14th international conference on Sciences and Techniques of Automatic control & computer engineering - STA'2013 Sousse, Tunisia, December 20-22, 2013
STA'2013-PID3-1)&
Direct Torque Control for Asynchronous Machine Using Artificial Neural Networks Souha Boukadida, Soufien Gdaim, Abdellatif Mtibaa Abstract—The aim of this paper is to present an improved Direct Torque Control based on the Artificial Neural Networks. Thanks to their advantages, in this paper we proposed the use of Xilinx System Generator toolbox added to Matlab / Simulink. This solution replaces the use of programming language. Obtained results demonstrate that the proposed control is able to obtain high performance.
The state model of an asynchronous machine can be expressed as follows:
Keywords— Direct torque control; Neural network; Xilinx System Generator, FPGA.
Where A and B are respectively the evolution and the control matrices.
I.
INTRODUCTION
Thanks to their good performance, their low cost, their robustness and their simple implementation, the asynchronous machine is currently the most used machine in the field industrial and gradually replacing the DC machine [1]. However, the asynchronous machine is a multivariate system. It is characterized by a nonlinear model [2], which makes the control very complicated. The Direct Torque Control (DTC) strategy is the most developed drive control technique of asynchronous machine [3] [4] [5]. It is characterized by a fast dynamic response, simple implementation and robustness essentially to the rotor parameter variation. However, the direct torque control has many disadvantages which are electromagnetic torque and stator flux ripples. This is why, many methods are used to overcome these disadvantages for example replacing the hysteresis torque and flux controllers with neural block [6] [7]. The artificial neural networks are capable to explore multivariate correlations between the outputs and inputs variables without knowing the mathematical model of the system. A neural network model allows to model and to synthesize any process. It is excellent estimators of nonlinear systems [2] [8]. In this study, an artificial neural network (ANN) is introduced to replace the two hysteresis controllers and the switching table [9] [10]. This paper is organized as follows. In section 1, a brief introduction of the state model of an asynchronous machine is presented. The principle of the Direct Torque Control is described in section 2. Section 3 presents a description of Xilinx System Generator (XSG) and discusses the proposed controller. In section 4 some simulations results are presented to test the performances of the proposed controller using Matlab \ Simulink and the tool XSG.
S.Boukadida is with Laboratory EµE of the FSM, National Engineering School of Monastir, Monastir, Tunisia (
[email protected]). S.Gdaim is with Laboratory EµE of the FSM, National Engineering School of Monastir, Monastir, Tunisia (
[email protected]). A.Mtibaa is with Laboratory EµE of the FSM, National Engineering School of Monastir, Monastir, Tunisia (
[email protected]).
978-1-4799-2953-5/13/$31.00 ©2013 IEEE
II.
THE STATE MODEL OF ASYNCHRONOUS MACHINE
d [X ] = [A][X ] + [B ][U ] dt
(1)
⎡ ⎛ Rs Rr ⎞ ωr ⎤ Rr −ωr ⎢−⎜ + ⎟ ⎥ σLrLs σLs ⎥ ⎢ ⎝σLs σLr ⎠ ⎢ ⎥ ⎛ Rs Rr ⎞ ωr Rr ⎥ ⎢ A= (2) ωr −⎜ + ⎟ − ⎢ ⎝σLs σLr ⎠ σLs σLrLs ⎥ ⎢ ⎥ -Rs 0 0 0 ⎥ ⎢ ⎢ 0 -Rs 0 0 ⎥⎦ ⎣ ⎡ 1 ⎤ 0 ⎥ ⎢σ * L s ⎢ ⎥ B= ⎢ (3) 1 ⎥ ⎢ 0 ⎥ σ * Ls ⎥ ⎢ ⎢ 0 0 ⎥ ⎢ ⎥ 0 ⎦⎥ ⎣⎢ 0 The state vector X is composed by stator current and flux components. The vector command U is constituted by the stator voltage components.
⎡i s α ⎤ ⎢i ⎥ ⎢ s β ⎥ , U= ⎡Vsα ⎤ X= ⎢V ⎥ ⎢ϕs α ⎥ ⎣ sβ ⎦ ⎢ ⎥ ⎢⎣ϕs β ⎥⎦
(4)
In terms of the stator current and flux, the electromagnetic torque is expressed by:
Te =
3 p (ϕ Sα iSβ − ϕ Sβ iSα ) 2
(5)
III.
PRINCIPLE OF THE DTC
IV.
