Abstract - â In this paper, speed controllers based on. Artificial Neural Networks for vector control of AC motors are used. ... shunt active power filters [12-14].
NONLINEAR AUTOREGRESSIVE MOVING AVERAGE (NARMA-L2) CONTROLLER FOR ADVANCED AC MOTOR CONTROL
A. Awwad
H. Abu-Rub IEEE, Senior Member
H. A. Toliyat IEEE, Fellow
Institut fur Informatik, FriedrichAlexande Universitat, Erlangen Nurenberg, Germany
Department of Electrical and Computer Engineering Texas A&M University at Qatar Doha, Qatar
Department of Electrical and Computer Engineering Texas A&M University College Station, TX 77843-3128
Abstract - — In this paper, speed controllers based on Artificial Neural Networks for vector control of AC motors are used. Tracking of the rotor speed is realized by adjusting the new weights of the network depending on the difference between the actual speed and the commanded speed. The controller is adaptive and is based on a nonlinear autoregressive moving average (NARMA-L2) algorithm. A comparative study between the proposed controllers and the conventional PI one will be presented and the advantages of the proposed solution over the conventional one will be shown. The rotor speed tracks the commanded one smoothly and rapidly, without overshoot and with very negligible steady state error. Computer simulation results are carried out to prove the claims. Keywords: Artificial Neural Networks, vector control, induction motor.
I. INTRODUCTION Electric motor drives absorb majority of all electrical energy produced. In the industrial countries, electric motors take more than 65% of all electrical energy generated [1, 2]. Most of the generated energy is used by ac induction motors, working at uncontrolled speed. In the last decade, ac motion control technology has grown significantly. The squirrel cage type of induction motor has been the workhorse in industry because of its ruggedness, reliability, efficiency, and low cost. Significant advancement in technology has resulted in widespread use of induction motor controlled drives. By using vector representation, it is possible to present the variables in an arbitrary coordinate system. If the coordinate system rotates together with a flux space vector, then we use a different terminology: flux-oriented control. In this way, it was possible to represent the electromagnetic torque as the product of a flux-producing current and a torque-producing current. By keeping constant flux, an induction machine may be controlled, like a separately
excited dc machine. Such a method will be selected to control our machine. Advanced control of an induction motor needs a fast and smooth response with minimum overshoot. The main problem while using a simple and linear PI controller is that it does not give an optimal response for different operating points and its tuning is difficult. Artificial intelligence methods, such as neural networks, can be used to identify and control non-linear dynamic systems since they can approximate a wide range of non-linear functions to any desired degree of accuracy. The ANNs have the advantage that they can be implemented in parallel, which gives relatively fast computation. Also they have the immunity from harmonic ripples and are fault tolerant. Since 1990s, investigation approaches showing the applications of artificial intelligence for ac motors control have appeared [2-14]. The NARMA model is an exact representation of the input– output behaviour of a finite-dimensional and nonlinear discrete time dynamic system in a neighbourhood of the equilibrium state [4, 6]. However, due to nonlinearities, it is relatively difficult to implement it for control systems in real time. To solve the computational problems related to use of this type of ANN in advanced control of electrical machines, two versions of NARMA are proposed in [4]: NARMA-L1 and NARMA-L2. The latter is more convenient to be practically implemented using multi-layer neural networks. The novelty of this paper is the use of NARMA-L2 for induction motor control. This method was used successfully for separately excited dc motor control and for three-phase shunt active power filters [12-14]. Regardless of the complicated representation of an induction motor with higher order nonlinearities used, this type of controller will be successfully used to improve its control approach. The ANN based controller will be used in rotor oriented vector control scheme. Simulation results using SIMULINK will be carried out.
