Speed Observer Based Load Angle Control of Induction Motor Drive


Published on

The performance of induction motor drives
gets improved in the scalar control mode with various
algorithms with speed /position feedback. In this paper
load angle control of induction motor with speed observer
is presented. This eliminates the physical presence of
speed sensor. The basic control of rotor flux vector with
stator current defines the dynamics of torque control. In
this scheme, estimation of feedback variables is obtained
by using algorithm with minimum number of machine
parameters. The speed obtained is thus used in feedback
loop to improve the machine performance. The proposed
algorithm also has a capability to estimate the active and
reactive power of the machine. This is further
incorporated to improve the operating efficiency of the
machine. The observer developed is tested for various
dynamics condition to verify its operating performance in

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Speed Observer Based Load Angle Control of Induction Motor Drive

  1. 1. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 Speed Observer Based Load Angle Control of Induction Motor Drive Gaurav N. Goyal1 and Dr. Mohan V.Aware2 1 Shri Ramdeobaba Kamla Nehru Engineering College /Electrical Engg. Department, Nagpur, India Email: gaurav.goyal13@gmail.com 2 Visvesvaraya National Institute of Technology/ Electrical Engg. Department, Nagpur, India Email: mva_win@yahoo.com Abstract— The performance of induction motor drives arrangement.Thus from the beginning of 1980’s theregets improved in the scalar control mode with various were serious research works throughout the world toalgorithms with speed /position feedback. In this paper control induction machine without the need for speedload angle control of induction motor with speed observer sensor [1]-[7]. It is possible to estimate the speedis presented. This eliminates the physical presence ofspeed sensor. The basic control of rotor flux vector with signal from machine terminal voltage and currentsstator current defines the dynamics of torque control. In with the help of digital signal processor (DSP).this scheme, estimation of feedback variables is obtained Different methods are used for flux and speedby using algorithm with minimum number of machine estimation. The calculation method of state variableparameters. The speed obtained is thus used in feedback may be classified as models and observers. Models inloop to improve the machine performance. The proposed comparison with observers are less complicated in thealgorithm also has a capability to estimate the active and case of induction motor. The accuracy of thesereactive power of the machine. This is further variables depends on the motor operating point,incorporated to improve the operating efficiency of the exactness of the parameter used, and the sensitivity ofmachine. The observer developed is tested for variousdynamics condition to verify its operating performance in the model to drift in these parameters. The voltageMATLAB/SIMULINK. model is not precise at low frequencies; however it is not sensitive to rotor resistance variations. On the Index Terms— Speed sensorless induction motor, Load other hand, the current model is sensitive to rotorangle control, speed observer, Energy efficiency resistance variations and is not accurate in calculating the rotor speed, especially at high speed. However, it I. NOMENCLATURE is more precise, compared to voltage model, and at lower frequencies .the mixed model integrates theus,is,Ψs, Ψr Stator voltage, current and flux, rotor advantage of both models. Because of these flux inaccuracies in calculating the flux linkage, in manyRs, Rr, Ls, Stator resistance, rotor resistance, solutions an observer by introducing an additional stator feedback loop is used. The load angle is the angleLr, Lm inductance, rotor inductance, between the flux ψr and the stator current I s. Since the magnetizing inductance flux is related to the applied voltage and is fixed, thusωr ,ωΨr ,ωI Rotor speed , rotor flux linkages speed, we cannot vary the magnitude of the vector ψr. But stator current angular frequency the speed at which it is rotating is not constant.x11,x12,x21,x22, variables of multiscalar