Comparative study of ANN DTC and conventional DTC controlled PMSM motor

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Comparative study of ANN DTC and conventional DTC controlled PMSM motor A. Ghamria , R. Boumaarafa , M.T. Benchouiaa ,∗, H. Meslouba , A. Goléaa , N. Goléab b

a Department of Electrical Engineering, LGEB laboratory, Biskra University, Algeria Electrical Engineering Department, LGEA laboratory, Oum El Bouaghi University, Algeria

Received 25 February 2019; received in revised form 13 September 2019; accepted 14 September 2019 Available online xxxx

Abstract In this paper an Artificial Neural Network (ANN) algorithm is presented in order to solve the problems associated with the conventional DTC approach. In order to improve the performances of the DTC controlled PMSM and to reject the disturbances, an ANN algorithm is used. This intelligent artificial technique is used to select the optimal voltage vector. In order to reduce the torque and flux ripples, the hysteresis comparators and the switching table have been substituted by the ANN technique. Simulation using Matlab/Simulink environment and experimental results around the Dspace-1104, are presented to test the performances of this approach. Simulation and experimental results show the high performances of the ANN-DTC compared to the conventional DTC; in particular the reduction of the ripples in torque and flux. c 2019 Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). ⃝ Keywords: Permanent magnet synchronous motor (PMSM); Direct torque control (DTC); Artificial neural networks (ANN)

1. Introduction Recently, a wide range of industrial applications, use the PMSM. Compared with a DC motor, the PMSM misses a commutator, so it is more reliable than the DC motor. The PMSM also has advantages when compared to an induction motor. PMSM generates the magnetic flux with rotor magnets, which gives higher efficiency. The classification of the PMSM, their merits and demerits, magnetic characteristics of the magnets used and the comparison with the induction motors are presented in [26]. Therefore PMSMs are used in some applications, which require high reliability and efficiency, such that electric vehicles, high-end white goods, high-end pumps and fans. PMSMs are synchronous machines which certainly require accompanying power electronics, but it also provides the basis for achieving high-quality actuator control [8]. Notwithstanding its advantages, such as high torque to current ratio, high power density and high efficiency, the PMSM remains complicated and difficult to control when good transient performance under all operating conditions is desired. This is due to the fact that the PMSM is a multivariable, nonlinear, time varying system and subjected to unknown disturbances and variable parameters. Abbreviations: PMSM, Permanent Magnet Synchronous Motor; ANN, Artificial Neural Networks; DTC, Direct Torque Control; FOC, Field Oriented Control ∗ Corresponding author. E-mail address: [email protected] (M.T. Benchouia). https://doi.org/10.1016/j.matcom.2019.09.006 c 2019 Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). 0378-4754/⃝

Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Abbreviations PMSM ANN DTC FOC

Permanent Magnet Synchronous Motor Artificial Neural Networks Direct Torque Control Field Oriented Control

Nomenclature Vabc iabc Vsα , Vsβ Isα , Isβ Φsα , Φsβ Te∗ Te δ ∅s σ p Rs IN Ld Lq φf J S1 , S2 , S3

Stator voltages Stator currents Stator voltage components in the α-β axes Stator current components in the α-β axes Stator flux components in α-β axes Reference value of electromagnetic torque Electromagnetic torque Position of the stator flux Stator flux amplitude Leakage factor Poles pairs Number Stator resistance Nominal Current Inductance d-axis Inductance q-axis PM flux linkage Moment of inertia Switching states

