J. Cent. South Univ. (2019) 26: 1886-1896

DOI: https://doi.org/10.1007/s11771-019-4142-3

Genetic algorithm and particle swarm optimization tuned fuzzy PID controller on direct torque control of dual star induction motor

BOUKHALFA Ghoulemallah¹, BELKACEM Sebti¹, CHIKHI Abdesselem², BENAGGOUNE Said¹

1. Faculty of Technology, Department of Electrical Engineering, University of Batna, Algeria;

2. Department of Science and Technology, Faculty of Technology, University of Batna, Algeria

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: This study presents analysis, control and comparison of three hybrid approaches for the direct torque control (DTC) of the dual star induction motor (DSIM) drive. Its objective consists of combining three different heuristic optimization techniques including PID-PSO, Fuzzy-PSO and GA-PSO to improve the DSIM speed controlled loop behavior. The GA and PSO algorithms are developed and implemented into MATLAB. As a result, fuzzy-PSO is the most appropriate scheme. The main performance of fuzzy-PSO is reducing high torque ripples, improving rise time and avoiding disturbances that affect the drive performance.

Key words: dual star induction motor drive; direct torque control; particle swarm optimization (PSO); fuzzy logic control; genetic algorithms

Cite this article as: BOUKHALFA Ghoulemallah, BELKACEM Sebti, CHIKHI Abdesselem, BENAGGOUNE Said. Genetic algorithm and particle swarm optimization tuned fuzzy PID controller on direct torque control of dual star induction motor [J]. Journal of Central South University, 2019, 26(7): 1886-1896. DOI: https://doi.org/10.1007/s11771- 019-4142-3.

1 Introduction

Nowadays, many actuators combining AC machines and static converters are showing new perspectives in the field of variable speed drive. Multiphase induction motors especially the dual star induction types are mostly used in advanced power applications [1-4]. The main superiority of these kinds of motors is [5]: higher efficiency and lower torque pulses. Vector control of the dual star induction motor (DSIM) is based on effective control of the magnetic state. However, this structure requires, in general, the installation of sensor on the shaft for the knowledge of a mechanical quantity. In addition, it remains very sensitive to machine parameters variations. However, the search for other algorithms has not ceased since and new control techniques have emerged [6-12].

Most current engineering control applications using proportional integral derivative (PID) control systems provide simpler and more efficient solutions. However, to meet the requirements of a variable speed drive, the PID controllers are poorly tuned.

Many tuning methods have been presented to remedy these problems. One of these proposed settings is the auto-adjustment of the PID controllers [13-15].

The arrival of heuristics and meta-heuristics has improved and facilitated the resolution of previously difficult or impossible to solve optimization problems [16-21]. Their general principle is to model the notions of evolution in nature as algorithms imitating natural evolution. Among them and recently, differential evolution (DE) [22], bat algorithm (BA) [23], CACO algorithm [24], hybrid GA [25], PSO [26], ant colony optimization (ACO) [27], bee colony algorithm (BC) [28, 29], imperialist competitive algorithm (IC) [30], hybrid PSO-GA [31, 32]. These methods have emerged as promising ones because of their ability to optimize in complex multimodal search spaces applied to non-differentiable functions.

The PSO is an evolutionary algorithm inspired by the social interaction of animals in nature. The particles, to evolve, are based on the imitation of the behavior of the best neighbor. Each particle is characterized by a position and speed. His experience is considered when updating his speed. Several approaches of PSO have been suggested in the literature [33]. For all these studies, the shared common feature is to avoid premature convergence to local optima.

Genetic a lgorithms (GAs) are an optimization technique that analyzes a vast research space and leads to more than one solution to the problem. In accordance with biological systems, the algorithms are based on genetic operators whose reproduction and mating lead to evolution. However, mutations explore the entire research space while avoiding premature convergence [34]. The result of the application of these three basic operations leads to the creation of new individuals whose qualities are better than their parent’s ones, and after several operations, the algorithm stops after it has reached an optimal solution.

In the past years, the fuzzy logic controller (FLC) has improved successfully as a result of complex and non-linear processes [35-37]. The design of an FLC has two disadvantages. The first is the difficulty of regulating the appropriate bases, while the second consists in selecting scale factors before to be fuzzified and after defuzzified. To overcome them, we use optimization methods to determine the gains of the fuzzy logic.