motor model Similarly in case of current vector the magnitude canKω,Tω Rotor flux speed PI controller be controlled but not ωi. ωi depends on the applied parameters frequency.a3,a4,ωδ,σ Motorcoefficients III. MATHEMATICAL MODEL OF II. INTRODUCTION INDUCTION MOTOR 1 The speed sensor is an inconvenient device and Induction Motor Modelhas many drawbacks. An incremental shaft mountedspeeder encoder is required for close loop speed or The fundamental equation, which is used to introduceposition control. A speed encoder is undesirable in a the relation ship for speed observer system, is thedrive because it adds cost and reliability problems, statorcircuit equation given bybeside the need for a shaft extension and mounting dψs u s = Rs is + + jωψs a (1) dt 1Gaurav N Goyal is with Department of Electrical Engineering, The d-and q-voltage component presented in the d-Shri Ramdeobaba Kamla Nehru College of Engineering, Nagpur as aAsst.Professor (E-mail: gaurav.goyal13@gmail.com). q reference frame with the rotor flux linkages oriented M.V. Aware is with the Department of Electrical Engineering, in the d-axis are given byVisvesvaraya National Institute of Technology, Nagpur,Maharashtra, INDIA(E-mail: mva_win @ yahoo.com). 34© 2010 ACEEEDOI: 01.ijepe.01.02.07
  2. 2. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 ˆ dψsd ˆ A. Mechanical Subsystem usd = Rs isd + −ω ψsq ˆψ ˆ (2) dt r dx12 1 dψsq ˆ = − x12 + v1 (10) ˆusq = Rs isq + +ω rψsd ˆψ ˆ (3) dt Ti dt dx11 Lm 1 = x12 − m0 (11) X 11 com - X 12 com Is Is pedictive usα com INVERTER dt JLr J PWM Load Angle Controller ωi stater current ωr controller us β com U V W ω2 + ωr ωi isα com isβ com isα isβ C. Electromagnetic Subsystem iU + - X 12 m cal P cal stater current measur The basic simplified machine variables are iV represented as atg atg of Q of --- δ com MM powers X 21 com X 22 com X 22m variable X 22m X 21m X 12 m M dx 21 R RL = −2 r x 21 + 2 r m x 22 X 21m simulation of X 21 variable isα u sα com (12) Rotor angular speed observer isβ dt Lr Lr ωr com u sβ dx22 1 RL 2 Figure 1. Proposed load angle control induction motor control = − x22 r m isx + v 2 (13) dt Ti Lr The estimated d-q components of stator flux where Ti is the time constant of the first-order delaylinkages are as follows element used for filtering stator current command, J is dψsd ˆ the inertia constant, and m0 the load torque.The new ˆ = u sd − Rs isd + ω ψ sq ˆψ ˆ (4) dt r state variables are not a function of the coordinate system. Therefore, it is not necessary to transform dψ sq ˆ ˆ = u sd − Rs isq − ωψ ψ sd ˆ ˆ (5) these variables from one coordinate to another one. dt r This is essential for the practical realization of control Equation (2) and (3) present the voltage model of systems because it gives significant simplification ofinduction motor in d-q reference frame. This flux the drive system. The fully decoupled subsystemssimulator operates in open loop without any feed back make it possible to use this method in the flux-from the rotor flux error. The flux is identified weakening region and to obtain simple systemcorrectly when the motor parameters are exactly structures, which are not addressed in the case ofknown .in a real system, motor parameter change with vector control methods. For control of the presentedoperating point and temperature ,as a result, the system it is essential to know the actual value of theestimator rotor flux and the actual flux are different, rotor flux vector. The use of the variablesand this different depends on the following: “instantaneous imaginary power” andproperties of the selected motor model; degree of “instantaneous real power” provides a simplificationaccuracy of parameter identification; degree of of the control system [10]. They proposed these newaccuracy of current and voltage measurement and definitions of instantaneous powers in three-phasemotor operating point .the use of feedback minimizes circuits based on instantaneous voltage and currentthe effect of the above factors on the identification of valuesthe rotor flux linkages.Four state variables have been p= usdisd + usqisqproposed for describing the motor model [9]. These (14)state variables may be interpreted as rotor angular q=usqisd -usdisqspeed, scalar and vector products of the stator