In the context of induction motor control, there are various control strategies used to separately control torque and flux. One common approach is known as Field-Oriented Control (FOC). This technique involves transforming the three-phase currents and voltages into a rotating reference frame, commonly referred to as the “ dq ” frame. In this frame, the torque/speed and flux components are decoupled, allowing for independent control, by doing so, the motor’s speed can be regulated accura tely and maintain a constant flux which is crucial to ensure optimal motor performance and efficiency. The research focused on studying and simulating a field-oriented control system using fuzzy control techniques for an induction motor. The aim was to address the issue of parameter variations, particularly the change in rotor resistance during motor operation, which causes the control system to deviate from the desired direction. This deviation implies to an increase in the magnetic flux value, specifically the flux component on the q-axis. By employing fuzzy logic techniques to regulate flux vector’s components in the dq frame, this problem was successfully resolved, ensuring that the magnetic flux value remains within the nominal limits. To enhance the control system’s performance, response speed, and efficiency of the motor, sliding mode controllers were implemented to regulate the current in the inner loop. The simulation results demonstrated the proficiency of the proposed methodology.
An electrical motor transforms electrical input into mechanical output, providing energy to diverse kinds of loads. AC motors are classified into synchronous, induction, and specialized motors. Among them, three-phase induction motors find extensive application in industrial settings, due to their self-starting capability. The designation of a three-phase induction motor indicates that the rotor current is induced by magnetic fields rather than direct electrical connections. This design allows for the production of a rotating magnetic field, eliminating the need for electrical connections to the rotor.
Induction motors have many advantages, the most important of which are [
• Self-starting.
• Explosion-proof (because to the lack of spark-producing brushes, commutators, or slip rings).
• Robust in its design.
• Inexpensive.
• Easier in maintaining up.
There are various methods available for controlling induction motors. Among these methods, V/f control stands as the oldest technique. However, this approach demonstrates limited dynamic performance due to its inability to achieve synchronized control over the amplitude, frequency, and phase of the stator current in induction motor drives. An alternative choice is vector control, widely recognized as field-oriented control [FOC], which offers superior dynamic performance despite the added complexities compared to scalar control systems. [
FOC control of an induction motor can be likened to regulating a DC motor with separate excitation. In this comparison, the voltage vector applied to the motor is divided into two components. The first component is responsible for governing the magnetic flux, while the second component is responsible for controlling the motor’s torque, thereby enabling adjustments to its speed.
Here, great importance should be given to the transition from a reference frame with three axes (abc) to a reference frame with only two axes (d, q). The rotation speed of the two axes must be calculated correctly in order to obtain the three components of the voltage vector applied to the motor for the sake of achieve robust dynamic performance and stability of the motor while maintaining at the appropriate flux value.
The main objective of using induction motor control systems, in addition to regulating the speed, is to maintain a constant value of the magnetic flux in the air gap, which allows the possibility of applying the full load of the machine on the one hand, and the absence of magnetic saturation on the other hand.
The importance of the research is in presenting an advanced driving system using Fuzzy logic technique, in which the rotor flux vector is regulated directly, as this contributes to reducing the effect of changing the rotor resistance value, which causes magnetic saturation. In the proposed drive system, the electric angular velocity (the voltage-frequency value (ws)) is treated as a third control signal in addition to the two components of the voltage vector (Vd, Vq), where (ws) is the control effort for regulate the flux on q-axis. Also, a sliding mode technique was used to regulate currents in inner loop for the sake of enhancing the performance and stability of the motor despite the presence of external disturbances or change in parameter values.
The design of vector control for induction motor utilizing different PI controllers was described in depth in [
In [
The results of simulations and tests on a squirrel cage induction motor showed the viability and efficacy of the suggested course of action in regulating the speed and overcoming the load torque, as well as regulating the magnetic flux with a small error value when there is a change in the motor parameters (rotor resistance).
A hybrid PI-Fuzzy controller was used in [
Direct Field Oriented Control to control the speed was discussed in [
The estimation of the rotor flux was conducted utilizing an open-loop model, and the rotor flux angle needed to calculate the angle of the voltage vector supplied to the motor was then calculated.
The purpose of paper [
In the previously mentioned studies, the focus was on simulating the motor’s vector control system and addressing the issue of pulse width modulation, or estimating the rotor flux to complete the control system, while other research focused on improving the time response characteristics in terms of rise and stability time or clarifying the effect of the control system on the harmonic distortion content, without giving due importance to the issue of the occurrence of magnetic saturation when the value of the rotor resistance changes when applying the traditional winding vector control system, or improving the motor performance by adding an internal control loop to regulate the currents.