II. INDUCTION MOTOR MODEL The squirrel cage type of induction motor has differential equations for the stator current and rotor flux vector components represented in coordinate system XY rotating with arbitrary angular speed given by: di sx R L2 R L2 R L L L s r r m i sx r m rx s i sy r m ry r u sx d Lr w Lr w w w
(1)
R L2 R L2 R L L L s r r m isy r m ry s isx r m rx r u sy (2) d Lr w Lr w w w d rx L R (3) r rx ( s r ) ry Rr m i sx d Lr Lr
disy
d ry d
d r d
L R r ry ( s r ) rx Rr m i sy Lr Lr L 1 m ( rx i sy ry i sx ) mo Lr J J
where w Lr Ls ; 1
L2m and Lr L s
(4) (5)
rx, ry, isx , isy are the
rotor flux and stator current vectors in coordinate system XY rotating with arbitrary speed, r is the angular speed of the rotor shaft. Rr , Rs , Lr , Ls are rotor and stator resistance and inductances respectively, Lm is a mutual inductance, J is the inertia, mo is the load torque. III. VECTOR CONTROL SYSTEM The idea of vector control of AC machines is based on vector representation and transformation from a stationary coordinate system to the rotating one. The produced torque Te in the machine has the form: L (6) Te m ( i i ) rq sd L J rd sq r where dq are the variables in rotating frame. If our coordinate system rotates with that of rotor flux r then the electromagnetic torque can be controlled by only one component while the second one is kept constant. This happens because the imaginary component of rotor flux, rq=0). This gives the next form: Te
L
m ( i ) L J rd sq r
(7)
If we keep constant isd then the rotor flux will keep constant.
This way the produced torque will linearly depend on the imaginary component of stator current (isq). The vector control system with ANN controller is shown in Fig. 1. IV. ROTOR ANGULAR SPEED CALCULATION While using the sensorless version of drive system the next equation could be used [15]: a x s i 2 a4 Q (8) r 2 122 i s is a3 x22 where a2, a3, a4 are motor parameters, si is the slip frequency and Q is the imaginary reactive power [16]. X12 and x22 are new variables defined below. The equation expressing imaginary reactive power is: (9) Qu i u i s s s s where and denote a stationary frame. The slip frequency is: R x (10) s i r 12 Lr x 22 and the new variables are [3]: (11) x i i r s
12
x
22
r s
i i r s r s
(12)
V. NONLINEAR AUTOREGRESSIVE MOVING AVERAGE (NARMA-L2) CONTROLLER The NARMA model is an exact representation of the input– output behaviour of a finite-dimensional and nonlinear discrete time dynamic system in a neighbourhood of the equilibrium state [4]. However, due to nonlinearities, it is relatively difficult to implement it for control systems in real time. To solve the computational problems related to use of this type of ANN in advanced control of electrical machines, two versions of NARMA are proposed in [4]: NARMA-L1 and NARMA-L2. However the latter is more convenient to be practically implemented using multi-layer neural networks. The main concept of a NARMA-L2 controller is to transform a nonlinear dynamic system into a linear dynamic system by revoking the nonlinearities, which makes it suitable for control of nonlinear dynamic systems such as an induction motor. NARMA-L2 is simply a rearrangement of the neural network of the system to be controlled, which is trained off-line and in a batch form. Thus, the first step in using NARMA-L2 control is to identify the system to be controlled. Nonlinear autoregressive moving average (NARMA) (eq. 1) is used to represent discrete time nonlinear systems [6].
UDC ωrc
isqref
ANN
+ Ψrc
PI
isdref
PI
usqref
d,q To
PI
usdref
α, β
usαref PWM
3-Ø
usβref
Inverter
+ -Ψr
-ωr
-
γs isq
α,β
isα
isd
To
isβ
d,q
A,B,C
iA
To
iB
α, β
Calculation Block
3-Ø
Fig. 1. Control system of induction motor with AI controller (Artificial Intelligence controller) y(k d ) N[ y(k 1),..., y(k n 1), u(k ), u(k 1),..., u(k n 1)]
(13) where u is the system input and y is the output. To force the system to follow some output y(k d ) yr (k d ) we need to develop a non-linear controller of the form [4]:
u (k ) G[ y (k ), y (k 1),..., y(k n 1), yr (k d ), u (k 1),
(14) ,..., u(k m 1)] However, training of the neural network to create the function G needs dynamic back propagation [5], which is quite slow. To solve this problem Narendra and Mukhopadhyay [4] have used the next approximate models to represent the system: NARMA-L1 Model y(k d ) f 0 [ y (k ), y (k 1),..., y (k n 1)] n 1
gi [ y (k ), y (k 1),..., y (k n 1)]u (k 1) i 0
NARMA-L2 Model
(15)
y(k d ) f 0 [ y(k ),..., y(k n 1), u(k 1),..., u(k n 1)] g0 [ y(k ),..., y(k n 1), u(k 1),..., u(k n 1)]u(k )