current (15)and rotor flux vectors, and the square of the rotor Taking into account the differential equations oflinkage flux, as follows: the stator current and rotor flux vectors in steady state x11 = ωr and using the new state variables, the following is (6) obtained: x12 = ψ rx isy − ψ ry isx = ψ r is sin(δ ) (7) Lm + 1 a 2 a is + 4 P a2 a2 x12 = (16) x21 = ψ rx 2 + ψ ry 2 (8) ω r i L Rr x22 = ψ rx isx + ψ ry isy = ψ r is cos(δ ) (9) a Q − ωi I s 2 x 22 = 4 (17) Where, δ is the angle between stator current and a 3ω irotor flux vectors. By using nonlinear feedback, it is Where 2 2possible to obtain a new model for the induction R L + R r Lmmotor with two fully decoupled subsystems: a1 = − s rmechanical and electromagnetic. This property is not Lr ω ia function of the motor source [10]. L R L L a3 = m a = r m a = r ω , 2 Lr ωδ , 4 ω δ δ 35© 2010 ACEEEDOI: 01.ijepe.01.02.07
  3. 3. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 Lm 2 The advantage of the above solution is that it is not ωδ = δ Lr Ls & δ = 1 − sensitive to any precise measurement or identification Lr Lr of rotor speed. The use of the above relationships avoids exact β ismeasurements of the flux, resistance, and angular ω ψr i ωrspeed of the rotor. Increasing the accuracy of δ ψcalculation of the new variables is possible using an ωa = 0 αobserver of the following form: Figure 2. Stator current and rotor flux vector ˆ dx12 1 = − x12 + v1 + k01 ( x12 − x12 m ) ˆ (18) B. Speed Observer System dt Ti The rotor flux observer is based on the dx22 1 = − x22 + is 2 + v2 + k20 ( x22 − x22 m ) ˆ (19) voltage model given by [9]. dt Ti dψ sd ˆ dt ˆ ( = u sd − Rs isd + ω rψ sq + k1 ψ rd ˆψ ˆ com −ψrd ˆ ) (25) The index denotes the calculated values using dψ sq ˆpower measurement. After assuming that motor = usq − Rs isq − ωψ rψ sd + k1 (ψ rq com −ψ rq ) ˆ ˆ ˆ ˆparameters are known and constant, it is possible to dtidentify the variable (26) Lr L L ˆ ψrd = ˆ ψsd −δ s r isd ˆ (27)x21 using the following model: Lm Lm ˆ dx21 R RL Lr Ls Lr ˆ = −2 r x21 + 2 r m x22 ˆ ˆ (20) ψrq ˆ = ψsq −δ ˆ isq (28) dt Lr Lr Lm Lm At steady state the left side of the above equation is In (4) and (5), a command flux quantity in feedbackzero, therefore, it is possible to show that the variable path is used instead of the actual quantity. Correctionx21 is part in (29) and (30) appears with K1 gain, which needs to be tuned in the simulation. The commanded x21 = Lm x22 m (21) components of rotor flux linkages are as follows: ψ rq com = 0 & ψ rd com = Lmiˆsd (29) IV. LOAD ANGLE AND SPEED OBSERVER Based on the estimated quantities of flux components, A. Load Angle Calculation it is possible to identify the angular speed of rotor During the control of an induction motor, the flux linkage vector using PI controller with zeroposition of each vector relative to the stationary command signalcoordinate system is not important. The vectors,which have position relative to each other, have (30)significant meaning. This relationship can beobserved in the electromagnetic torque description me = k . Im(ψ r i s ) = kψ r i s sin δ (22) The vectors of stator current and rotor flux are Rr i sqpresented in Fig. 2. If it is assumed that the magnitude ω =ω − ˆr ˆψ (31)of stator current and rotor flux vectors are kept at the r Lr i sdsame level by control system, then it is possible to Where ωψ r ˆ is the estimated angular speed of thecontrol the motor torque by changing load angle δ .By using the definition of new state variables it is rotor flux linkage vector. And isq & isd are thepossible to calculate the load angle (the angle estimated currents using the measured currents andbetween rotor flux linkage and stator current vectors) defined in the stationary reference frame and usingas follows: the transformation from αβ system to dq reference x12 frame using the estimated angle δ = arctg (23) x 22 After substituting (16) and (17) in (23) the load 1 Θ= ω r ˆψ (32)angle is obtained as s (24) Rotor speed estimation is good only at steady state, but during the transients there is an error, which increases with a decreasing speed response [8], [9]. This is relative to the delays provided by integrating the q -axis component of the rotor flux vector. A decrease in this error may be achieved by providing a 36© 2010 ACEEEDOI: 01.ijepe.01.02.07