The research aims to develop a simplified vector control system for an induction motor based on the hybrid fuzzy PI logic technique for the sake of Enhancing the performance and stability of the motor despite the presence of external disturbances or change in the parameter values.
This issue can be done by providing a special controller to obtain the voltage-frequency value (ws) and dispensing with the open-loop model used in traditional vector control for its computation, which tested by using MATLAB program [License No: 40692431].
This is expected to achieve greater motor performance and stability while maintaining rotor flux within the nominal values, also to have the ability to simplify the flux estimation process without the need for highly complex estimators.
The mathematical representation of a 3-phase induction motor in a dq frame is [
d i s d d t = − a 5 i s d + ω s i s q + a 3 Φ r d + a 4 ω Φ r q + b v s d (1)
d i s q d t = − ω s i s d − a 5 i s q − a 4 ω Φ r d + a 3 Φ r q + b v s q (2)
d Φ r d d t = a 2 i s d − a 1 Φ r d + ( ω s − ω ) Φ r q (3)
d Φ r q d t = a 2 i s q − ( ω s − ω ) Φ r d − a 1 Φ r q (4)
d ω d t = p J ( G Φ r d i s q − G Φ r q i s d − T d ) − f J ω (5)
where:
a 1 = R r L r , a 2 = L m R r L r , a 3 = L m R r σ L s L r 2 , a 4 = L m σ L s L r , a 5 = L r 2 R s + L m 2 R r σ L s L r 2 , b = 1 σ L s , G = P L m L r , σ = 1 − L m 2 L s L r , ω = P Ω
where:
ω s : synchronous speed
ω : electric speed
Ω: mechanical speed
v s q , v s d : Elements of stator voltage vector
i s q , i s d : Elements of stator current vector
Φ r q , Φ r d : Elements of rotor flux vector
P: pole pairs
L m : magnetizing inductance
L s : stator inductance
L r : rotor inductance
J: rotor inertia
f: friction coefficient
T d : load torque.
The primary goal of FOC methodology is to make the relationship between the electromagnetic torque and flux linear, as is the case in DC motors with separate excitation, in order to open up the potential of decoupling flux control from torque\speed control.
In order to achieve decoupling, the rotor flux vector is aligned with the d-axis, thereby ensuring that the rotor flux component Qrq remains consistently zero. This approach allows for independent control and manipulation of the rotor flux and the torque components in the motor, then [
Φ _ r = Φ r d (6)
Φ r q = 0 (7)
d Φ r q d t = 0 (8)
Based on the above, two outer control loops are used to implement the FOC scheme: one controls the rotor flux, and the other the motor’s angular velocity. The motor speed is measured and the slip angular frequency is computed, then the sum of them determines the angle of the applied voltage vector.
PI controller is a simply and easily, it is the most frequently used in driving the electrical machine and control systems. However, they have certain drawbacks include their sensitivity to changing system parameters, which can lead to unpredictable results. For the application of these controls, it is necessary to have a linearized model of the system.
Depending on Equations (1) and (3), it is possible, using Laplace transforms, to represent the induction motor model according to the d-axis, as in
So, the controlling of Φrd is done through Vsd and the controlling of the speed is done through Vsq.
Relationship (4) can be set up to be as follows in order to obtain ω s :
ω s = ω + i s q a 2 / Φ r d (9)
Fuzzy logic is a subdivision of artificial intelligence that emulates human thinking and endeavors to express thoughts using linguistic terms to facilitate decision-making. Its objective is to develop intelligent technologies that closely resemble human cognition.
