Summary of engineering doctoral thesis: Research and develop the control algorithms using artifical neural network to estimate motor parameters and control ac motors

The objectives of the thesis: Propose algorithms for controlling speed and flux of AC motors; propose rotor speed and flux estimation algorithms for speed sensorless controlller of AC motors.

VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY …… ….***………… LE HUNG LINH RESEARCH AND DEVELOP THE CONTROL ALGORITHMS USING ARTIFICAL NEURAL NETWORK TO ESTIMATE MOTOR PARAMETERS AND CONTROL AC MOTORS Major: Control Engineering and Automation Code: 62 52 02 16 SUMMARY OF ENGINEERING DOCTORAL THESIS Hanoi - 2016 This thesis is accomplished at: Graduate University of Science and Technology, Vietnam Academy of Science and Technology Supervisors 1: Assoc Prof DSc Pham Thuong Cat Supervisors 2: Dr Pham Minh Tuan Examiner 1: Examiner 2: Examiner 3: The thesis is to be presented to the Defense Committee of the Graduate University of Science and Technology - Vietnam Academy of Science and Technology At Date Month Year 2016 The complete thesis is availabe at the library: - Graduate University of Science and Technology - Vietnam National Library INTRODUCTION A thesis statement necessary Nowadays, AC motor is widely used both in industrial applications and in domestics ones because of perfective technique specifications such as impact, high power, economic, convinient design, control and maintenance AC motor is used in pumps, compressors, oil and gas industry, industrial or domestic fan, elevator, crane in construction industry, robotic etc… Therefore, the three last decades, AC motor is used instead of DC motor because of eleminating the disadvantages of dc motor such as high maintenance cost for brush – commutator system, vibration environments, iginite flammable environments Consequently AC motor is widely applied However, there are still some control problems of AC motor when it can be more applied Many researches want to improve the effective operation, reduce the production price but the results are still drawbacks For example, the effect of control methods using Kalman filter, nonlinear filters or observers using sliding mode control to estimate rotor speed and flux depends on control algorithm, estimation of some parameters and the accuracy of the motor model The mathmetic model of motor is quite difficult to obtain as desired because of uncertain parameters similaryly friction coeffection, inertia, resistance The uncertain parameters change when the system is operating In addition, the speed and flux estimation insteading of sensor with the high requirement of accuracy is quite difficult and it is necessary to research Recently the development of artifical neural network is very helpful to solve the control problem, specially controlling nonlinear subjects with uncertain parameters Artifical neural network can solve the nonlinearity effectively with self-tuning parameters when the system operates In this thesis, we concentrate on research and develop some control and estimation algorithm for ac motor with uncertain parameters The objectives of the thesis - Propose algorithms for controlling speed and flux of AC motors - Propose rotor speed and flux estimation algorithms for speed sensorless controlller of AC motors The main contents of the thesis Two control algorithms and two estimation algorithms of motor parameters are proposed a) The speed control algorithm for AC motor with uncertain parameters and changing loads on rotating coordinate (d,q) using artifical neural network b) The speed and flux control algorithm for AC motor with uncertain parameters and changing loads on stationay coordinate (α,β) using the decoupling method c) The speed estiamtion algorithm for AC motor using artifical neural network and selfadaptation d) The speed estiamtion algorithm for AC motor using self-adaptation Lyapunov stability theory and Barbalats’s lemma are used to prove the system asympotic stability of the algorithms Simulations will be implemented on Matlab Outline: Chapter 1, Presenting some problems of motor control Chapter 2, Developing control algorithm of asynchrounous motors Chapter 3, Developing estimation algorithms of speed and flux of asynchronous motors Conclusion CHAPTER OVERVIEW 1.1 Problem statement - Obtaining accurately economically rotor flux and speed estimator algorithm, - Developing AC motor control algorithm