Recent years, various robust control methods have been developed in order to improve the efficiency of the PMSM in all operating circumstances. However, the widely used approach consists in using linear control theory with the disturbance estimate [13,29]. In [28], the robustness is ensured by using H∞ control theory. In addition to the relative simplicity of the DTC control structure, yet performs at least as well as the Field Oriented Control (FOC) technique. It is also known that DTC drive is less sensitive to parameters variation (only stator resistor is used to estimate the stator flux) and provides a high dynamic performance compared to the classical vector control (fastest response of torque and flux). A decoupled control of flux and torque can be obtained without using speed or position sensors. For both stator flux and electromagnetic torque, the nonlinear hysteresis controller introduces limitations such as a high and uncontrollable switching frequency [23]. This controller out-turns a variable switching frequency and in consequence large torque and flux ripples and high currents distortion. The DTC is used in the objective to have high dynamic performances, to minimize the ripples and the flux’s distortion. It is fundamentally based on a switching table which allows selecting the voltage vector to apply to the inverter according to the stator flux vector position and of the direct control of the stator flux and the electromagnetic torque. In recent times, direct torque control is applied to control different machines such as induction motor [14], reluctance motor [5], induction motor [21], permanent magnet synchronous machine [9], and DFIG [1,22]. Many studies are oriented for the limitation of the flux and torque ripples. In this sense, the intelligent techniques are used to improve the dynamic performance of the system with ripples minimization. This method relies on the substitution of the hysteresis controllers and the switching table by a controller based on artificial neural networks in order to lead the flux and the torque towards their reference values during a fixed time period. Artificial intelligence techniques (fuzzy logic, neural networks, genetic algorithms, etc.) have been introduced in recent years in identification and nonlinear control systems [2,12]. This is principally due to their capacity learning and generalization. Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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In this paper in order to show the efficiency of the control of the permanent magnet synchronous machine using neural networks compared to the conventional DTC control, a detailed study has been envisaged. These algorithms are implemented in simulation by using Matlab Simulink and to validate these results, a test bench around a DPACE 1104 is implemented. Simulation results as well as experimental results prove the efficiency and performance of the ANN control applied to the PMSM machine compared to that of the conventional DTC. 2. Mathematical model of the PMSM The model of the PMSM is given with the following simplifying assumptions: • Saturation is neglected. • Magneto-motive forces are distributed sinusoidal in the air gap of the machine. • Hysteresis and eddy current losses are not considered in the magnetic parts. Variation of the resistances as a function of the temperature is negligible. In these conditions we can write the equation of the voltages, currents and magnetic fluxes of the machine in the referential (α − β) as follows: { L S Isα = −Rs Isα + ω∅ f + Vsα (1) L S Isβ = −Rs Isβ + ω∅ f + Vsβ { ∅sα = −Rs Isα + Vsα (2) ∅sβ = −Rs Isβ + Vsβ The electromagnetic torque Te is given by: ) 3 ( Te = P ∅sα Isβ − ∅sβ Isα (3) 2 The DTC command is based on the direct control of the torque and flux without going through the current as is the case in FOC. In the literature we find several solutions for this command [14]. The DTC command has many advantages including a lower dependence of the parameters of the machine, a simplified implementation and a dynamic response of the faster torque,√compared to the Rotor Field Oriented Control (RFOC). The stator flux amplitude ∅s = ∅2sα + ∅2sβ and position δ= tan−1 (∅sα /∅sβ ) are computed from the flux components evaluation given by: { ∫T ∅sα = 0 s (Vsα − Rs Isα ) dt + ∅sα0 ∫T ( ) (4) ∅sβ = 0 s Vsβ − Rs Isβ dt + ∅sβ 0 where I sα, I sβ and V sα, V sβ are respectively stator current and voltage components in the (α, β) axes and ∅sα, ∅sβ are the stator magnetic flux components in the (α, β) axes. 3. Conventional DTC Isao Takahashi and Depenbrock proposed DTC for induction machines in the middle of 1980s [25], more than one decade has passed. Different approaches have been developed [17,24]. DTC based PMSM control has been developed in 1990. Several advantages are present by the DTC, such as less machine parameter dependence, simpler implementation and a high dynamic torque response. There is no current controller needed in DTC, because it selects the voltage space vectors according to the errors of stator flux and torque. The DTC is carried out using a switching table and hysteresis controllers. Fig. 1 shows a control scheme of a conventional DTC. It includes flux and torque estimators, flux and torque hysteresis controllers and a switching table. Generally a DC bus voltage sensor and two current sensors are needed for the flux and torque estimation. Speed sensor is not necessary for the torque and flux control. The switching state of the inverter is actualized in each sampling time. In each sampling interval, the inverter maintains the state until the output states of the hysteresis controller change. Therefore, the switching frequency is generally not fixed; it changes with the rotor speed, load and bandwidth of the flux and torque controllers. However, in this paper a new algorithm is presented. First the basic conventional DTC control is presented [24]. The control scheme of conventional DTC is given in Fig. 1. The stator flux equations of the PMSM, in the (α − β) reference are given by: Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Fig. 1. Conventional DTC.