In figure 1 a possible schematic of Direct Torque Control is shown. There are two different loops corresponding to the magnitudes of the stator flux and torque. The reference values for the stator flux φs*and the torque Te*are compared with the actual values, and the resulting error values are fed into the two level and three level hysteresis block respectively. The outputs of the stator flux error and torque error hysteresis blocks, together with the position of the stator flux are used as inputs of the switching table. + E φ* s φs Eφ Eφ E S1 S2 S3 S4 S5 S6 Sa - + 1 V V V V V V Voltage s N 1 -10 VV VV VV VV VV VV Sb source 1 V V V V V V Sc 0 V V V V V V 0 E inverter Te T Te
2
3
4
5
6
1
7
0
7
0
7
0
6
1
2
3
4
5
3
4
5
6
1
2
0
7
0
7
0
7
-1 V5 V6 V1 V2 V3 V4
+
Switching Table
Te*
Stator Flux & Torque Estimators
iA
3 p (ϕ s α i s β − ϕ s β i s α ) 2
iB
Te =
Compared to standard architecture of Digital Signal Processor (DSP) and Microprocessor, FPGA technology gives hardware architecture within a flexible programmable environment. It allows the designer a new degree of freedom. However, in varied cases, the design of Field programmable gate array based controller architectures requires from the designer to control several different knowledges (e.g., electrical machine theories, micro- electronics and control). It is especially true for a complex algorithm for example the drive control applications. Accordingly, in order to make the design of control algorithms less intuitive and more manageable, several authors have presented interesting design methodologies. An important part of the design steps is achieved within the Matlab\Simulink friendly environment. The Xilinx System Generator is a toolbox developed by Xilinx to be integrated into the environment Matlab \ Simulink. For the fast prototyping, the choice of this tool is easy to explain. The system of control must be verified during all the development, it is much simpler to analyze the results with Matlab than with tools usually associated to the VHDL, such as Modelsim.
ϕ S = ∫ (V S − R S I S ) dt
V.
IM Figure 1. Diagram of the basic DTC method
In a fixed reference frame (α, β) of Concordia, the equation of the stator voltage circuits is:
v
s
= R s .i
s
+
dϕs dt
(6)
The stator flux on the stationary reference axes αβ is estimated as follows:
⎧⎪ϕ sα = (Vsα − Rs isα )dt ∫ ⎨ ⎪⎩ϕ sβ = ∫ (Vsβ − Rs isβ )dt
(7)
A. Principle of Artificial Neural Networks ANN An ANN is an information processing that is determined by the way biological nervous systems, like the brain, process information. The use of ANN is mainly guided by their properties such as their ability to learn and improve their operation using a set of example. An Artificial Neural Networks is composed by a large number of neurons interconnected working in unison to solve specific problems. The mathematical model of a neuron is given by:
Y
The developed electromagnetic torque Te of the motor can be evaluated by equation 9 and the shifted angle θs is given by equation 10.
x3
θ s = tan
−1
⎛ ϕ sα ⎜ ⎜ϕ ⎝ sβ
⎞ ⎟ ⎟ ⎠
)
i
∗x
i
+b)
(9)
(10)
(11)
Where f is the activation function, (x1, x2… xM) are inputs signal of the neuron, (w1, w2,… wM) are the corresponding weights , b is the bias of the neuron and Y is the output signal. A neuron model is presented in Figure 2.
x2
3 p (i s β ϕ s α − i sα ϕ s β 2
M
= f (∑ w i =1
(8)
Te =
DTC OBTAINED VIA THE ARTIFICIAL NEURAL NETWORKS
Inputs x1
The module of the stator flux is given by equation 8:
φ s = ϕ s2α + ϕ s2β
DESCRIPTION OF XILINX SYSTEM GENERATOR
Output
∑
Fonction 'f'
Y
. xM
b Figure 2. Neuron model
Every neural network possesses knowledge which is contained in the values of the connections bias and weights. Changing the knowledge stored in the neural network as a function of experience implies a learning rule for changing the values of the bias and weights.
X1
W111
W11n
X2
b 11 W211 W212
W112
W121
of the network are therefore updated using the following relationship:
b21
W21m
y1
w ji (k + 1) = w ji (k ) − η
b22
W122
y2 …..
.…
…..
……... W1n2
Xn
b2m
W2n1
ym
b1n
W1nn
W2nm
Hidden Layer
Input Layer
Output Layer
Figure 3. Structure of neural network
A learning algorithm performs the adaptation of bias and weights of the network to minimize the error between the input vector and the neural output vector. The criterion of error minimization is:
ε = ∑(d i − x i )2
(15)
The value of η may to be chosen carefully. Because low values will cause slow convergence, whereas large values will cause may accelerate the Artificial Neural Networks learning and consequently fast convergence but may cause oscillations in the network output.
W12n
W1n1
∂E (k ) ∂w ji (k )
(12)
Block diagram of Direct Torque Neural Network Control: The structure of the Direct Torque Neural Network Control (DTNNC) of asynchronous machine is shown in Figure 4. The figure shows that the two hysteresis controllers and the switching table selector are replaced by the artificial neural network. After several tests with MATLAB we take an architecture containing two hidden layer with number of neurons 10. The ANN inputs are the error between the reference value and its estimated value, the difference between the estimated electromagnetic torque and the torque reference, the difference between the estimated flux stator and the flux reference and the number of sector. The ANN output layer is composed of three neurons, each neuron represent the state of one of the three pairs of vector that will be applied to the asynchronous machine.
i
It is not assured to generate an acceptable solution for all input–output association problems. The training result depends on several factors [11]: •
Number of layers, number of neurons in each layer.