with uncertain parameters - Designing intelligent motor controller based on the advanced production technology of electronics 1.2 AC control method AC motor control methods are classified as following diagram AC motor control Vector control Scalar control U/f = const is=f(ωr) stator current Field oriented control Rotor flux Oriented Direct RFO Indirect IRFO Stator flux oriented Direct torque control DTC Circular flux trajectory Hexagonal flux trajectory Natural Field Orientation NFO Figure 1.1 Classification of IM variable frequency control Nowadays motion control in industrial aplications is required accurately Motor control methods are used as scalar control voltage/frequency (V/F), direct torque control and filed oriented control In this thesis, field oreinted control method is ued to research and apply for three-phase AC motor with speed and moment control high performance requirement Recent researches are focus on identifying the effection of rotor resistance without considering uncertain parameters such as friction coefficient, inertia or changing load Therefore, this thesis proposes control algorithm and speed estimation of AC motor with uncertain parameters 1.3 Research problems - Developing rotor speed and flux estimation of AC motor - Developing AC motor control algorithm with uncertain parameters - Using Lyapunov stability theory and Barbalat’s lemma to prove global asympotic stability of system and then using Matlab to simulate and check the validity of proposed control algorithm and estimator CHAPTER DEVELOPING FLUX AND SPEED CONTROL ALGORITHM OF AC MOTOR WITH UNCERTAIN PARAMETERS This chapter will present two flux and speed control algorithm - Speed and flux control algorithm of AC motor uses artifical neural network with online learning rules to compensate uncertain on rotating coordiante (d,q) - Speed and flux control algorithm of AC motor does not decouple and then using artifical neural network to compensate uncertain on static coordiante (α,β) 2.1 AC motor control The model of AC motor is written on static coordinate (,):  dis  R R  R    s   Lm r  is   r  r   r   us  dt  L L L  L r  r s  s   di    s    Rs   Lm Rr  is   r   Rr  r   us  dt Lr  Lr  Ls   Ls (2.13)  Rr Rr  d r  dt   L  r   r   L Lmis r r   d r  R R   r  r  r   r Lmis  Lr Lr  dt 3z L d mM  p m  r is  r  is   J  B  mL (2.14) Lr dt The model of AC motor is written on ratating coordinate (d,q):  disd  R R  R    s   Lm r  isd  s isq   r  rd   rq  usd  dt  L L L  L r  r s  s   di    sq  s isd   Rs   Lm Rr  isq   rd   Rr  rq  usq  dt Lr  Lr  Ls   Ls (2.15)  Rr Rr  d rd  dt   L  rd  s    rq  L Lmisd r r   d rq R R   s    rd  r  rq  r Lmisq  Lr Lr  dt 3z L d mM  p m  rd isq  rq isd   J  B  mL (2.16) Lr dt The mathmethic model of AC motor on rotating coordinate (d,q) when flux  rq on axis q is eliminated From the equation (2.15) results  disd  R R  R    s   Lm r  isd  s isq   r  rd  usd  dt  L L L  L r  r s  s   di  R R   sq  s isd   s   Lm r  isq   rd  usq (2.17)  dt  L L  L s r s     d R R  rd   r  rd  r Lmisd Lr Lr  dt 3z L d (2.18) mM  p m  rd isq  J  B  mL Lr dt 2.2 Build speed control algorithm for three-phase asynchronous as motor with uncertain parameters on rotating coordinate (d,q) Lm  r ref * isd u sd Current controller u sq * sq i ref  -  dq tu us us Vector tv modulation tw Speed controller u isq  isd is  is dq isq s 3~ uvw  v w isu isv isd Flux model M3~ mL Figure 2.2 Motor control model 2.2.1 Build a controller model From the equation (2.16), results in d Ku (t )  J  B  mL (2.22) dt where u (t )  ( rd isq  rqisd ) is control voltage When  rq is eliminated, yields * * u (t )  ( rd isq  rq isd )   rd isq From equation (2.22), we rewrite: u(t )  J k  Bk  mk (2.23) J  B  m where: J k   J k  J k ; Bk   Bk  Bk ; mk  L ; K K K   J k , Bk are known; J k , Bk are unknown set f  mk  J k  Bk (2.24)   (2.26) u (t )  J k  Bk  f In summary, the motor control problem becomes determining the control signal u(t) that regulates motor speed  reaching reference speed ref when there some uncertain parameters 2.2.2 Build a speed control algorithm of motor We choose: u(t )  u0  u1 (2.27) where u0 is feedback signal written in PD form and u1 a signal compemsating unkown parameters f And then:   (2.28) u0  J k ( ref  K D (  ref ))  Bk Speed error :     ref , f u K We set u '  1 , f    , K D'  D Jk Jk Jk ' ' (2.31)   K D  u  f  Finally, the motor control problem becomes determining the control signal u ' to