Fuzzy Logic Speed Controller for Dual Stator Induction Motor Based On Indirect Vector Control

Abstract

The purpose of this paper is to improve the dynamic response performance of a double star induction motor (DSIM) based on indirect field oriented control by using the Artificial Intelligence techniques (AI) and more precisely the Fuzzy Logic. Furthermore, this work presents a model of this motor in (dq) reference frame fed by two pulse width modulation (PWM) inverters and their simulation. Firstly, the speed control of the motor is made up with help of classic proportional-integral PI regulator. Then, a fuzzy logic controller (FLC) is adopted in the control loop instead of the traditional PI regulator in order to catch the diferences of the dynamic behavior of the machine. Finally, a comparison study between the two controllers is made on MATLAB/SIMULINK, the simulation results show that the intelligent controller achieved an amelioration in terms of settling time, rise time, precision and more stability against parametric and torque load variations. Also, the proposed fuzzy logic controller in this work succeeded to accomplish better results in terms of rise time by comparison to previous studies.

Keywords

• eol>Double Star Induction Machine
• Proportional Integral Controller
• Fuzzy Logic Controller

1. Introduction

It can withstand the loss of one or even two phases, making it exceptionally reliable in demanding applications The AC motors and more precisely the induction motors, [1], [ 2 ], [ 3 ]. has guaranteed an essential part in the industrial and Multiple approaches have been suggested to guarantee domestic fields in the last decades and plays a crucial role an eficient control of this machine. One viable option in it, especially after the quick development of power is employing the famous method of vector orientation electronics. to achieve an optimal control of the (PWM) inverters

In recent years, there has been a growing trend to- supplied (DSIM) [ 4 ]. This method has a simple structure wards the adoption of multiphase machines, particularly and is widely employed in industrial processes [ 5 ]. the dual star induction motor (DSIM). This type of ma- The (FOC) techniques’ primary concepts are drawn chine is essentially an AC induction motor with two from the d-q model of the induction motor, which entails stators that are shifted by 30 or 60 electrical degrees. The directing the flux with the d-axis and preserving this DSIM finds applications in a wide range of fields, includ- orientation while the torque is orientated with the q-axis. ing electric vehicles, naval ship propulsion, industrial The two amounts can then be managed independently machinery and manufacturing. Its many benefits over as a result, and the very coupled and complicated (DSIM) the conventional three phase induction motor are one can then be controller as a simple (DC) motor [ 6 ]. of the key factors contributing to its increasing demand In general, the (FOC) strategy can be classified to diin the industry. Firstly, it ofers an improved magneto rect and indirect approaches. Both of these types usually motive force (MMF) waveform, resulting in enhanced use conventional controllers like PID, PD, IP and PI [ 6 ] performance. Additionally, the DSIM helps reduce rotor due to their cost-efectiveness and ease of implementacurrent harmonics and allows for a decrease in current tion. The main disadvantages of conventional controllers per phase without requiring a voltage increase. This mo- and specifically the proportional integral-derivative (PID) tor also minimizes torque ripples and exhibits a higher and the proportional-integral (PI) are their sensitivity to torque density. However, perhaps the most significant variations in system parameters, inadequate rejection of advantage of the DSIM is its high fault tolerant capability. internal perturbations and load changes and the fact that designing these controllers depend on the exact machine e6mthaItnitcesr,nDaeticoenmabl eHry6b-r7i,d2C0o2n3fGerueenlcme aO,nAIlngfeorrima atics And Applied Math- model with precise parameters [1]. * Corresponding author. Therefore, Researchers had tried to employ the Artifi$ [e-mail] (N. Benayad); cial Intelligence techniques in the field of control theory [e-mail] (A. Aouiche); in order to overcome the shortness’s of classic PID and [e-mail] (A. Djeddi) PI regulators. (A.0A00o9u-i0c0h0e0);-20908060--30903022-(1N6.03B-e3n2a6y7a(dA);. 0D0j0e0d-d0i0)03-1378-7941 Fuzzy Logic proposed by Lotfi A. Zedeh in 1965 and © 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License developed later by several researchers; is one among the Attribution 4.0 International (CC BY 4.0). advanced techniques used in control engineering field for a wide range of applications from stability control of electric vehicles to Self-Tuning Controllers of induction motor drives [ 7 ]. Moreover, among all the diferent advanced regulators, Fuzzy Logic Controller (FLC) is the most simple, robust with less sensitivity for both source and load, also it can save more energy consumed by the induction motor especially during the transitional periods [ 8 ].