  4. 4. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010proper initial value for the integrator. In this case, a usα comproper initial value might be the angular speed of isd isq ωψr αβ usd ωψr dq Flux ψ rq Rotorrotor flux vector at steady state. From the steady state -- PI com u sq ψ rq = 0 Simulator com controlle r speed u sβrelationships, it is possible to calculate the rotor speed isα equation ψ rd + ω ψ rm calcul ωr isd com ψ rd +as follows [9], [10]. αβ Lm ω rm + ω isd isq dq 2m X12m −a3 x12 −ωi i 2 s + a4 q isβ isq • Rr Lm ωrm • = (33) X 21m Lr a3 x22 Where ω i and is are the angular frequency and Θ 1 Sstator current vector, respectively. Figure 3. Rotor angular speed observer system Using the steady state relationships of inductionmotor, it is possible to modify the described estimator B. Proposed Speed Sensorless Control(31) in the following form: The block B in fig.4 represents the estimator which is replaced by the estimator represented by block A.  1   1  Lm x12 m  (34) ωψ r = − K 1 + ˆ  T s ψ rq + 1 + T s  ω rm + Rr L x  ˆ    This modified speed sensor has many advantages  w   w  r 21m  over open loop estimator which can be better understand by performance result. The control Where Tw is the time constant of the first order strategy of modified speed sensor is as explaineddelay filter. The first part of (34) is the equation of PI below.controller (30) and the second part is the filteredvalue of the rotor flux vector. The block diagram of amodified speed observer is presented in Fig. 3. Aswill be shown in the simulation results for the speedobserver system from Fig. 1, the error at steady stateis about 2%. This error is less than the case of usingan observer without taking into account angular speedof flux linkages calculated from the steady statecondition. V. PROPOSED CONTROL SCHEME A. Control scheme with speed feedback Figure 4. Actual and Proposed Scheme In fig 4, block A represents the estimator which isdescribed and presented in fig 5.This is an open loop In the presented system, the vectors are statorestimator which estimates the slip frequency ωsl as a current and rotor flux linkage. The load angle may beresult of which we can get rotor speed ωr in the kept constant by changing the position of statorstationery reference frame. The simulation parameters current vector as a result of tuning its pulsation. Theare given in Table1. current frequency ω i may be changed directly using TABLE 1 load angle controller or indirectly by changing theParameters of Induction Motor for Simulation slip frequency ω 2 . Rotor Squrrel Frequency 50Hz Type Cage ωi = ω2 + ωr (35) Voltage 440V Nominal 2238W The calculated stator current frequency is provided to the PWM block. The command values of load angle δ (Vrms) Power com Stator Rs=1.05Ω Rotor Rr=0.98Ω resistance and stator current amplitude Is, are adjusted by the resistance Stator Rotor Proportional–integral (PI) controllers. Rotor angular inductance Lls=0.004 inductance Llr=0.004 speed may be measured Mutual H 0.13H Friction 4H 0.005752 (I com 2 ) = (x 12 ) + (x com 2 22 com 2 ) (36) inductance Factor(f) N.ms s (x ) 21 com (Lm) And the load angle is Inertia(J) 0.2 kg.m^2 Pair of Poles(P) 2  x com  δ com = arctg  12 com  x  (37)  22  37© 2010 ACEEEDOI: 01.ijepe.01.02.07
  5. 5. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 Usd + control simplifies the structure of the control system Σ Lr/Lm 1/p by eliminating the stator voltage filtering block. - Isd VI. SIMULATION AND PERFORMANCE EVALUATION Rs+Ls’p + Lm/Tr ωr The Proposed scheme with its controller action is Σ / simulated in MATLAB/SIMULINK. The induction - + Σ motor with load is presented in details with voltage + source inverter in SVPWM mode in SIMULINK. The Isq Rs+Ls’p performance results are presented in the following sections: - Usq + A. Open Loop Control Scheme Σ Lr/Lm 1/p The proposed control scheme is simulated in MATLAB/SIMULINK and performance is observed ω sl under different dynamic conditions. Ψ rd - ωr 1.Step change in load p +Σ R P Ψ rq The shaft load is changed after the free running of the motor. The performance is shown in fig. 8 to 9. Figure 5. Estimator represented by Block A The dynamic performance of motor as well as estimator under