guarantee the system (2.31) asympotic stability when f ' is unknown f ' is aproximated by a neural network with output fˆ Theorem [1][2]: Speed of induction motor ω (2.16), (2.22) aproaches the disired speed ωref while friction coefficicent B, inertia moment J and load moment mL are unkonwn if control rule u(t) and study rule w of neural network are defined as below    (2.34) u (t )  J k ( ref  K D (  ref ))  Bk  J ku '   u '  (1  n) fˆ      w  n where optional parameters K D , n,  Proof: We choose a positive definite function V such as : V    w2    V   K D   (   )   K D        V   K D     (2.35) (2.36) (2.37) (2.38) (2.40) Based on the equation (2.40), Obviously, V  and V  with ∀   ; V  while   , therefore  ,  are always finite V  , semi negative definite does not guarrantee the sysstem asymtopic stability The system is non-autonomous because neural system is varied by time Hence, it is nescessary to use Barbalats’s lemma From (2.38), we obtain:  V  2 K D  2   (2.41) sign( ) where  ,  are finite, so V is always finite => V is continuous by time In addition, from Basbalat’s lemma V is continuous then V    ,   From the equation (2.31), f  u1 and   ref meaning motor speed ω aproaches the disired speed ωref with error is equal to Rotor speed regulator as shown on Figure 2.3     u1  J k (1  n) fˆ       fˆ  w w  n u1 ref  -    J k ( ref  K D (  ref ))  Bk u0 u(t ) isq*  rd* Figure 2.3 Rotor speed regulator of the motor 2.2.3 Current regulator Rewrite the equation (2.17) in vector form  di sdq  dt  Ai sdq  Bu sdq  h rd   d rd   Rr  rd  Rr Lmisd  dt Lr Lr where:   Rs       L      m  s  L      Ls  s   B ; ; h  A     Rs       s    Lm        L  s  We find the stator voltage: u sdq  B 1  Ai sdq  i*sdq  Gξ  h rd   (2.42)      Ls  (2.43) where G is positive diagonal matrix and ξ  isdq  i sdq is error vector between the disired cunrrenr and regulated current ξ  i*sdq  i sdq  i*sdq  ( Ai sdq  Bu sdq  h rd ) (2.44) Subtituting the equation (2.43) into (2.42) results: ξ  Gξ => ξ  Gξ  (2.45) Hence the error vector ξ  meaning i sdq  i sdq Building the current regulator as shown on Figure 2.4: d dt i * sdq ξ + + G + + h A i sdq  rd Rr Lm Lr s  Rr isd u sdq - - - B 1 Figure 2.4 Current regulator model 2.2.4 Simulation results Motor control system model with uncertain parameters and speed feedback signal as shown on Figure 2.2 Simulation was conducted using a four-pole squirrel-cage induction motor from LEROY SOMER with the parameters shown in Table The reference angular velocity varies in a trapezoid shape as seen in Figure 2.5 with the maximum ref  100 Rad/s (956 prm) and reference flux  r ref =1.5 (Wb) Motor is mounted on the driller system * Table Motor parameters Rated Power 1.5 KW Stator inductance (Ls) Rated stator voltage 220/380 V Rotor inductance (Lr) Rated stator current 6.1/3.4 A Mutual inducatnce (Lm) Stator resistance(Rs) 4.58 Ω Motor inertia (J) Rotor resistance (Rr) 4.468 Ω Viscous coefficient friction (B) Figure 2.5 is rotor desired speed and is started in time t=0,1(s) 0.253 H 0.253 H 0.213 H 0.023 Nms2/rad 0.0026 Nms/rad 100 Rad/s 80 60 Omega.ref 40 20 10 15 20 25 Time (s) 30 35 40 45 50 Figure 2.5 Desired speed ref The motor speed control system was simulated with these assumed uncertain parameters:    B  B  B; B  0.05B J  J  J ; J  0.20 J sin(100t ) Load mL varies in a shape as seen in Figure 2.6c mL  mL1  mL  mL (Nm) where : mL1 is steady load of system, (Nm), mL2 is unknown load while drill on the material as shown on Figure 2.6a mL is unknown load depended on the structure of material as shown on Figure 2.6b Nm 0 10 15 20 25 Time (s) 30 35 40 45 50 Figure 2.6a mL2 unknown load while drill on the material Nm 0.5 -0.5 -1 10 15 20 25 Time (s) 30 35 40 45 50 Figure 2.6b ΔmL unknown load depended on the structure of material Nm 10 15 20 25 Time (s) 30 35 40 45 50 40 45 50 Figure 2.6c mL load of the system Rad/s -1 -2 -3 -4 10 15 20 25 Time (s) 30 35 Figure 2.8 Error between desired rotor speed and real rotor speed using neural network 11 2.3.2 Speed and flux control method We denote: s = e + Ce (2.57) where C is the positive definite diagonal matrix; e  x - xref is the error between the  x1 ref   ref   x1     actual value x       and the desired value x ref     ˆ   x x  2  r   ref   r ref  Therefore, when s  , then e  s1  w11  f1   w1ii  f   w2ii i 1 w12 w21 s2  w22 i 1 Figure 2.13 The neural network structure The form of the neural network: (2.58) f  fˆ  η  Wθ  η  w11 w12  1  