The major contribution of this work is to compare three approaches based on the meta- heuristic DTC optimization technique of the DSIM. The first technique uses the merits of PSO to judiciously adjust the scale factors of the PID, the second one associates fuzzy control as a constraint for an efficient optimization solution based on a PSO algorithm and the latest strategy combines genetic algorithms with fuzzy control for their optimization. It allows a judicious choice of a relative scaling factor for the PID controller of the DSIM.

2 Dynamic behavior of DSIM

The DSIM dynamics model is written as follows [5]:

           (1)

where the fluxes expressions are:

                (2)

The rotor speed formulation ispresented as follows:

                      (3)

The explanation of the torque T_em given below [3]:

  (4)

Figure 1 Windings diagram of DISM

3 Traditional DTC of DSIM

To overcome the problems of sensitivity to parametric variations, many control methods have been developed in which the stator flux and the electromagnetic torque are estimated from the only electrical quantities accessible to the stator, without recourse to mechanical sensors [38].

Direct torque control (DTC), based on the stator flux orientation, is one of the methods introduced by TAKAHASHI et al [38]. This type of control has been presented as an alternative to vector control by rotor flux orientation (RFO), which has the major disadvantage of being relatively sensitive to the machine parameters variations. DTC is created by this algorithm:

At each sampling instant, partition the complex plan into short time periods;

Measure the phase voltages and line currents for each time;

Estimate the electromagnetic torque, stator flux and the measurement line currents;

Introduce the difference between the reference torque and the estimated torque in a three-level hysteresis regulator, which gives the value +1 to increase the flux, -1 for reduce it and 0 to keep it constant. This choice increasing the number of levels, and this advantage reduces the switching frequency, since the dynamics of the torque is generally faster than that of the flux;

Using the switching table, the operating sequences of the drive are determined;

The division of the complex plane into six angular sectors makes it possible to determine, for each given sector, the control sequence of the switches of the inverter corresponds to different states of the variables control and according to the logic of the flux control and the torque with respect to the application of a stator voltage vector.

Figure 2 shows the illustrative block of the classical DTC of DSIM.

4 Presentation of PSO technique

Meta-heuristics are optimization methods to obtain an approximate value of the optimal solution in a reasonable time. They have objective for the resolution of a set of problems in different fields without having to modify the basic algorithm of the principle method. A particular interest is brought to the approach of optimization PSO. It is based on the “social interactions” between “agents” called “particles”, in order to achieve a given goal in a common research space where each particle has a certain capacity for memorizing and processing information. This stochastic meta-heuristic optimization was proposed in by EBERHART et al [19].

Figure 2 Classical DTC of dual star induction motor drive

Knowing that the swarm has a dimension n, that the research space is m, and since the place of the ith particle is disposed as x_i=(x_i1, x_i2, …, x_d). The best earlier locations of the ith particle are considered by EBERHART et al [19].

pbest_i=(pbest_i1, pbest_i2, …, pbest_id)           (5)

The most interesting agent of the group is gbest_d and its speed is given by:

v_i=(v_i1, v_i2, …, v_id)                        (6)

The speed and position of each agent undergoing change can be determined with the aid of the current and the distance of pbesti_d, shown on Eqs. (7) and (8) [31]:

                    (7)

i=1, 2, …, n, m=1, 2, …, d   (8)

4.1 Basic steps of PSO

The different steps of the PSO algorithm are established as follows.

First step: We define the values of the inertia factor w with C₁=C₂ representing the constants of the PSO algorithm which must optimize the three main scaling factors of the fuzzy regulator, deduced from the optimal value of the swarm research.

Second step: We have randomly chosen a search space of “50” agents by adopting (x_i1, x_i2, x_i3), (v_i1, v_i2, v_i3) as the first prediction of the speed, to reach the optimal function pbest₁.

Third step: Perform the PSO algorithm with n iterations, to find the best “gbest” position of the fitness function. Table 1 displays the parameters of the PSO.

Updated speed and position are illustrated in Figure 3.

The flowchart of the fuzzy PSO-DTC-DSIM is shown schematically in Figure 4.