In our system we added a special controller to enhance a simplified vector control system for an induction motor based on the hybrid fuzzy PI logic technique in order to improve the performance and stability of the motor despite the presence of external disturbances or change in the parameter values, rather than open-loop model closed-loop model used to obtain the voltage-frequency value (ws) as shows in
The fuzzy logic controller is distinguished from other controllers by the ability to deal with the non-linear system, and its performance is less affected by the differences in the system parameters. Moreover, fuzzy techniques use a grammar base that is designed by taking advantage of qualitative aspects of the system and expert knowledge. These features eliminate the need for an accurate mathematical model of the studied system [
| Δe/e | NB | NS | Z | PS | PB |
|---|---|---|---|---|---|
| NB | NB | NB | NB | NS | Z |
| NS | NB | NB | NS | Z | PS |
| Z | NB | NS | Z | PS | PB |
| PS | NS | Z | PS | PB | PB |
| PB | Z | PS | PB | PB | PB |
| Δe/e | NB | NS | Z | PS | PB |
|---|---|---|---|---|---|
| NB | PB | PB | PB | PM | Z |
| NS | PB | PS | PS | Z | NS |
| Z | PB | PS | Z | NS | NB |
| PS | PS | Z | NS | NM | NB |
| PB | Z | NS | NB | NB | NB |
The sliding mode was studied for the first time in the former Soviet Union, it is characterized by its durability, its ability to resist changes in machine parameters, its relative ease of application, and its high dynamic performance [
- regulation isd current
The switching surface of isd current-regulating loop can be written as:
S i d = I s d − r e f − I s d (10)
By deriving the previous relationship, we find:
S ˙ i d = d I s d − r e f d t − d I s d d t (11)
Based on
S ˙ i d = d I s d − r e f d t + a 5 i s d − b V s d (12)
In order for the current to be compelled to move toward the sliding surface, S ˙ i d must be compensated for by an appropriate law of attraction:
S ˙ i d = − K 1 sig S i d − Q 1 S i d (13)
By equating relations (18) and (14), we get:
V s d = 1 b ( d I s d − r e f d t + a 5 i s d + K 1 sig S i d + Q 1 S i d ) (14)
- regulation isq current
The switching surface of isq current-regulating loop can be written as:
S i q = I s q − r e f − I s q (15)
By deriving the previous relationship, we find:
S ˙ i q = d I s q − r e f d t − d I s q d t (16)
Based on
S ˙ i q = d I s q − r e f d t + a 5 i s q − b V s q (17)
In order for the current to be compelled to move toward the sliding surface, S ˙ i d must be compensated for by an appropriate law of attraction:
S ˙ i q = − K 2 sig S i q − Q 2 S i q (18)
By equating relations (18) and (14), we get:
V s q = 1 b ( d I s q − r e f d t + a 5 i s q + K 2 sig S i q + Q 2 S i q ) (19)
The motor’s rotational velocity is controlled at 282.7 rad/sec, and a load torque is imposed after 1 second, while maintaining the motor parameters at their designated values.
In order to regulate the two components of the rotor magnetic flux,
So, we can say here that both the traditional (PI controllers) and proposed (Fuzzy SMC) control methodologies achieve the desired goal in terms of regulating the speed at the required reference value and the flux at the nominal value in the steady state, with the proposed methodology superior in transient case, taking into account that the comparison was made for nominal values of motor’s parameters, but what if the values of these parameters change, this is what will be discussed in the following paragraph.
In the next paragraph, the effectiveness of the control systems is retested for an increase in the rotor resistance value of 40% and an increase in the stator resistance value of 20%.
In order to regulate the two components of the magnetic flux of the rotor,
magnetic saturation, an increase in thermal heating and a decrease in motor efficiency.
As a result of the previous discussion, it can be said that the proposed methodology achieves the desired goal, as the speed is precisely regulated while the flux values are maintained within the nominal limits despite the change in the motor parameter values.
In the realm of electrical motor control, achieving precise regulation of torque
and flux is imperative for optimal performance. This study delves into the application of a field-oriented control system for an induction motor, integrating fuzzy control techniques. The primary focus lies in addressing the formidable challenge posed by parameter variations, particularly fluctuations in rotor resistance during motor operation. Such variations can lead to deviations in the control system, manifesting as undesired increases in magnetic flux, with the flux component on the q-axis deviating from its intended zero value.
To surmount this challenge, the research employs fuzzy logic techniques to regulate the components of the flux vector in the dq frame. This nuanced approach proves to be highly effective in mitigating deviations and ensuring that the magnetic flux remains within the specified nominal values. Beyond addressing parameter variations, the study also seeks to enhance the overall performance of the control system, emphasizing response speed and motor efficiency, especially in transient scenarios.
To bolster the control system’s robustness and adaptability, sliding mode controllers are introduced to govern the current in the inner loop of the control system. This methodology, combining fuzzy control for flux regulation and sliding mode controllers for inner loop current regulation, is meticulously simulated to validate its effectiveness. The results of these simulations unequivocally demonstrate the prowess of this proposed control strategy in achieving precise and stable motor control, showcasing improved performance and efficiency in dynamic operating conditions.
In a future work, we can focus on studying and improving the pulse width modulation phase using direct drive methods, or go towards estimating the rotor flux using sliding mode observe (SMO), as this is necessary to complement the vector control system.
The authors declare no conflicts of interest regarding the publication of this paper.
Tahhan, A. and Temurtaş, F. (2024) Enhanced Fuzzy Logic Control Model and Sliding Mode Based on Field Oriented Control of Induction Motor. World Journal of Engineering and Technology, 12, 65-79. https://doi.org/10.4236/wjet.2024.121004