θ  where W   is a weighted matrix;    output function vector of input  w21 w22   2 neuron i; τ bounded approximation error: η   Therefore, to make s  and error e  (x - xref )  we need to choose v and the learning rule for the weighted W to make the system (2.56) asymptotically stable Theorem [4][6]: Speed andflux of the AC motor in equation (2.14) approach the 2 2 desired values   ref ,  r   r   r    r ref while J , B , Rr and changeable load TL   are unknown if the control signal v and weighted W are defined as below: ˆ  + Nx ˆ +  v =  Hs  Mx x ref - Ce + v v1     1 Wθ   (2.59) s s (2.60)  i  si w (2.61) where H is a positive definite diagonal matrix, wi is the i column of the weighted th matrix W and   ,      with   Proof: Applying Lyapunov’s stability theory, we chose a positive definite function V suchas: 1 V  sTs   w iT w i (2.62) 2 i V  sT Hs  s T  v1 -    1 Wθ - η  (2.65) V  s T Hs   s  (2.66) From equation (2.66), it is clearly that V  and V  with  s  ; V  when s  and from equation (2.58), it is obviously that η, η are always finite Because of V  12 negative definite, the system is not guaranteed to be asympotic stability Therefore, we need use Barbalat’s lemma to stabilize the non-autonoumous system asympotical stability From the equation (2.65), we obtain: sT s T (2.67) V  2sT Hs    s η  s T η s where s, s and η, η are always finite, then V is finite, V is continuous by time Applying Barbalat’s lemma when V is uniform continuous then V   s, s  From (2.57), error e  Therefore, x  xref in other words, rotor speed and flux converge to their respective desired values with error e = Rotor speed and flux controller of the AC motor as seen as Figure 2.14   v = Hs  Mx + Nx +  x ref - Ce + v e - xref e + Ce v1     1 Wθ   s s s v   D v-Q   us  i  si w x Figure 2.14 The overall motor control system 2.3.3 Simulation results Assuming that three-phase ac motor as in 2.2.4 and the desired flux  r ref =2.25 (Wb2) Rotor resistance Rr  Rˆ r  Rr , where ΔRr is changed when the motor operates, the changing shape of ΔRr as seen in the Figure 2.15 Ohm 0.8 0.6 0.4 0.2 0 10 15 20 25 Time (s) 30 35 40 45 50 40 45 50 Figure 2.15 ΔRr changes by time 0.1 Rad/s 0.05 -0.05 -0.1 -0.15 10 15 20 25 Time (s) 30 35 Figure 2.17 Error between desired rotor speed and real rotor speed 13 0.02 Rad/s -0.02 -0.04 -0.06 -0.08 0.5 1.5 2.5 Time (s) 3.5 4.5 40 45 50 Figure 2.18 Setting time the load mL -3 Wb x 10 -5 10 15 20 25 Time (s) 30 35 Figure 2.19 Error between desired flux  r2 ref and real flux  r2 0.5 Wb -0.5 -1 -1.5 -2 0.05 0.1 0.15 Time (s) 0.2 0.25 0.3 Figure 2.20 Setting time of real flux  r2 and desired flux  r2 ref with the load mL Rotor speed and flux of induction motor are reached the desired speed and flux - When the motor starts, rotor speed and flux have the setting period with an error of about 0,08% to speed and 70% to rotor flux - When the load changed suddenly while the motor was operating normally, speed and rotor flux had a transient period with an error of about 0,2% to rotor angular velocity and 0.001% to rotor flux - The setting time of rotor speed and flux is very small 14 2.4 Conclusion of chapter In this chapter, the two algorithm control of speed and flux with uncertain parameters (friction coefficient B, inertia moment J, rotor resistance Rr, changing load) for the model on rotating coordinate (d,q) and on stationary coordinate (α,β) are represented The algorithm control of ac motor using the artifical neural network with online study to compensate the uncertain parameters on rotating coordinate (d,q) The stability theory Lyapunov and Barbalat’s lemma are used to prove the asympotic global stability of the system The simulation results in 2.2.4 show the efficient of the proposed contorl algorithm The two algorithm control of speed and flux of ac motor without decoupling and selfadaptive using the artifical neural network with online study to approximate uncertain parameters on stationary coordinate (α,β) The simulation results in 2.3.3 show the efficient of the proposed contorl algorithm Based on the simulation results in 2.2.4 and 2.3.3, the control algorithm of rotor speed and flux in 2.3.2 is better than in 2.2.2 and current control in 2.2.3 - When the motor starts, rotor speed and flux have the setting period with the error of about 0,08% in 2.3.2 while it is about 3,5% in 2.2.2 and 2.2.3 - When the load changed suddenly while the motor was operating normally, the error