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  • Humility Entrepreneurship Teamwork Sliding mode field oriented control of 3-phase induction motor Presented by M.M.V Prabhakar 07341D4207 Department of Electrical Engineering GMR Institute of Technology Rajam, Srikakulam(D.T)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork ABSTRACT • The design includes rotor speed estimation from measured stator terminals of voltages and currents. • The estimated speed is used as feedback in an IFOC system achieving the speed control without the use of ‘shaft mounted transducers’. • This paper presents a new sensor less vector control consisting on the One hand of speed estimation algorithm which overcomes the necessity of the speed sensor and on the other hand of a variable structure control law with an integral sliding surface, that compensates the uncerta inities that are present in the system.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork • Now a days, AC drives become popular in many applications because of the advances in power electronics and microelectronics technology • It is well known that field-oriented control (FOC) is an effective scheme for the variable speed control of IM drives. However, difficulties arise from the modelling uncertainties due to parameter variations, magnetic saturation, load disturbances and unmodelled dynamicsDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork ABSTRACT • The design includes rotor speed estimation from measured stator terminals of voltages and currents. • The estimated speed is used as feedback in an IFOC system achieving the speed control without the use of ‘shaft mounted transducers’. • This paper presents a new sensor less vector control consisting on the One hand of speed estimation algorithm which overcomes the necessity of the speed sensor and on the other hand of a variable structure control law with an integral sliding surface, that compensates the uncerta inities that are present in the system.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Why FOC ? • IM is superior to DC machine with respect to size, weight, inertia, cost, speed  DC motor is superior to IM with respect to ease of control – High performance with simple control due de-coupling component of torque and flux  FOC transforms the dynamics of IM to become similar to the DC motor’s – decoupling the torque and flux componentsDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Basic Principles DC machine By keeping flux constant, torque can be controlled by controlling armature current φa Te = k If Ia Current in φf Current outDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Basic Principles of IM φs a φr Stator current produce stator flux c’ b’ Stator flux induces rotor current → produces rotor flux Interaction between stator and rotor fluxes produces b torque c Space angle between stator and rotor fluxes varies with load, and speedDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Introduction to speed control  Scalar control • Magnitude variation of control variables  Vector control • Both the magnitude and phase alignment of vector variables • Scalar control is somewhat simple to implement, but the inherent coupling effect i.e. both the torque and flux are functions of V or I & f, gives sluggish response & system is easily prone to instability because of a high order system harmonics. • Ex. If torque is increased by incrementing the slip (frequency), the flux tends to decrease. This is then compensated by sluggish flux control loop feeding in additional voltage. The temporary dipping of flux reduces the torque sensitivity with slip & lengthen the response time.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork DC DRIVE ANALOGY Ia ψa If Te = K t Ψf Ψa = K t I a I f If Torque component ψf Decoupled Field component (Neglecting armature reaction & field saturation) I qs ^ Ids Te = K t Ψ r I qs = K t I qs I ds * I ds ωe * I qs ∧ (Synchronously rotating frame) ψrDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Principle of vector control Control Machine * I ds I ds* s * Ia Ia s I ds d s − s I ds d −q a −b − c q machine d −q e e s s * * Ib Ib to to I qs to I qs* s to * s I qs I qs d e −q e I Ic d s − qs de − e q d s −q s a −b −c c mod el I qs I ds ωe cos θ e sin θ e cos θ e sin θ e ∧ ψr Inverse Machine model Transformation transformationDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork . FOC is called as decouple, orthogonal and Trans vector control . FOC technique dpcouples the 2 components of stator current. One providing the airgap flux & another producing the torque. It provides independent control of flux and torque , another control charecterstics are liniarized. . The stator currents are converted to synchronously rotating reference frame aligned with the flux vector and transformed back to the stator frame before feeding back to the machine. . The 2 components of currents are d-axis Ids analogous to armature current, q-axis Iqs analogous to field current. . FOC offers more precauce control of A.C motor compare to vector control. Therefore FOC is used in high performance drives like Robotic actuators, centrifuges and servos.