Table 1 Simulation parameters of PSO algorithm

Figure 3 Representation of PSO algorithm

Figure 4 Organigram for fuzzy PSO based DTC

4.2 Performance of fitness function

The IAE criterion is widely used to evaluate the performance of the system [21]:

                          (9)

5 GA-based fuzzy-PID controller tuning

Heuristic optimization proposes a hybrid approach integrating the merits of two techniques, the FLC and the GA. GAs is an optimization approach using the basis of genetics and the principles of natural evolution: crosses, mutations, selections, etc, GAs is finest suited for complicated problems. Moreover, every agent is evaluated according to its fitness to contribute the objective function. The GA parameters are described in Table 2.

Figure 5 shows the flowchart for fuzzy GA-DTC-DSIM.

Table 2 GA setup parameters

Figure 5 Organigram for fuzzy GA-DTC-DSIM

6 Hybrid PID-PSO type FLC

The determination of the scaling factors of the FLC by PSO algorithm is presented respectively by the input and output as {e}, and {e_c} as given bellow:

                         (10)

                            (11)

Table 3 depicts the optimized PID controller by PSO algorithm.

Table 3 Results of PID controller optimized by PSO

When using fuzzy logic in a PID controller, emphasis is placed on fuzzy proportional integral action (F-PI) despite its unsatisfactory response during the transient regime. However, the action fuzzy proportional derivative (F-PD) cannot ensure a reliable steady state. Therefore, the combination of F-PI and F-PD is more convenient to create a regulator F-PID in order to obtain PID action of the regulator. It is essential to control F-PID by adding the output of the fuzzy PD controller and its integral part whose model is shown in Figure 6 and the scale factors are shown in Table 4.

The output u of the fuzzy regulator is illustrated by:

                         (12)

The value of the output according to the input is illustrated in Eq. (13):

Figure 6 Fuzzy speed controller structure associated with PSO or GA

Table 4 Results of optimization by fuzzy regulator

                       (13)

Thus, combining Eqs. (12) and (13), the output of the controller is obtained as follows:

          (14)

6.1 Fuzzification

During the fuzzification interface, we defined the triangular membership functions forms for the output and input variables (e, e_c, dT_em) as represented in Figures 7 and 8 for the proposed regulator. However, the transition from these physical quantities to linguistic variables (NL, NM, NS, ZE, PS, PM, PL) can be treated by inference rules.

Figure 7 Seven appurtenance functions of input error and derivative error

6.2 Inference and defuzzification

Defuzzification using the MIN manner to obtain the degree μ (dT_em) relative to each inference rule, so we write

During defuzzification, a value of torque is obtained by the output function as:

Figure 8 Seven appurtenance functions of output dT_em

                     (15)

6.3 Rules of inference

The fuzzy rule table represents the heart of the system and combines these rules to describe the behavior of the system:

If e is PL and e_c is PL then dT_em is PL.

We notice that the difference is very important between the speed response and its reference (e is PL), so we must reinforce the gain (dT_em is PL) so that the speed reaches its reference. The inference rules are given in Table 5.

Table 5 Inference rules

7 Simulation and analysis

To have a more appreciation of the results obtained through the different approaches PID-PSO, fuzzy-PSO and fuzzy-GA, it is necessary to make a comparison of the static and dynamic characteristics of the three control techniques under the same operating conditions (references, disturbance loads, …) and in the same simulation configuration, then make a choice of the type of control according to the desired application. We performed a simulation under MATLAB/ SIMULINK environment. Table 6 gives the rated values of the DSIM. The scheme of the simulated techniques is illustrated in Figure 9. The simulation results obtained are given through the following figures.

Table 6 DSIM parameters[5]

In Figure 10, the speeds controlled by the three controllers are presented. When the DSIM is operated at 100 rad/s under a load torque of 14 N·m at t=0.6 s. We can view that the use of fuzzy-PSO controller gives good performances, very rapid rejection of the applied load torque, small settling time, without overshoot and with reduced steady state error, contrary to a Fuzzy-GA controller where the speed has suffered a slight rejection which is more visible with a hybrid controller PID-PSO.

For a more comprehensive analysis, one compares through Table 7 the results obtained for the different controllers according to the different errors ISE (integral squared error), integral absolute error (IAE) and integral time squared error (ITSE). We conclude that the fuzzy-PSO approach provides good performance.