of the control algorithm on stationary coordinate (α,β) in 2.3.2 is 0,2% while the error of control algorithm on rotating coordinate (d,q) in 2.2.2 and current control 2.2.3 is about 1,5% The above results are published in [1][2][4] and [6] of the publication list 15 CHAPTER DEVELOPPING THE SPEED AND FLUX ESTIMATION ALGORITHM OF THE AC MOTOR WITH UNCERTAIN PARAMETERS 3.1 Speed and flux estimation Problem of AC motor In this chapter, we propose the speed and flux estimation algorithm on the reference model: - Neural network and self-adaptive speed estimation algorithm of asynchronous three phase ac motor with uncertain parameters - Self-adaptive speed and flux estimation algorithm of asynchronous three phase AC motor with uncertain parameters We also combine two control algorithms proposed in the chapter with two estimation algorithms in chapter in the sensorless motor control model 3.2 Developping speed and flux estimation algorithm of asynchronous three phase ac motor with uncertain parameters 3.2.1 Build a self-adaptive neural network controller of motor speed The speed estimator of three phase AC motor as seen in Figure 3.3, input signals consist of stator current vector i s ; statorvoltage vector u s and output signals consist of estimated speed of motor ˆ , rotor time constant ˆ and angular of rotor flux ˆ r On stationary coordinate  ,   , rotor flux and stator current equation are represented as below:    di s  R  (3.1)  ψ r   s   Lm  i s  us  dt  Ls   Ls         dψ r (3.2)    ψ r   Lm i s    dt   is Caculate us ˆi based on t s ˆi s ς Calculate t (Theorem 3) t l - εe ˆl Calculate ˆl based on ˆ and ˆ Estimation Algorithm (Theorem 4) Find the angular of rotor flux ˆ ˆ ˆs Figure 3.3 Speed estimator, the inverse value of rotor time constant and rotor flux The procedure for estimating rotor speed and flux includes the following steps: Step 1: Separate parts of  and  from stator current and voltage measurement Build the neural network to approximate l (contains two parameters ω, η as in the equation 3.5 by theorem 3) Step 2: Base on the value t (from theorem 3),we find the approximation current ˆi s , while the error vector of stator current ς  (ˆi s - i s )  then results t=-l Step 3: Build the self-tuning rule ˆ ,ˆ by theorem 16 Step 4:Base the value of vector l (we already found in the step 2), measured value of stator and ˆ ,ˆ (from theorem 4), we calculate vector ˆl by equation (3.15) The error ε e  (ˆl - l )  means that ˆ ,ˆ are acurately estimated 3.2.1.1 Separate parts of  and  The approximating current is calculated by the following equation:  R  dˆi s    s  ˆi s  ut (3.3) dt  Ls   Ls  Donate ς  ˆi - i is the error vector between a approximate current ˆi and measured stator s s s current dòng stator i s , results: R dς   s ς  l   t dt  Ls (3.4)      where l     (3.5) ψ r   Lm i s          The neural network RBF consisting of inputs, outputs, three layers is used to approximate the parameter l The input signal of neural network is a speed error ς(t ) ; output signal consists linear neurons The hidden layer is composed of two neurons having the following Gauss distribution function The neural network is considered as below: l = Wζ  χ (3.6) w w    where W   11 12  is a weighted matrix; ζ    output function vector of input  w21 w22    neuron i and  bounded approximation error: |||| ≤ 0 Therefore, to make current error ς  (ˆi s - i s )  , we need to choose t and the learning rule for the weighted W to make the system (3.4) asymptotically stable Theorem [3]: The current observer (3.4) is asympotic stability and the current error is eliminated lim ς(t )  while regulation signa t and network weights W are defined as t  below: t     1 Wζ   ς ς  i   iς w where wi is the coulumn ith of the weight matix W and   0;   0 Proof: we chose a positive definite function V suchas: 1  V   ςT ς   w Ti w i  2 i 1  R V   s ς  ςT   1 Wζ  χ  t   Ls R V   S ς  (   ) ς   Ls (3.7) (3.8) (3.9) (3.11) (3.12) 17 From equation (3.12), it is obviuously V  and V  with ς  and V  when ς  , so ς ,ς are always finite From equation (3.6), χ , χ are always finite Because of V  negative semi-definite, the system is not guaranteed to be asympotical stability The system is non-autonomous system since weights of neural network change by time Hence it is sure that the system is asympotic stability we need to use Barbalat’s lemma From equation (3.11), yields: R ςT ς T (3.12b) V  2 s ςT ς    ς χ  ςT χ  Ls ς where