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork FOC of IM drive Torque equation : 3p Te = ψ s × is 22 3 p Lm Te = ψ r × is In d-q axis : 2 2 Lr 3 p Lm Te = (ψ rd i sq − ψ rq i sd ) 2 2 Lr Choose a frame such that: ψ ψr rd = ψr ψ ψr = 0 rqDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork FOC of IM drive Choose a frame such that: ψψ = ψr rd r ψψ = 0 r rq qs As seen by stator reference frame: is isq Ψr 3 p Lm Ψrq Te = (ψ rd isq − ψ rq isd ) 2 2 Lr isd Ψrd dsDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork FOC of IM drive Choose a frame such that: ψψ = ψr rd r ψψ = 0 rq r qs Rotating reference frame: q Ψr Te = 3 p Lm (ψ rd i sq − ψ rq i sd ) is d Ψr 2 2 Lr Ψr Ψ isqr Ψ isdr 3 p Lm ψ Te = ψ r isqr 2 2 Lr dsDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Direct vector control Feedback Indirect vector control FeedforwordDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Direct vector control iqs qe ^ Ψ = Ψr cos θe s dr Ψqr s ^ qs Ψ = Ψ sin θe s qrr ids − iqs θe Ψs Ψr^ cos θe = dr e Ψ ^ Ψ dr d s r Ψ s sin θ qr e = d s Ψr ^ ˆ = Ψ s2 + Ψ s2 Ψr dr qrDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Indirect Vector Control qe iqs ψ qr = 0 ψ qr s ∧ qs θ ids I s s iqs ∧ ids ψ dr = ψ r θe θ sl ωsl θr de ψ s dr r ωe d ωr Rotor s d AxisDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork The stator voltage equations in d-q equivalent circuit is given as, Lm d v = s ds (Ψ dr ) + ( Rs + σ Ls S )ids s s Lr dt Lm d v = s qs (Ψ qr ) + ( Rs + σ Ls S )iqs s s Lr dt where L2 σ= − m 1 Lr Ls Which is called the motor leakage coefficientDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Salient Features of vector control : The machine is essentially self controlled . No fear of instability The transient response will be fast Speed control is possible in four quadrantsDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Sliding mode control  A sliding mode control with a variable control structure is basically an adaptive control that gives robust performance of a drive with parameter variation load torque disturbance.  The control is nonlinear and can be applied to a linear or nonlinear plant.  The drive response is forced to tract or slide along a predefined trajectory or reference model in a phase plane by a switching control algorithm, irrespective of the plant’s parameter variation.  SMC is sensor less vector control, where the speed signal is estimated from the machine terminal voltage without using any speed sensor or any other type of secondary transducer.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Sliding mode field oriented control * * iqs iabc ω * r i* qs e(t) VSC limiter * ids dq-abc Current Controller ωr* ωr controller Ψ dr* e θe pulses 1 ωr i * ds s Field PWM calculation weakening ωe inverter iabc ωr Wr & We vabc estimator IMDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork The mechanical equation of the induction motor is given by, • J wm + Bwm +TL =Te • ω +aω + f =bi m m e qs The speed tracking error is given as, e(t ) = ω m (t ) − ω m (t ) * • • • * e(t ) = ω m − ω m = − ae(t ) + u (t ) + d (t ) Where u (t) and d (t) are collected as,Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork • u (t ) = bi e qs (t ) − aω* m (t ) − f (t ) −ωm (t ) * d (t ) = −∆aωm (t ) − ∆f (t ) + ∆bi e qs (t ) Now we are defined the sliding variable s (t) with an integral component as, t s (t ) = e(t ) − ∫ ( k − a )e(τ ) dτ 0 The sliding surface is defined as, t s (t ) = e(t ) − ∫ ( k − a )e(τ )dτ = 0 0Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork The variable structure speed controller is designed as, u (t ) = ke(t ) − β sgn( s ) In order to obtained the speed trajectory two assumption are taken as, 1.The gain k must be chosen such that the term (k-a) is strictly negative, so K<0 2. The gain β must be chosen so that β ≥ |d(t)| for all time. if assumptions are verified, the control law leads the rotor mechanical speed wm(t) so that the speed tracking error e (t) tends to zero as the time tends to infinity.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork The proof of this theorem will be carried out using the Lyapunov stability theory. 1 v (t ) = s (t ) s (t ) 2 Its time derivative is . V (t ) . . = s (t ) s (t ) = s[e− (k − a )e] = s[(− ae + u + d ) − (ke − ae)] = s[u + d − ke] = s[ke − β sgn( s ) + d − ke] = s[d − β sgn( s)] ≤ −[ β − | d | s ] ≤ 0 When the sliding mode occurs on the sliding surface , and the dynamic behavior of the tracking problem is equivalently governed by the following equationDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Current controller: The block current controller consists of three hysteresis band current PWM control. it is basically an instantaneous feedback current control method of PWM where the actual current continuously tracks the current command within a hysteresis band. SPWM i* K2 K1 + s PWM i φDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork The control circuit generates the sin reference current wave of desired magnitude and frequency and it is compared with the actual phase current wave. As the current exceeds the prescribed hysteresis band, the upper switch in the half bridge is turned off and lower is turned on. The output voltage transitions from +0.5Vd to -0.5Vd. As the current crosses the lower band limit the lower is turned off and upper