Figure 11 illustrates the electromagnetic torque response of the DSIM by the proposed three methods. The technical DTC-PID suffers from two major drawbacks which are the static error and exaggerated fluctuations. Though, Fuzzy-PSO brings the necessary correction to the operation of the system. Nevertheless, the fuzzy-GA is less satisfactory.

Figure 9 Illustrative diagram of proposed GA or PSO based DTC for speed controller of DSIM

Figure 10 Simulation results for speed regulation of three controllers

Table 7 Performance comparison of three controllers

Figure 11 Comparison of torque results for proposed three approaches

Figure 12 illustrates the sinusoidal shape of the currents and the important role played by the fuzzy-PSO by significantly reducing the current ripple relative to the other controllers. The results reveal that the fuzzy-PSO algorithm is best suited for PID gaintuning.

We notice that the stator flux trajectories for the three controllers shown in the Figure 13 are superimposed, however, the blurred PSO shows less fluctuations.

The variation of the speed error (fitness) is summarized in Figures 14 and 15.It is worthy to mention that, fuzzy-PSO method outperforms fuzzy-GA method (see Table 7).

Figure 12 Phase current in stator winding (1) of three controllers

Figure 13 Stator flux trajectory in stator (1) of three controllers

Figure 14 Speed error (fitness function) of fuzzy-GA (Table 4)

8 Conclusions

In this study, we have presented a strategy for optimizing the operation of direct torque control of the DSIM. The latter is based on the substitution of the classical PID speed controller by different recent heuristic optimization techniques which are the association of fuzzy logic with genetic algorithms fuzzy-GA and the combination of fuzzy logic with particle swarm optimization fuzzy-PSO. The most efficient training of our system was obtained according to the results of simulations with the conjunction of fuzzy logic with particle swarm optimization regulator. Indeed, the latter has shown its ability to significantly reduce torque ripples and provide drive by eliminating the steady state error.

Figure 15 Speed error (fitness function) of Fuzzy-PSO (Table 3)

Nomenclature

V_ds1, V_qs1, V_ds2,V_qs2

Statorique voltages

I_ds1, I_qs1, I_ds2, I_qs2

Statoriquecurrents

I_dr, I_qr

Rotoriquecurrents

φ_ds1, φ_qs1, φ_ds2

Stator flux vectors

φ_dr, φ_qr

Rotor fluxes

T_em

Electromagnetic moment

T_r

Torque load

Ω_r

Mechanical speed

ω_r

Rotor angular speed

ω_s

Stator angular speed

n

Number of particles

d

Dimension indices

v^t_i,m

Speed of particle

w

Weight factor ofinertia

rand ()

Random number

pbest_i

Best previous position

gbest

Best particle

C₁, C₂

Acceleration constant

NL

Negative large

NM

Negative medium

NS

Negative small

ZE

Zero equal

PS

Positive small

PM

Positive medium

PL

Positive large

ISE

Integral squared error

IAE

Integral absolute Error

ITSE

Integral time squared error

PID

Proportional integral derivative

FLC

Fuzzy logic control

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(Edited by HE Yun-bin)

中文导读

基于遗传算法和粒子群优化的模糊PID控制器在双星感应电机直接转矩控制中的应用

摘要：本文对双星感应电动机直接转矩控制的三种混合方法进行了分析、控制和比较，目的是将PID-PSO、模糊PSO和GA-PSO三种不同的启发式优化技术相结合，以改善DSIM速度控制回路的性能。将遗传算法和粒子群优化算法应用于MATLAB，得到模糊粒子群算法是最合适的方案。模糊粒子群算法的主要性能是减小了大扭矩波动，加快了上升时间，避免了影响驱动性能的干扰。

关键词：双星感应电机驱动；直接转矩控制；粒子群优化(PSO)；模糊逻辑控制；遗传算法

Foundation item: Project supported by Faculty of Technology, Department of Electrical Engineering, University of Batna, Algeria

Received date: 2018-02-14; Accepted date: 2018-10-31

Corresponding author: BOUKHALFA Ghoulemallah, PhD Candidate; Tel: +213-66-8888620; E-mail: ghoulem1987@gmail.com; ORCID: 0000-0002-9427-9983