ς ,ς and χ , χ are finite V is always finite, so V is uniform continuous by time Hence V   ς,ς  In other hands estimated current reaches the real current ˆi s  i s 3.2.1.2 Build speed estimator  and the inverse value of rotor time constant  Taking derivative both side of (3.5) and assuming that rotor speed and the inverse value of rotor time constant change l       l   L i (3.14) m s       Building a estimator:  ˆ ˆ  ˆ  (3.15) l    l   Lmˆi s  ε e ˆ ˆ      where ˆ ,ˆ are the estimated values of , ;  is positive constant, ε  ˆl - l is error e between ˆl and l      ε e     l   Lmi s  ε e        (3.16) Theorem [3]: Speed estimator and rotor time constant (3.16) is asympotic stability and error vector lim ε e (t )  if speed update rule ˆ and the inverse value of rotor time constant t  ˆ can be formulated as:  ˆ  ε e T l ˆ  ε e T (l   Lmi s )  T where l  l - l  Proof: We choose a following positive function V: V   ε e Tε e       2  V   ε e  (3.17) (3.18) (3.19) (3.22) From equation (3.22), It is certain that V  and V  with every εe  and V  for εe  , so εe ,ε e are always finite and: V  2εTe ε e (3.22b) Because ε ,ε are finite, accordingly V is finte, so V is uniform continuous by time e e 18 According to Barbalat’s lemma: V   εe ,ε e  From equation (3.17), (3.18) yields ˆ  , ˆ  It means   and   From equation (3.16), we obtain :      (3.23)  l   Lmi s   (l   Lmi s )   l           T T where l   Lmi s  l -  Lmis l   Lmis  ; l  l -l  Because of two independent linear equations,the equation (3.23) is equal to only if   0;   or ˆ   and ˆ   We can find the estimating flux: ˆr  ˆ ˆ  dψ ˆ r  ˆ Lm i s (3.24)   ψ ˆ ˆ    dt   ˆ ˆs  arctan( r  ) (3.25) ˆ r In summary, we can calculate the value of rotor and the value of rotor time constant inverse  from update rule (3.17) and (3.18) without sensors 3.2.2 Build self-adaptive estimator of speed and flux Figure 3.4 shows the diagram of speed stimator, the valuve of rotor time constant inverse and rotor flux based on self-adaptive method is us m Calculate the value of m m Calculate ˆ based on m c , c , ˆ , ˆ ˆ m δe Estimation algorithm (Theorem 5) c c Calculate flux ˆr ψ ˆ ˆ Figure 3.4 Speed and flux estimation, the inverse value of rotor time constant diagram The procedure for estimating rotor speed and flux as seen in Figure 3.4 includes the following steps: Step 1: Calculate the value of vector m based on the the measurement of stator current and voltage Step 2: Build a self – tuning rule ˆ ,ˆ and c ,c by theorem ˆ based on the value of vector m resulting in step Step 3: Calculate the value of vector m 1, the value of stator current measured and ˆ ,ˆ c ,c (Theorem 5) Hence the error ˆ  m)  It is certain that ˆ ,ˆ are precisely estimated δe  (m The above procedure can be deduced as: From the stator current and rotor flux, we set: dψ r (3.26) m dt From (3.1), (3.2) and (3.26) yield: 19 di s R R (3.27)  s i s  s us dt  Ls  Ls Rotor speed  and the inverse value of rotor time constant  change slowly with changing speed of current and flux of motor       (3.28) m m  Lmi s       We build the estimator: ˆ    (ˆ  c ) (ˆ  c )  m  L ˆi (3.29) m m s  (ˆ   ) (ˆ   )  c c   ˆ  m is the where ˆ ,ˆ are estimated values of , ; c ,c are control signal, δe  m ˆ and real value m error between estimated value m Substracting (3.28) from (3.29), we obtain the error equation:  c c       (3.30) δ e    m      m  Lmi s         c  c m   Theorem [5]: The speed estimatorand the inverse value of rotor time constant (3.30) is asympotic stability and the error vector lim δe (t )  if the update speed rule ˆ , the inverse t  value of estimated rotor time constant ˆ and controll signal and c ,c calculated as below: c   m m  (3.31)     m  m  Zδe   c    ˆ  δe Tm (3.32) T ˆ  δe (m  Lmi s ) (3.33) T  where m   m - m  , Z is positive definite matrix Proof: We choose a posivetive definite function: (3.34) V   δe Tδe       V    m  m  δe T Zδe  (3.36) From (3.36), It is sure that V  V  every δe  and V  when δe  , so δe , δ e are always finite From(2.35), we rewrriten:   δe T Zδe   m  m  δe T Zδ e V  2  m Tm (3.37)  are siniuous function shaped in sinuous Therefore, V is bounded  V where m, m uniform continuos Following Barbalat’s when V is uniform sininuous and V   δe  , δ e  (3.30) we wriiten as 20    m  Lmis    m  0     (3.39)   m    m  Lmis   0  Becuase m, i s independent coninuous linear equations so   0,  We estimate ˆ  ,ˆ   1  ˆ ˆ  ˆ r   We obtain ψ (3.40)  ˆ Lm i s  m   ˆ ˆ  