•
Initial parameter value w (0) and b (0).
•
The learning-rate constant.
•
Neural architectures.
•
The details of the input–output mapping.
Training Neural Network: The Back Propagation network is considered such as the quintessential Neural Net [12][13]. The network is initialized with small random weights and bias. Then, the input is applied and the output calculated.
y
l i
= f
l
(∑ w
Figure 4. Structure of DTC using ANN strategy. ij
l −1 j
×y
l i
+b )
(13)
j
Next in the backward phase, the error of each neuron is calculated, which is essentially: Target - Actual Output.
E (k ) =
1 N
N
∑ (d ( k ) − y ( k ) )
2
i
i
(14)
i =1
Where yi is the actual output produced by the network in response to the input xi, di is the desired response, and N is the number of input-output training data. It is during this phase that modifications are applied to the initial weights of the network to minimize the error E (k) in a statistical sense. The weights associated with the output layer
Simulation and interpretation result: To study the performance of neural network control with Direct Torque Control, the simulation of the system was conducted using MATLAB\SIMILUNK. The electromagnetic torque and flux references used in the simulation results are 10 N.m and 0.92 Wb respectively. The sampling period of the system is 50 μs. Figure 5, 6 and 7 shows a comparison between the conventional DTC and Direct Torque Neural Network Control.
(13)
The trajectory of the stator flux is illustrated by Figure 7. It takes an almost circular shape with a slight deviation at the border while it’s enhanced in the case of DTNNC. VI.
ARCHITECTURE OF NEURAL BLOCK OBTAINED WITH XILINX SYSTEM GENERATOR
A. Presentation of neural block The neural processing propagates the inputs (error flux, error torque and sector) to outputs (SA, SB and SC). Propagation occurs through the different layers of neurons, each neuron Nm,j of the layer m calculates the output Xm,j. The neural block in XSG is presented as follows:
a. Conventional DTC. b. Neural network DTC. Figure 5. Electromagnetic torque response Figure 8. The neural block in XSG
First layer: The first hidden layer contains 10 neurons. The internal structure of each neuron is shown in Figure 9.
c. Conventional DTC. d.
Neural network DTC.
Figure 6. Flux réponse Figure 9. Structure of a neuron
The approximation of the sigmoid function, defined as Mcode XSG is presented in Figure 10.
e. Conventional DTC. f.
Neural network DTC.
Figure 7. The stator flux vector trajectory
Figure 5 shows the evolution of the electromagnetic torque. It can be seen that the torque's ripples is reduced appreciably compared with conventional DTC. We can notice in Figure 6.c that the stator flux reached immediately its reference value with a high overshoot which has decreased in the case of Neural network DTC as shown in Figure 6.d.
Figure 10. Function approximation tansig
Second layer: The second layer comprises 10 neurons. The processing in this block is similar to that determined in the first layer. The content of each neuron in the second layer is presented in Figure 11. The internal structure of a neuron is composed of a set of adders and multipliers.
B. Simulation and interpretation The simulation of the neural network control is performed with the library XSG Simulink. We obtain in Figure 13, Figure 14, Figure 15, Figure 16 the evolution of electromagnetic torque, zoom electromagnetic torque, stator flux magnitude and stator flux trajectory in the cases of DTC and DTNNC scheme respectively.
a. Conventional DTC. b. Neural network DTC. Figure 13. Electromagnetic torque response
Figure 11. Structure of a neuron of the second layer
Third layer: The third layer contains only three neurons (the output layer). This last layer selects the vector to be applied to the inverter; this vector contains the components (SA, SB, and SC). The mathematical processing in this block is similar to that determined later. It is presented in Figure 12.
3
∑X
2,i
×w i ,3
i =1
c. Conventional DTC. d. Neural network DTC. Figure 14. Zoom Electromagnetic torque reponse
e. Conventional DTC. f. Neural network DTC. Figure 15. Flux reponse
g. Conventional DTC. h. Neural network DTC. Figure 16. The stator flux trajectory
Figure 12. Structure of the third layer
We can notice the contribution of the application of neural network control of asynchronous machines by comparing the electromagnetic torque produced by the DTC and that the neural control. It can be seen that the torque's
ripples with neural direct torque control in steady state is reduced appreciably compared with conventional DTC. Compared with the conventional DTC, ripple of stator flux with neural network DTC is reduced significantly. In all simulation presented can be observed a much better behavior of the performance achieving the main objectives of the present work which was to reduce the flux and torque ripple and maintain a good torque response as the conventional DTC. VII. CONCLUSION A new approach to simulate Direct Torque Control algorithm of asynchronous machine has been proposed by using an intelligent techniques approach using Xilinx System Generator. We have succeeded in presenting a new technique (XSG) to get the VHDL code without being forced to make a difficult programming mainly in our case. For the next work we will try to see the experimental results. REFERENCES [1] [2] [3]
[4] [5]
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