load TL=70 N-m applied at time Controller for state variable X12 and X21are used in t=2000 ms, with with the terminal voltage V=440V.this research. The controller command signals of the The estimated torque and speed are shown the fig. com comvariables X 12 and X 22 on the basis of these 8 and 9 respectively.Because of the stator voltagequantities the square of the current amplitude is characteristics it is essential to filter the voltage to getcalculated as the fundamental harmonic. Filtering the voltage signal com com complicates the control system and provides undesired X 11 X 12 delay in the measurement channel. Is - com X 11 Is com X 21 atg δ com com -- X 22 X 21m Fig 6 As a result, the control system performs usingactual values of stator currents and delayed values ofstator voltage, which leads to non precise variableidentification. B. Simulation of the Proposed Speed Sensorless control In the proposed control system, two different current Induction Motorcontrollers, hysteresis [7] and predictive [8], [9] areused. In the control system it is possible to use 1. Step change in Loadcommand stator current and predicted voltage, which The performance results are shown for step changeappears at the output of the predictive controller with load torque from 0 to 70 N-m at time t=0.2 secbecause there is an access to first harmonics of the with voltage V=440V in Fig. 12 to Fig.18. Thecurrents and voltages. The use of predictive current estimated and actual speed of the motor are shown thecontroller in the control system with load angle fig.12. The stator current is observed and is shown in the fig.13. There is slight increment in the stator current because of increase in load torque at 0.2 sec. 38© 2010 ACEEEDOI: 01.ijepe.01.02.07
  6. 6. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 CONCLUSION A speed observer system for sensorless control of induction is developed. The rotor peed as been calculated using steady state relationship applied to the observer system. It has high accuracy and behaves satisfactory under all the speed range. An observer system has been adopted for the nonlinear control of The state variables of the estimator are shown in fig induction motor. The simulation results illustrated14 to fig 16. The estimated active power and reactive that the system operates correctly for the differentpower is shown in fig.18. This shows that there is motor running conditions. The proposed scheme isincrement in the active power at t=0.2sec and also the working in closed loop control of the induction motorslight increment in reactive power. control. The speed sensorless induction motor with torque angle control has better dynamic performance. The power estimate algorithm is also tested with the given induction motor model. References [1] Guoliang Zhang and Philip T. Krein “Torque-Angle Oriented Control of Induction Machines” [2] A. B. Plunkett, J. D. DAtre, and T. A. Lipo, "Synchronous control of a static AC induction motor drive," IEEE Trans. Industry Applications, vol. IA-15, pp. 430-437, 1979. [3] N. R. N. Idris, A. H. M. Yatim, "An improved stator flux estimation in steady-state operation for direct torque control of induction machines," IEEE Trans. Industry Applications, vol. 38, pp. 11I0-116, 2002. [4] M. Tsuji, S. Chen, T. Ohta, K. Izumi, and E. Yamada, “A speed sensor-less vector-controlled method for induction motor using . -axis flux,” in Proc. Int. Power Electron. Motion Contr. Conf., Hangzhou, China, 1997,pp. 353– 358. [5] Z. Krzeminski and J. Guzinski, “DSP based sensorless control system of the induction motor,” in Proc.Power Electron. Intell. Motion, Nuremberg, Germany, 1998, pp. 137–146. [6] H. Abu-Rub and J. Guzinski, “Rotor angular speed, rotor resistance and state variables estimation in a nonlinear system control of induction motor,” in Proc. Fourth Int. symp. Methods Models Automation and Robotics, Miedzyzdroje, Poland, 1997, pp. 613–618. [7] H. Akagi, Y. Kanazawa, and A. Nabae, “Generalized theory of the instantaneous reactive power in three-phase circuits,” in Proc. IPEC, Tokyo, Japan, 1998, pp. 1375– 1386. [8] P.C.Krause, O. Wasynczuk, and S.D. Sudhoff, Analysis of electric machinery and drive systems, 3 rd ed. New York : IEEE Press , 2002. 39© 2010 ACEEEDOI: 01.ijepe.01.02.07