is on. Upper band HB Hysterisis band 2HB Sine reference wave Lower band HB Actual current +0.5Vd 0 ωt -0.5VdDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Estimation of rotor speed The rotor flux equation in the stationary frame is • Lm 1 Ψ dr = ids − ω r Ψ qr − Ψ dr Tr Tr • Lm 1 Ψqr = iqs + ωr Ψdr − Ψqr Tr Tr The angle between the rotor flux in relation to d axis of the stationary frame is Ψ θ =arctan( e qr ) Ψdr • • • Ψ Ψ −Ψ Ψ qr θe =ω = e dr qr dr Ψ +Ψ 2 dr 2 qr Lm Ψ dr iqs − Ψ qr ids ωe = ωr − ( ) Tr Ψ dr + Ψ qr 2 2 1 • • L ω r = 2 [Ψ dr Ψ qr − Ψ qr Ψ dr + m (Ψ dr iqs − Ψ qr ids )] Ψr TrDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Field weakening controller The block field weakening gives the flux command based on the rotor speed ,so that the PWM controller does not saturate. if ω r < ω b , Ψ * = Ψ drRated dr ωb ω r > ω b , Ψ = Ψ drRated × * dr ωr With the proper mentioned field orientation, the dynamic of the rotor flux is given as: e dΨdr Rr e Lm + Ψdr − Rr ids − ωsl Ψqr = 0 e dt Lr Lr dΨ e qr For decoupling Ψ e = 0, qr =0 dt Lr dΨ e dr +Ψ = Lm ids e dr Rr dt Ψ = Lm ids dr In other words the rotor flux is directly proportional to the current ids in steady stateDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship TeamworkDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Results and discussion Reference and estimated rotor speed signal (rad/sec) -------ω m * ------ -ω mDeliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Plot of motor torque vs time Stator current isa (A) 80 60 60 50 40 40 30 20 current(A) torque(N-M ) 20 0 10 -20 0 -40 -10 -60 0 0.5 1 1.5 0 0.5 1 1.5 tim e(s) time(s)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Time (s) stator voltage Vsa (V)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Stator current ids (A) Stator current iqs(A) 60 80 40 60 20 40 0 20 current(A) current -20 0 -40 -20 -60 -40 -80 0 0.5 1 1.5 -60 0 0.5 1 1.5 time(s) time(s) Time (s) Time (s)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Total rotor flux 200 180 160 140 120 total flux 100 80 60 40 20 0 0 0.5 1 1.5 time(s)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork UNDER LOAD TORQUE VARIATIONReference and estimated rotor speedsignal (rad/sec) Plot of motor torque vs time 200 6000 150 4000 100 2000 50speed(rad/sec) torque(N-M) 0 0 -50 -2000 -100 -4000 -150 -200 -6000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 time(S) time(s)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Data for the sliding mode control Electrical parameter Mechanical parameter Sl. Name of the Numerical Sl Name of the Numerical No Parameters value No Parameters value 1. J (Moment of 1.662 kg- 1. Pole 4 Nos Inertia) m.sq 2. Rs (Stator 0.6 Ohms 2. B( Frictional 0.1 Nms resistance) constant) 3. Rr (Rotor 0.412 resistance) Ohms Controlling parameter 4. Ls(Stator 1.9 mH Sl Name of the Numerical inductance) No Parameters value 5. Lr (rotor 1.9 mH 1. K (Constant gain) -100 inductance) 6. Lm(Mutual 41.2 mH 2. Β (switching gain) 30 inductance)Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork Conclusion and future work Sliding Mode Control (SMC) is a robust control scheme based on the concept of changing the structure of the controller in response to the changing state of the system in order to obtain a desired response. The biggest advantage of this system is stabilizing properties are preserved, even in the presence of large disturbance signals. The dynamic behavior of the system may be tailored by the particular choice of switching function and the closed-loop response becomes totally insensitive to a particular class of uncertainty. One of the problems associated with implementation of SMC is Chattering which is essentially a high frequency switching of the control. Chattering in torque & speed may large, but can be minimized by small computation sampling time higher pwm frequency & minimizing additional delay in feedback signal. Scope of future work.  Application of higher order sliding mode control to other non linear systems may be attempted. A higher order discrete sliding mode control law may be developed.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork References [1] Nihat Inanc “A new sliding mode flux and current observer for direct field oriented induction motor drives” Electric Power Systems Research 63 (2002) 113-118. [2] Nihat Inanc “A robust sliding mode flux and speed observer for speed sensorless control of an indirect field oriented induction motor drives” Electric Power Systems Research 77(2007)1681-1688 [3] B.K. Bose, Modern Power Electronics and AC Drives, Prentice Hall, New Jersey, 2001. [4] P. Vas, Vector Control of AC Machines, Oxford Science Publications, Oxford, 1994.Deliver The Promise Learning Social Responsibility Respect for Individual
  • Humility Entrepreneurship Teamwork [5] Williams, B. W., Goodfellow, J. K. and Green, T. C. “Sensorless speed measurement of inverter driven squirrel cage induction motors.” in Proc.. IEEE 4th Int. Con$ Power Electron. Variable Speed Drives, (1987). [6] Benchaib, A. Edwards, C. “Nonlinear sliding mode control of an induction motor.” Int. J. Adapt. Control Signal Process. Vol. 14, (2000): pp. 201–221.Deliver The Promise Learning Social Responsibility Respect for Individual