The designing process of (FLC) composes from three 03 main procedures; the first is fuzzification process that converts the crisp inputs into fuzzy sets. Then it comes the inference engine phase, which applies fuzzy rules base to determine the fuzzy output sets, and finally the defuzzification step, that converts the fuzzy output sets back into crisp output data.

The whole procedure of (FLC) makes the controlling decisions more flexible and human-like manner, it can handle easily the imprecise and uncertain informations witch consequently afects positively on the dynamic response of the system to be controlled (multiphase motor in this case) and overcome the shortages of PI regulators.

This paper is structured into six sections; the second section contain the dynamic model of the dual star induction motor (DSIM), the indirect field oriented control is presented in section three and fuzzy logic control technic is detailed in section four 04. While the simulation results are presented and discussed in section five 05, and finally the 6th section concludes the paper.

2. Induction Machine Modelling

The system of equations below represents the electric equations for the model of (DSIM) in the (dq) reference frame [ 9 ]: 1 − . 1 2 − . 2 1 + . 1 2 + . 2 − ( − ). = 0 + ( − ). = 0 ⎧ ⎪ 1 = .1 + ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 2 = .2 + ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨ 1 = .1 + ⎪ 2 = .2 + ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ = . + ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩ = . +

(1) Where the stators and rotor flux linkages are expressed by the system of equations bellow in the (dq) reference frame [ 9 ]: ⎧ 1 = .1 + .(1 + 2 + ) ⎪ ⎪⎪ 2 = .2 + .(1 + 2 + ) ⎪ ⎪ ⎪⎨ 1 = .1 + .(1 + 2 + ) ⎪ 2 = .2 + .(1 + 2 + ) ⎪⎪ = . + .(1 + 2 + ) ⎪ ⎪ ⎪⎩ = . + .(1 + 2 + )

(2) and electromagnetic torque can be expressed as [ 9 ]: = .

+

(3) While the expression that describes the mechanical dynamic behavior is [ 9 ]: .[ .(1+2)− .(1+2)] As it name indicates, the dual star induction motor com- Ω poses from 02 two stators spatially shifted with 30 electri- . = − − .Ω (4) cal degrees and share a common magnetic core as shown in figure1 bellow; Also, they are assumed identical in Where: all intern parameters (resistance, inductance, number of , , and are the resistances and inductances phases . . . ) with a sinusoidaly distributed windings and of the stator and rotor respectively, is the cyclic muneglected saturation for the magnetic circuit [1], [ 4 ], [ 5 ]. tual inductance between stator 1, stator 2 and rotor. 1,2, 1,2, 1,2 and 1,2 are the two 02 stators voltages and currents respectively in the (dq) reference frame; while , , and are rotor voltages and currents.

Also, we have the synchronous reference frame and rotor electrical angular speeds , With the moment of inertia, the load torque, the coeficient of viscous friction, and Ω the mechanical rotor speed.

3. Field oriented control model

The control approach discussed in this paper enables the tracking of the drive operating point to guarantee the best possible operating conditions. This control strategy is based on indirect vector control orientation which has made conceivable use of motor drives for industrial * = . . * .(1 + 2) (9) applications operates under high performance needed + [ 5 ], [ 10 ]. The system of equations (7) is composed of two terms and

A double star induction motor can be presented by it is clearly obvious they are not completely independent utilizing four 04 quadrature current components (02 for from each other and the quadrature stators currents with every stator) instead of dual three-phase currents origi- flux reference still not perfectly free to be controlled [ 11 ], nally fed to the motor. The two currents alimenting each [ 12 ]. stator are known as direct (id) and quadrature (iq), they To fix that shortness it is good idea to use the decomare in charge of creating flux and torque separately in position method to guarantee flux and torque completely motor and each one of those four currents is controlled decoupling, The system (7) will be decomposed into two with its correspondent regulator [ 10 ]. parts [ 11 ], [ 12 ]:

The orientation of the synchronously rotating frame (dq) such that the d-axis aligned along the rotor flux First Part (Linear Part). consists of introducing the vector and q-axis with with the last one equal linear stators voltages 1 , 2 , 1 and 2 to zero will eventually ensure decoupling between the which they are directly related to the stators currents torque and flux and an AC motor behavior similar to DC 1, 2, 1 and 2 respectively [ 11 ], [ 12 ]. motor [ 6 ].