(16) These models are in companion form, where the controller input u(k) is not contained inside the nonlinearity. The advantage of this form is that it is possible to solve for the control input that causes the system output to follow the reference yr. As shown in eq. (2) NARMA-L1 f0 and gi are functions of only the previous values of the output y. Also the inputs occur in linear form in the right hand side. The NARMA-L2 is described by two functions, but these functions depend on both output and input signals. It is clear that Neural Network implementation of NARMA-L1 requires n+1 networks to represent f0 and gi. In contrast to this the NARMA-L2 model requires only two neural networks to approximate the functions f0 and g0. Therefore, from a practical stand-point, the NARMA-L2 model is found to be simpler to realize than the NARMA-L1 model. The resulting controller makes the output follow the reference yr and has the next form [4]:
yr (k d ) f [ y (k ), y (k 1),..., y(k n 1), u (k 1),
tested at different operating points and results from using the NARMA-L2 controller and the PI one are carried out for comparison. As mentioned previously the Neural networks are trained offline and in batch form. We have used 9 hidden layers and 10000 sample data are generated to train the network. 100 training epochs and employing training as a training function were enough to get good results. The performance of the training is shown in fig 3 and the testing and validation data are shown in Fig 4, 5 and 6 respectively. The response of the control system on unit step change of motor speed is shown in figure 7 while figure 8 presents the response after step change in motor speed and load torque. The load torque was introduced 7 seconds after the motor started. The response of the ANN controller is compared with the PI one for the same conditions. Tuning of the PI controller was done by trial and error. The ANN controller significantly improved the response and decreased the steady state and transient errors. Both controllers worked stably however the ANN controller made it possible to get much better results than the conventional one. This controller may be used in drive systems in which the response is of more importance than the simplicity of the used controller.
,..., u (k n 1)] g[ y (k ), y (k 1),..., y(k n 1), u (k 1),..., u( k n 1)] (17) Using this equation directly can cause realization problems [4], because we must determine the control input u(k) based on the output at the same time instant, y(k). So, instead, we may use the next model form [6]: y (k d ) f [ y(k ), y (k 1),..., y(k n 1), , u (k ), u (k 1),..., u (k n 1)] g[ y (k ),..., y(k n 1), u (k ),..., u( k n 1)] u(k 1) (18) Where d>1. The final form of the controller is the next: u (k )
yr (k d ) f [ y(k ),..., y(k n 1), u (k ),..., u (k n 1)] g[ y(k ),..., y(k n 1), u (k ),..., u (k n 1)] (19) The block diagram at figure 2 shows the NARMA-L2 controller applied for induction motor control. u (k )
VI. SIMULATION INVESTIGATION The investigated control system is shown in figure 2. Speed controller based on NARMA-L2 replaces the conventional PI one in the vector control scheme. The whole system with an induction motor was simulated in Simulink. The system was yr Reference
+ Multi Layer Neural Networks
f
-
+
y Induction Motor
(f)
Multi Layer Neural Networks
g
/
u
(g)
NARMA-L2 Controller
Delay
Delay
Fig. 2 block diagram of applying NARMA-L2 for induction motor control
Input 2
50
1
0
0
-50
-1
Performance is 1.20494e-008, Goal is 0
-6
10
Training-Blue Validation-Green Test-Red
Plant Output
100
-100 -7
10
0
10 -3
1
x 10
20
0
10
Error
20
NN Output 2
0.5 -8
-2
1
0
10
0 -0.5 -1
-1 -1.5
-9
10
0
10
20
30
40
50 60 100 Epochs
70
80
90
Fig 3 training performance of NARMA-L2 controller
Input 2
50
1
0
0
-50
-1
0
20 -3
15
x 10
0
10 time (s)
40
-2
0
Error
20
40
0
10 time (s)
Input
20
Plant Output 2
50
1
0
0
-50
-1
-100
0
10 -3
2
4
1
2
x 10
20
-2
0
Error
10
20
NN Output 2 1
0
0
5
-2
100
NN Output
10
20
Fig 4 testing data of NARMA-L2 controller
Plant Output
100
-100
100
0 -2
-1
0 -5
0
20 time (s)
40
-2
-1
-4
0
20 time (s)
Fig 5 training data of NARMA-L2 controller
40
-6
0
10 time (s)
20
-2
0
10 time (s)
Fig 6 validation data of NARMA-L2 controller
20
speed response , reference input[solid], NARMA-L2 response[dashdot] , PI response[dotted] 0.7
0.6
0.6
0.5
0.5
0.4
0.4
speed(pu)
speed(pu)
speed response , reference input[solid], NARMA-L2 response[dashdot] , PI response[dotted] 0.7
0.3
0.3
0.2
0.2
0.1
0.1
0
0
-0.1
0
5
10
15
20
25 30 time(seconds)
35
40
45
Fig. 7 System response after unit step change of motor speed
I.
