 35 rad/s is simulated. From Fig. 4. Speed and position estimation, phase currents and total torque without observer, with semicontinuos observer and with screet time observer.
6 these figures, the proposed observer shows a good performance for fast implementation, but it is sensitivity to larger sampling times. V. CONCLUSION In this paper a sling mode observer was applied to eliminate the position encoder of a switched reluctance motor drive. The observer requires terminal measurements of phase voltages and currents. The implication of sample rate was examined. The next study will be focused on the fast observer real time implementation using DSP and FPGA REFERENCES [1] R. A. McCann, I. Husain, Application of a sling mode observer for switched reluctance motor drives Proc. of IEEE Applications Conference, New Orleans, USA, 1997, pp vol.1 [2] R. McCann, M.S. Islam and I. Husain, "Application of Sling Mode Observer for Switched Reluctance Motor Drives," IEEE Trans. on Industry Applications, Vol. 37, No. 1, pp , Jan.-Feb [3] M. S. Islam, I. Husain, R.J. Veillette and C. Batur, "Design and Performance Analysis of Sling- Mode Observers for Sensorless Operation of Switched Reluctance Motors," IEEE Trans. on Control Systems Tech., Vol. 11, No. 3, pp , May, [4] Y.J. Zhan, C.C. Chan, and K.T. Chau, A novel position and velocity observer for robust control of switched reluctance motors, Proc. of IEEE Power Electronics Specialists Conference 1998, pp [5] H.-W. Park, J.-H. Park, S.-J. Kwon, J.-G. Park, C.-U Kim, A Novel High Performance Position Sensorless Control of Switched Reluctance Motor Drives Proc. of IEEE International Symposium on. Industrial Electronics, Pusuan, Korea 2001, pp [6] I.-W. Yang and Y.-S. Kim, Rotor speed and position sensorless control of a switched reluctance motor using the binary observer IEE Proceengs - Electric Power Applications -,Volume 147, Issue 3, May 2000 pp [7] J. Deskur, A. Maciejuk Modelling of switched reluctance motor drive, Proc. of Symposium on Electromagnetic Phenomena in Nonlinear Circuits, Maribor, Slovenia 2006 Acknowledgement: The paper was supported by a grant No 3 T10A of Polish Ministry of Science and Information.
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