When the technique of rotor field orientation applied on the (DSIM) model, we will have the following conditions [ 11 ]: ⎧ 1 ⎪⎪⎪⎪⎪⎪ 1 = .1 + . 2 ⎪⎨ 2 = .2 + .

1 ⎪⎪⎪⎪⎪⎪ 1 = .1 + . 2 ⎪⎩ 2 = .2 + .

Second part (Compensation part). Consists of intro(6) ducing the compensating stator voltages 1 , 2 , 1 and 2 which they are calculated on function of stators currents, synchronism pulsation, slip speed and the reference of rotor flux [ 11 ], [ 12 ]. ︂{ =

= 0 And the flux linkages expression will become [ 11 ]: ⎧ 1 = 1.1 + .. 2 + . ⎪ ⎪⎨ 2 = 2.2 + .. 1 + . ⎪ 1 = 1.1 + .. 2 ⎪⎩ 2 = 2.2 + .. 1 * * With: = + and: 1,2 = 1,2 + . ⎧ 1 ⎪⎪⎪⎪ 1() =.1 + 1. − ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪⎪ 2 ⎪⎪⎪⎪ 2() =.2 + 2. − ⎪ ⎪ ⎪ ⎨ ⎪⎪⎪⎪⎪ 1() =.1 + 1. 1 + ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪⎪⎪⎪⎪⎪⎪ 2() =.2 + 2. 2 + ⎪ ⎩ * .(.1 + * ) * .(.2 + * ) * .(.1 + . * .*()) * .(.2 + . * .*()) (5) (7) (10) (11) The main expression of voltages will be as follow [ 11 ]: ⎧⎪⎪⎨ 12 == ** ..((..12 ++ .. ** ..** )) ⎪ 1 = * .(.1 + * ) ⎪⎩ 2 = * .(.2 + * ) With: = and: *() = * −

Also, we will have the following expressions of the component references of slip speed and electromagnetic torque [ 4 ], [ 11 ]: * =

. ( + ). * .(1 + 2) (8)

In order to get perfect decoupling, a control loops for stators currents are added and the stator voltages are obtained at their outputs [ 12 ].

Finally, the block diagram for an indirect field oriented controller of (DSIM) is represented in “Fig. 2” above (in previous page).

Speed control of induction motors is crucial in industrial applications for precise control over rotational speed, leading to increased eficiency and performance.

Advanced AI techniques, including fuzzy logic, machine learning and deep learning algorithms, ofer numerous benefits over traditional methods, such as improved eficiency, accurate speed regulation (in terms of: rising time, settling time, overshot elimination and precision in steady-state), enhanced overall performance, fault detection and adaptability plus reducing complex systems. By optimizing energy consumption, ensuring consistent product quality, and adapting to variable load conditions, cost savings, sustainability, and enhanced productivity in industries relying on induction motors for their processes.

Speed controllers plays vital role in IRFOC, because it determines the reference torque needed to maintain the corresponding reference speed.

The dynamic model of speed control for double stator induction motor is represented by “Fig. 3” bellow [ 6 ],[ 9 ]: The closed buckle’s transfer function for speed control if By comparison, of the dominator with respect to that of a system of second order, we find [ 6 ]: ⎨⎧ = 2

2 ⎩ = . − speed control system that has two inputs and one single output. It is composed generally from three 03 main units [ 4 ], [ 8 ], [ 13 ]:

The first is fuzzification unit that includes the wise choose by an expert for the membership functions, lin(12) guistic variables and universe of discourses. For example, in our study we have decided to use triangular mfs because the subject of control (speed error) varies in range of –X to X and it is preferred in such cases to use symmetric membership function.

The second unit is fuzzy inference system; it contains (13) linguistic fuzzy base rules based on method of Mamdani, the following examples explains the logic behind selecting our fuzzy rules: ΔE NB NM NS Z PS PM PB

E

NB NB NB NB NM NS NVS

Z

NM NB NB NM NS NVS

Z PVS

NS NB NM NS NVS

Z PVS PS

Z NM NS NVS

Z PVS PS PM

PS NS NVS

Z PVS PS PM PB

PM NVS

Z PVS PS PM PB PB

PB

Z PVS

PS PM PB PB PB • If speed error is negative and speed derivative • “B”, “M” and “S” refers for Big, Medium and Small, • “Z” refers for Zero.

tively, In addition, to ensure better performance of the con- controller based on its two inputs.