In sumary, rotor speed and the inverse value of rotor time constant can be calculated from the control signal (3.31) and update rule (3.32), (3.33) without sensors 3.3 The application model of the sensorless speed control algorithm of three-phase asynchrounous ac motor with uncertain parameters on rotating coordinate (d,q)  r ref * isd Lm * sq i  ref Current controller usd usq  dq tu us us Vector tv modulation tw Speed controller - isd 3~ u isq is  is dq ˆs  us Speed and flux estimator ˆ uvw us uvw  v w isu isv usu usv mL M3~ Figure 3.5 Motor control model using the speed estimator 3.3.1 Using the speed estimator from item 3.2.1 Rad/s -1 -2 -3 10 15 20 25 Time (s) 30 35 40 45 Figure 3.7 Error between desired rotor speed and estimated rotor speed It is obviously that the rotor speed is controlled to reach the desired speed 50 21 - When the motor starts, the error of rotor speed between the desired and estimated values is about 2,5% - When the load changed suddenly while the motor was operating normally, the error is about 1,5% - The setting time to rotor speed reaching the desired value is about second 3.3.2 Using the speed estimator from item 3.2.2 Rad/s -1 -2 -3 -4 10 15 20 25 Time (s) 30 35 40 45 50 Figure 3.14 Error between desired rotor speed and estimated rotor speed It is clear that the rotor speed is controlled to reach the desired speed - When the motor starts, the error of rotor speed between the desired value and the estimated one is about 5,5% - When the load changed suddenly while the motor was operating normally, the error is about 2,2% - The setting time to rotor speed reaching the desired value is about 1,2 second 3.4 The application model of the sensorless speed control algorithm of three-phase asynchrounous ac motor with uncertain parameters on stationary coordinate (α,β) -  r2ref ref e2 + ˆ e1 + Speed and flux controller ˆ r ˆ r2 us Vector modulation us tv tw 3~ u ˆ r  is Speed and flux estimator tu is us us uvw  v w isu isv usu usv M3~ Figure 3.19 Motor control model using the speed and flux estimator mL 22 3.4.1 Using the speed estimator from item 3.2.1 Rad/s -2 -4 -6 -8 10 15 20 25 Time (s) 30 35 40 45 50 Figure 3.21 Error between desired rotor speed and estimated rotor speed -3 Wb x 10 -5 10 15 20 25 Time (s) Figure 3.24 Error between desired flux 30 r2 ref 35 40 45 and estimated flux 50 r2 - The estimated rotor speed reaches the desired speed as seen in Figure 3.21 When the motor starts, the error of rotor speed between the desired value and the estimated one is about 10% When the load changed suddenly while the motor was operating normally, the error is only 4% - The estimated rotor flux reaches the desired flux as seen in Figure 3.24 When the motor starts, the error of rotor flux between the desired value and the estimated one is about 70% but the estimated flux reaches the desired one after short time When the load changes during the operation of motor, the error is only 0,02% - The setting time to rotor speed reaching the desired value is about second 3.4.2 Using the speed estimator from item 3.2.2 0.3 0.2 Rad/s 0.1 -0.1 -0.2 -0.3 -0.4 10 15 20 25 Time (s) 30 35 40 45 50 Figure 3.31 Error between desired rotor speed and estimated rotor speed 23 -3 Wb x 10 -5 10 15 20 25 Time (s) Fugure 3.34 Error between desired flux 30 r2 ref 35 40 45 and estimated flux 50 r2 - The estimated rotor speed reaches the desired speed as seen in Figure 3.31 When the motor starts, the error of rotor speed between the desired value and the estimated one is about 0,6% When the load changed suddenly while the motor was operating normally, the error is only 0,03% - The estimated rotor flux reaches the desired flux as seen in Figure 3.34 When the motor starts, the error of rotor flux between the desired value and the estimated one is about 70% but the estimated flux reaches the desired one after short time When the load changes during the operation of motor, the error is only 0,001% - The setting time to rotor speed reaching the desired value is about seconds 3.5 Conclusion In this chapter, we represent the rotor speed estimation algorithm as seen item 3.2.1, and the rotor speed and flux estimation algorithm as seen item 3.2.2 Consequently we combine these algorithms to two control algorithms proposed in the chapter to build four sensorless speed control model of motor To check the validity of proposed algorithms, we take simulations on Matlab In the four posibility sensorless