-0.1
50
CONCLUSION
In this paper an ANN controller for sensorless control of an induction motor was used. The (NARMA-L2) Controller was used for the first time successfully for induction motor control and was compared with a conventional PI one. The results obtained from simulation show that the ANN controller has significantly better performance than the classical PI controller. The actual speed could track the commanded one rapidly, smoothly and with relatively small steady state error with the use of this controller for the advanced control of squirrel cage induction motor
[6]
[7]
[8]
[2] [3]
[4]
[5]
10
15
20
25 30 time(seconds)
35
40
45
50
H. Demuth , M. Beale, M. Hagan., Neural network toolbox user’s guide for use with MATLAB (Natick, MA: The Math Works, Inc., 2006). G. Simoes and B. K. Bose, “Neural network based estimation of feedback signals for a vector controlled induction motor drive,” IEEE Trans. Ind. Applicat., vol. 31, pp. 620–629, May/June 1995. Abu-Rub, H., Awwad, A. and Motan, N. “Artificial Intelligence Sensorless Control of Induction Motor, CPE 2007, 5th International Conference-Workshop Compatibility in Power Electronics
May 29 – June 1, 2007, Gdansk, Poland. [9]
[10] [11]
M. A. Rahman, “High Efficiency IPM Motor Drives for Hybrid Electric Vehicles”, Canadian Conference on Electrical and Computer Engineering (CCECE2007), 2007, pp. 252-255. Bose, Bimal K., "Artificial Neural Network Applications in Power Electronics" IEEE Trans pp 1631-1638, 2001. Kaźmierkowski, M. and Sobczuk, D. "Investigation of neural network current regulator for VS-PWM inverters", Int. Con. on Power Electronics Motion Control PEMC’94, Warsaw, vol. II pp. 10091014, 1994. Narendra, K.S., and S. Mukhopadhyay, “Adaptive Control Using Neural Networks and Approximate Models,” IEEE Transactions on Neural Networks, Vol. 8, 1997, pp. 475–485. Hagan, M.T., O. De Jesus, and R. Schultz, “Training Recurrent Networks for Filtering and Control,” Chapter 12 in Recurrent Neural Networks: Design and Applications, L. Medsker and L.C. Jain, Eds., CRC Press, pp. 311–340.
5
Fig. 8 System response after change of motor speed and load
REFERENCES [1]
0
[12]
[13] [14] [15]
[16]
D. Fodor, J. P. Six, and D. Diana, “Neural networks applied for induction motor speed sensorless estimation,” in Proc. ISIE’95, 1995, pp. 181–186. Russell, s. and Norvig, P. “Artificial Intelligent A modern Approach”, Prentice Hall, 1995. Wlas, M., Krzeminski, Z., Guzinski, J., Abu-Rub, H. And Toliyat, H.: Artificial Neural Network-Based Sensorless Nonlinear Control of Induction Motors, IEEE Trans. On Energy Conversion, Vol. 20, issue 3, pp. 520-528, September 2005. M. George, “Artificial intelligence based three-phase unified power quality conditioner”, Journal of Computer Science, 3 (7), 2007, pp. 465-477. M. George and K. P. Basu, “Three-phase shunt active filter”, American Journal of Applied Science 5 (8), 2008, pp.909-916. M. George, “Speed control of separately excited dc motor”, American Journal of Applied Science 5, 2008, pp. 227-233. Abu-Rub H., Hashlamoun W., A comprehensive analysis and comparative study of several sensorless control system of asynchronous motor, accepted to ETEP journal (European Trans. On Electrical Power), Vol. 11, No. 3, May/June 2001. H. Akagi, E. H. Watanabe and M. Aredes, “Instantaneous Power Theory and Applications to Power Conditioning”, IEEE Press, WileyInterscience, 2007.