Moreover, the control surface of the output U is shown

5. Simulation Results and

Interpretation

In this section, we present the simulation results and comparative analysis of speed controllers for a dual stator induction motor utilizing both Proportional-Integral (PI) and Fuzzy Logic controller (FLC). The simulations were conducted over a time span of 4 seconds for each test scenario to evaluate the controllers’ performance under various operating conditions. The primary objective of these tests is to assess and compare the efectiveness of both controllers in regulating the motor’s speed, especially in the presence of load torque variations and abrupt changes in rotor reference speed; the key metrics considered for evaluation included the rising time, settling time, overshot and steady-state error. These metrics will provide valuable insights into the controllers’ capabilities in achieving accurate and robust speed control.

5.1. Normal Conditions Test:

The first test involved running the motor under normal operating conditions, without any external disturbances or load variations. This scenario serves as the baseline for assessing the controllers’ ability to reach the nominal speed and achieve good performances especially in the transitional period.

The “fig.7” above represents the dynamic speed response of (DSIM) with both FLC and PI controllers’ in function of time. We notice that the speed curve of FLC controller has better rise and settling time compared to the green curve of PI controller; also, we noticed that the last one had a small overshot of 0.12% contrary to the intelligent controller that reached the reference speed without any influencing shortness in term of overshot or undershot (only 0.01%).

While the figure after, represents the electromagnetic torque in function of time, we notice that the curve of FLC had less amplitude of torque ripples in steady state, which minimizes the electrodynamic efect on the motor.

The third and fourth figure of rotor flux and currents in the (dq) rotating reference frame proves that the main Principe of indirect field oriented control (IFOC) is achieved successfully.

5.2. Load Torque Variation Test

In the second test, a load torque of 20 (N*m) was applied to the motor beginning at 2s until the whole remaining time. This test aimed to evaluate how well the speed controllers adapt and command the motor’s speed in the presence of sudden load charges. and 0.006s compared to 0.6 rad/s and 0.014s in the classic regulator). In addition, the torque ripples in “fig.12” were less intense in the curve of (FLC) and the decoupling Principe remained stable in “fig.13” and “fig.14”.

We conclude from this test that the intelligent controller adapts very well against the sudden load changes.

We notice in “fig.11” that the application of load torque at 2s has resulted in transitory decrease of speed. Both controllers managed to overcome the load torque but the impact in fuzzy logic controller of speed was less remarkable in both amplitude and period of drop (0.35 rad/s

5.3. Test of multiple changes in speed reference Combined with applied load torque

The third test involved a maneuver of sudden and multiple changes in speed reference with simultaneous load torque of 20 (N*m) applied beginning at 1 second, this test examine the controllers’ robustness and challenges its ability to respond promptly and maintain speed stability during multiple dynamic changes. speed reference faster in terms of rise and settling time in all cases (150 rad/s 250 rad/s and 314 rad/s), even with presence of load torque, which proves its eficiency. In addition, the electromagnetic torque ripples with (FLC) were less intense which minimizes the electrodynamic efects on the motor and extends its lifespans.

Figure 16 and 17 of rotor fluxes and currents in (dq) reference frame proves that the decoupling Principe of ifeld oriented control (FOC) is realized.

5.4. Test of Inverting rotor direction sense combined with applied load torque

In the fourth test, the machine will face a continuingly external disturbance represented in load torque of 20 N*m beginning at 1s threw the whole left time of simulation, and the rotor direction sense will get inversed exactly at 2s.

This scenario assesse the controllers’ performance and robustness in more complex and demanding condition.

During the third test, we notice that the blue curve of fuzzy logic speed controller was able to reach the

We notice in “fig.19” that the advanced controller easily managed to invert the speed rotation sense with good dynamic performance despite the presence of load torque.

Moreover, the rotor flux and currents in (dq) reference frame proves the existence of essential decoupling Principe of field oriented control (FOC).