control model, the model using the control algorthm in item 2.3 with the estimation algorithm in item 3.2.2 shows the best results After considering the affect of neural network parameters and the self-adaptation of the estimator, it impacts on the converge posibility and the processing time of system It is necessary to analyse the processing time and the speed error to choose the most effective parameters The results in the chapter are published in [3] and [5] of the publication list General conclusion 4.1 The main researches - Analyse advanced speed control methods, problems on buidling the speed controller for AC motors - Build two control algorithms: the speed control algorithms with uncertain parameters and changing load on rotating coordinate (d,q) and stationary coordinate (α,β) The global asympotic stability of system are proved by Lyapunov stability theory and Barbalat’s lemma The simulation results on Matlab show the validity of these proposed control algorithms 24 - Build two estimation algorithms: the speed estimation algorithms using artifical neural network and self-adaptation; the self- adative speed and flux estimation algorithms without using artifical neural network The asympotic stability of these algorithms is proved by Lyapunov stability theory and Barbalat’s lemma - Combine four possibility models between the speed and flux control algorithms and speed and flux estimation algorithms based sensorless model - Valuate the impacts of the neural network parameters on the control system - Simulate on Matlab to check the validility of proposed control and estimation algorithm 4.2 The contributions There are four contributions in ac motor control algorithms a) The speed control algorithm for AC motor with uncertain parameters on rotating coordinate (d,q) ( Theorem 1) b) The speed and flux control algorithm for AC motor with uncertain parameters on stationay coordinate (α,β) ( Theorem 2) c) The speed estiamtion algorithm for AC motor using artifical neural network and selfadaptation (Theorem1 and Theorem 4) d) The speed estiamtion algorithm for AC motor using self-adaptation (Theorem 5) 4.3 Future research - Continue researching and developping the intelligent speed control algorithms using in real applications - Build the implementation system on the real devices to check the validity of the proposed algorithms - Research, implement intelligent controller based on FPGA and others advancedproduction techology of microtroller unit LIST OF WORKS HAS BEEN PUBLISHED [1] Pham Minh Tuan, Le Hung Linh (2009), Control of AC motor Using Artifical Neural Network, Journal of computer science and cybernetics, Vol 25, No 3, pp 288-299 [2] Pham Thuong Cat, Le Hung Linh, Pham Minh Tuan (2010), Speed Control of 3-Phase Asynchronus Motor Using Artificial Neural Network, 2010 8th IEEE International Conference on Control and Automation, pp 832-836 [3] Le Hung Linh, Pham Thuong Cat, Pham Minh Tuan (2013), Control of Three-phase AC Motor With Uncertain Parameters Usisng a Speed Estimator, Journal of computer science and cybernetics, Vol 29, No 4, pp 313-324 [4] Le Hung Linh, Pham Thuong Cat, Pham Minh Tuan (2013), Speed And Flux Control of Three-phase With Uncertain Parameters Using Artifical Neural Network, The Proceeding ò the 2nd Vietnam Conference on Control and Autoamtion- VCCA-2013, pp 255-261 [5] Hung Linh Le, Thuong Cat Pham and Minh Tuan Pham (2014), Speed and flux control of three-phase AC induction motor with uncertain parameters using a speed estimator, 2014 IEEE International Conference on Robotics and Biomimetics, pp 1578-1583 [6] Hung Linh Le, Thuong Cat Pham and Minh Tuan Pham (2015), An ANN-based speed and flux controller of three-phase AC motors with uncertain parameters, Acta Polytechnica Hungarica – Journal of Applied Sciences Vol 12, No 2, pp 179-192 (SCI-E, IF=0.471) ... sensorless controlller of AC motors The main contents of the thesis Two control algorithms and two estimation algorithms of motor parameters are proposed a) The speed control algorithm for AC motor. .. proposes control algorithm and speed estimation of AC motor with uncertain parameters 1.3 Research problems - Developing rotor speed and flux estimation of AC motor - Developing AC motor control. .. algorithm for ac motor with uncertain parameters The objectives of the thesis - Propose algorithms for controlling speed and flux of AC motors - Propose rotor speed and flux estimation algorithms