Fig. 2. Vectors of stator voltages provided by a two level inverter.

The flux components and magnitude estimation: ⎧ ∫t ⎪ ∅sα est = 0 (Vsα − Rs Isα ) dt ⎪ ⎪ ⎨ ∫t ( ) ∅sβ est = 0 Vsβ − Rs Isβ dt ⎪ √ ⎪ ⎪ ⎩∅s est = ∅2sα + ∅2 sβest est

(5)

The electromagnetic torque estimation: ) 3 ( P ∅sα est Isβ − ∅sβ est Isα (6) 2 It is well known that the three phase inverter can produce eight output states, which represent eight space vectors. Six are of equal magnitude and arranged 60◦ apart in space diagram, and two vectors are null as shown in Fig. 2. Table 1 called Switching Table, generates binary signals applied to the branches of the inverter. The selection of the appropriate voltage vector is precisely based on this table, where the input quantities are the stator flux sector and the outputs of the two hysteresis comparators, when the outputs are the voltage vectors. Te =

Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Table 1 Switching table for DTC_6 sectors. Sector

S1

S2

S3

S4

S5

S6

∆∅ = 1

∆Te = 1 ∆Te = 0 ∆Te = −1

V2 V7 V6

V3 V0 V1

V4 V7 V2

V5 V0 V3

V6 V7 V4

V1 V0 V5

∆∅ = 0

∆Te = 1 ∆Te = 0 ∆Te = −1

V3 V0 V5

V4 V7 V6

V5 V0 V1

V6 V7 V2

V1 V0 V3

V2 V7 V4

Fig. 3. Architecture of ANN.

4. Principles of artificial neural network Numerous advances have been made in developing intelligent systems, some inspired by biological neural networks [18]. Researchers from many scientific disciplines are designing artificial neural networks to solve a variety of problems in pattern recognition, prediction, optimization, associative memory and control. The advantages of ANNs are their capability of arbitrary mapping from any real input space to an output space without regard for the underlying system dynamics; which can be difficult to model in some situations [4]. To solve these problems, conventional approaches have been proposed. Although successful applications can be found in certain well-constrained environments, none is flexible enough to perform well outside its domain. ANNs provide exciting alternatives, and many applications could benefit from using them. A dense interconnected computing node is used by ANNs to approximate nonlinear functions [11]. Each node constitutes a neuron and performs the multiplication of input signals by constant weights sums up the results and maps them to nonlinear function the result is then transferred to its output. A feed forward ANN is organized in layers: an input layer, one or more hidden layers and an output layer [19], Fig. 3 5. DTC structure based on ANN A neural network is a similar machine like the human brain with learning capacity and growth. They need a lot of training to seize the model of the plant. The basic specificity of this network is that it can estimate complicated nonlinear functions [3]. It constitutes an approach which has great flexibility to deal with problems of perception, memory, learning and analysis under new angles. The parallel treatment of information, gives emerging and very promising properties that overcome the limitations of conventional numerical methods and to be able to solve complex problems [10,15]. Fig. 4 illustrates the structure of the ANN-DTC based control of PMSM. Three neural networks are proposed. First the position δ of the stator flux is estimated (Figs. 5–1). This is the angle between the rotor flux and the stator flux. This neural network is associated with two inputs and one output feed-forward network with 3 layers. The input layer has six neurons of hyperbolic tangent “sigmoid” transfer Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Fig. 4. Basic ANN scheme based direct torque control.