6. Conclusion

In this paper, we have made a study about speed control for the double stator induction motor (DSIM), firstly the model of motor was presented, then we successfully managed to achieve indirect field oriented control for the machine, this method needs speed controller. This task is usually carried out using a conventional (PI) controller due to it is strong, reliable, and most importantly has reasonable price. However, unfortunately they sufer from many shortness’s especially in the transitional period. Therefore, in order to resolve it we tried to benefit from the artificial intelligence, we implemented the fuzzy logic theory to design a suficient controller. the experimental tests made with MATLAB/Simulink has proved its eficiency by achieving very good results in terms of rising time, settling time, overshot and precision compared to the classic (PI) regulator.

In addition, the (FLC) proved its robustness and superiority in every assessment where made over the traditional PI controller. These results can still be improved by integrating the advantages of fuzzy logic with artificial neural networks and use the Adaptive neuro-fuzzy inference system (ANFIS) to achieve even better results.

7. Appendices

N = 3000 RPM 2 = 3.72 Ω 2 = 0.022 = 0.0662 .2 = 50

P = 5.5 KW = 2.12 Ω = 0.006 = 0.001 = 1

PI Speed Controller Parameters Fuzzy Logic Speed Controller Parameters

= 0.01 = 0.0005 = 10 [1] E. Zaidi, K. Marouani, H. Bouadi, Speed control for multi-phase induction machine fed by multilevel converters using new neuro-fuzzy, in: Renewable Energy for Smart and Sustainable Cities: Artificial Intelligence in Renewable Energetic Systems 2, Springer, 2019, pp. 457–468.

References

[2] M. J. Zandzadeh , R. Kianinezhad , M. Saniei , Comparative analysis of space vector pwm for six-phase induction motor configurations based on commonmode voltage and current losses , Iranian Journal of Science and Technology, Transactions of Electrical Engineering 43 ( 2019 ) 897 - 908 .

[3] V. Rathore , K. Yadav , Direct torque control of asymmetrical multiphase (6-phase) induction motor using modified space vector modulation , in: Recent Advances in Power Electronics and Drives: Select Proceedings of EPREC 2020 , Springer, 2021 , pp. 511 - 516 .

[4] L. Hellali , S. Belhamdi , Speed control of doubly star induction motor (dsim) using direct field oriented control (dfoc) based on fuzzy logic controller (flc ), Advances in Modelling and analysis C 73 ( 2018 ) 128 - 136 .

[5] M. Nesri , K. Nounou , K. Marouani , A. Houari , M. F. Benkhoris , Eficiency improvement of a vectorcontrolled dual star induction machine drive system , Electrical Engineering 102 ( 2020 ) 939 - 952 .

[6] L. Youssfi , N. Benayad , A. Aouiche , A. Djeddi , Advanced speed control of induction machine based on vector contro ( 2024 ).

[7] M. Elgbaily , F. Anayi , M. Packianather , Performance improvement based torque ripple minimization for direct torque control drive fed induction motor using fuzzy logic control , in: Control, Instrumentation and Mechatronics: Theory and Practice , Springer, 2022 , pp. 416 - 428 .

[8] S. Chandrasekaran , S. Durairaj , S. Padmavathi, A performance improvement of the fuzzy controllerbased multi-level inverter-fed three-phase induction motor with enhanced time and speed of response , Journal of Electrical Engineering & Technology 16 ( 2021 ) 1131 - 1141 .

[9] Z. Tir , Y. Soufi , M. N. Hashemnia , O. P. Malik , K. Marouani , Fuzzy logic field oriented control of double star induction motor drive , Electrical Engineering 99 ( 2017 ) 495 - 503 .

[10] B. Venu Gopal , E. Shivakumar, H. Ramesh , An experimental setup for implementation of fuzzy logic control for indirect vector-controlled induction motor drive , in: Advances in Control Instrumentation Systems: Select Proceedings of CISCON 2019 , Springer, 2020 , pp. 193 - 203 .

[11] C. HADJI , Contribution à la commande robuste de la machine asynchrone à double étoile , Ph.D. thesis , Univ M'sila, 2020 .

[12] H. RAHALI , Commandes non linéaires hybrides et robustes de la machine asynchrone à double étoile «MASDE» , Ph.D. thesis , UNIVERSITE MOHAMED BOUDIAF-M'SILA , 2020 .

[13] G. Joshi , P. P. AJ , Fuzzy logic controller for indirect vector control of induction motor , in: Advances in Communication, Signal Processing, VLSI, and Embedded Systems: Select Proceedings of VSPICE 2019 , Springer, 2020 , pp. 519 - 534 .