Fig. 5. ANN structure.

function. First hidden layer has 4 neurons of log sigmoid transfer function and the output layer has one neuron of linear function. The adjustment of the weights associated with hidden neurons can be found in [6]. The training method used is the back-propagation method [7,20,27]. The sector zone for the estimated value of δ is determined by the second neural network. In total there are six sectors, of π /3 rad each. Three layers of neurons are used again but with a 5-4-1 feed forward configuration (Figs. 5–2). The transfer function of the input layer is a log sigmoid, hidden layer is a hyperbolic tangent sigmoid function and finally, the transfer function of the output layer is a linear. The back-propagation used is the training method [7]. The input given is the angle δ, since sector selection is purely based on δ. The last neural network is for the selection of voltage vector as given in (Figs. 5–3), which is based on three inputs, flux and torque errors and the sector. The network taken in this case is a 3-5-1 feed-forward network with first layer of log sigmoid transfer function, the second layer of hyperbolic tangent sigmoid transfer function and the third layer is a linear transfer function. The training method used was again the back-propagation. All the three neural networks were trained to performance 0.0001 sec. The training function used is Levenberg–Marquardt back propagation, it updates weights and bias values according to Levenberg–Marquardt optimization [16]. As soon as the training procedure is over, the neural network gives almost the same output pattern for the same or nearby values of input. This tendency of the neural networks which approximates the output for new input data is the reason for which they are used as intelligent systems. 6. Simulation and experimental results A simulation model of the system was developed in the Matlab/Simulink environment. A comparative analysis using simulation results between the ANN-DTC and the conventional DTC was carried out. The torque and the flux references used in both methods are (+2 N.min 0 s, −2 N.min 0.5 s) and 0.3 Wb respectively. The experimental device based on DSP 1104 was developed and a comparison is carried out. Table 2, presents the parameters used in the experiment bench. The machine is running at 1500tr/min. The sampling period of the system is 10−4 ms. Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Fig. 6. Comparison graph of torque (Nm).

Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Fig. 7. Comparison graph of the Stator Flux Amplitude (Wb). Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Fig. 8. Comparison graph of trajectory of flux (Fsα, Fsβ).

For comparison between ANN DTC and conventional DTC controlled PMSM, simulation and experimental results are shown in Figures 6 to 9 respectively. The simulation results are presented in Figs. 6(a, b) and the experimental results are shown in Figs. 6(c, d) respectively. Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Fig. 9. Comparison graph of stator currents (A).

Please cite this article as: A. Ghamri, R. Boumaaraf, M.T. Benchouia et al., Comparative study of ANN DTC and conventional DTC controlled PMSM motor, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.006.

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Table 2 Main parameters of the prototype. PMSM parameters Number of pairs of poles Stator resistance Nominal current Inductance d-axis Inductance q-axis Lq PM flux linkage Moment of inertia

p Rs IN Ld Lq φf J

2 2.6  4.5 A 43 mH 43 mH 0.178 Wb 85e−6 kgm2

It can be seen that the ripples in the conventional DTC torque are about 1 Nm but with ANN DTC the ripples are about 0.1 Nm, in the same operating conditions. So, the DTC-ANN gives more performances then the conventional DTC in terms of ripples. Figs. 7(a, b) and Figs. 7(c, d) show the response of stator flux magnitude of both methods ANN-DTC and conventional DTC. Figs. 7(a, b) illustrate the response of the stator flux magnitude in simulation and experimental test. The results show the fast response in transient state and the reduction in ripples compared with conventional DTC. In conventional DTC, the flux presents high ripples compared to the ANN-DTC (Figs. 7(c, d)). Figs. 8(a, b) show that in ANN-DTC, the stator flux vector describes a trajectory almost circular in both simulation and experimental test. Figs. 8(c, d) show the trajectory described by the stator flux vector in the conventional DTC. Finally, to prove the effectiveness of the ANN DTC, the steady state current response is presented in Figs. 9(a, b). The waveform of the stator current is improved with reduction in ripples. The stator current in the conventional DTC presents very high ripples (see Figs. 9(c, d)). 7. Conclusion In this paper an ANN-DTC approach controlled PMSM is presented. To validate the performances of this approach, simulation and experimental results are compared with the conventional DTC. The results show that the ANN-DTC gives more performances compared to the conventional DTC. The reduction in torque and flux ripples and the high dynamic of the torque are remarkably observed with the ANN-DTC approach. The ANN-DTC shows also an improvement in the waveform of the stator current with a constant switching frequency. The ANN-DTC enables to the system a very high accuracy; especially it can enhance the ability of rejecting the load disturbance which leads to a good robustness. Appendix See Table 2.

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