Jamal A. ALI1,2, Mahammad A. HANNAN1 and Azah MOHAMED1 Dept. of Electrical, Electronic & System Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia (1) General company of electricity production middle region, Ministry of electricity, Iraq (2) doi:10.15199/48.2016.08.54

Gravitational search optimization approach to improve fuzzy logic speed controller for induction motor drive Abstract. Fuzzy logic controller (FLC) is very useful for controlling speed and torque variables in the three-phase induction motor (TIM) operation. However, the conventional FLC has the exhaustive traditional trial and error procedure in obtaining membership functions (MFs). This paper presents an adaptive FLC design technique for TIM using a gravitational search algorithm (GSA) optimization technique. This technique provides the numerical values to limit the error and change in error of the MFs based on the evaluation results of the objective function formulated by the GSA. The root mean square error (RMSE) of the speed response is used as a fitness function. An optimal GSA- based FLC (GSAF) fitness function is also employed to tune and minimize the RMSE for improving the performance of the TIM in terms of changes speed and torque. Space vector pulse width modulation (SVPWM) technique is utilized to generate signals via voltage/frequency control strategy for variable frequency inverter. Results obtained from the GSAF are compared with those obtained through particle swarm optimization (PSO) to validate the developed controller. The robustness of the GSAF is better than that of the PSO controller in all tested cases in terms of damping capability and transient response under different load and speed. Streszczenie. W artykule zaprezentowano adaptacyjny sterownik typu fuzzy logic przeznaczony do trójfazowego silnika indukcyjnego wykorzystujący algorytm optymalizacyjny badania grawitacyjnego. Jako funkcję fitness użyto błąd rms odpowiedzi prędkości. Do zasilania silnika wykorzystano metodę modulacji szerokości impulsu. Optymalizacja typu grawitacyjne badanie jako metoda poprawy jakości sterownika fuzzy logic zastosowanego do silnika indukcyjnego

Keywords: Fuzzy logic control, gravitational search algorithm, particle swarm optimization, induction motor, inverter. Słowa kluczowe: sterowanie fuzzy logic, algorytm grawitacyjnego badania, silnik indukcyjny

Introduction TIMs supplied by a pulse-width modulation (PWM) voltage source inverter are widely utilized for industrial applications because of their simple structure, easy maintenance, ruggedness, low cost, robustness, and high degree of reliability [1]. Control of a TIM dynamical system is nonlinear and difficult to explain theoretically due to TIM drive systems are exposed to sudden changes in mechanical load or speed variation in most applications. The variable voltage and frequency of TIMs are generally employed to control the speed and torque of the TIM drives [2]. One of these methods is voltage/frequency (V/f) scalar control strategy applied to TIM drives to develop the performance and dynamic response of the TIM [3]. Many PWM techniques are employed to control three-phase inverters. SVPWM method is one of the best methods because of its capability to minimize harmonic distortion SVPWM control is utilized in TIMs to specify each switching vector as a point in complex space[1,4]. Several TIM speed controllers have been studied recently. For example, the proportional-integral-derivative (PID) controller is widely utilized in industrial applications due to its easy design and structure, but it has required a for the mathematical model and also to trial and error to find the PI controller parameters for designing [5]. Fuzzy logic controllers (FLCs) are preferred over traditional controllers because the former is less dependent on the mathematical model and system parameters [6]. Artificial neural networks [7], [8] ANFIS used as controller on the speed and torque in the vector controller. However, the above mentioned controllers encounter problems because of their huge data requirement and long training and learning time. Many researchers have proven that FLC controller due to that it is simple to implement; it does not require a mathematical model of the controlled system [6,9]. FLC performance improvement depends on some limitations which is the MFs. Given the symmetric changes in a system, selecting the correct limits of MFs this is difficult. Fixed membership functions are generally insufficient for investigating optimal TIM performance because of the tuning limits of these functions [6]. In [10], the speed

200

controller design procedure is developed based on PSO algorithm for TIM. In this study, the GSA optimization is developed to improve the performance of the TIM speed controller by tuning the free parameters and selecting the best MFs limits. The results obtained from the developed speed controller and the PSO optimization algorithm are compared in terms of the control process and robustness under the condition of sudden change in speed and mechanical load. High-performance membership functions are also obtained by minimizing the error function using the root mean square error (RMSE) of the system. Moreover, used the SVPWM switching algorithm is employed to develop a GSA optimization-based FLC speed controller for TIM drives. FLC based speeed Controller The FLC speed controller is very popular because of its capability to nonlinear controller systems, simplicity, and low implementation cost; it does not rely on a mathematical model [9]. This section explains the FLC structure, GSA algorithm, and GSA-based FLC control and its operational flow. An FLC speed controller was designed as a modified speed controller to improve the controller performance in TIM via new optimization techniques. The controller trains all the sudden changes that occur in TIM as speed and mechanical load to achieve strong control. Speed error ω n and speed change of error Δe n e n ω∗ n e n e n 1 in the developed fuzzy speed controller are the input variables. Desired slip speed ω is the output variable. The FLC structure design consists of a fuzzifier, knowledge base rule and fuzzy sets, an inference engine, and a defuzzifier [1]. According to fuzzy set theory, fuzzification transforms the input values into conversely fuzzy values. The numbers of fuzzy sets are specified to calculate the speed of the fuzzy speed controller. In this study, the fuzzy set is represented for each input and output as left 3 (L3), left 2 (L2), left 1 (L1), center (C), right 1 (R1), right 2 (R2) and right 3 (R3) [1].

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The fuzzy rule consists of the linguistic term if–then and output membership functions requiring to be operated by the fuzzy rule relation between the output and input. For example, the relations between input variables e and Δe and output variable ω were defined in [1]. The details of the 49 rules are shown in Table 1. Table 1. Fuzzy rules of the TIM speed controller ∆ L3 L2 L1 C R1 L3 L3 L3 L3 L3 L2 L2 L3 L3 L3 L2 L1 L1 L3 L3 L2 L1 C C L3 L2 L1 C R1 R1 L2 L1 C R1 R2 R2 L1 C R1 R2 R3 R3 C R1 R2 R3 R3

R2 L1 C R1 R2 R3 R3 R3

R3 C R1 R2 R3 R3 R3 R3

The inference fuzzy output variables were converted into crisp values in the defuzzification stage. The crisp value was calculated as the center of gravity (COG) of the membership functions as follows [11].

1



∑ ∑



Gravitational search algorithm Many optimization methods have been developed to improve system performance. Examples of these methods include genetic algorithm, simulated annealing, ant colony search algorithm, PSO, and GSA [13]. GSA optimization allows for the achievement of desired goals according to several modern optimizations [13-15]. In this research, GSA optimization technique was utilized depending on the law of gravity and mass interactions introduced in [14]. The GSA operating principle is based on the laws of motion and the law of Newtonian gravity.

2





where F is the value of the gravitational force; G is the constant value of the gravitational; M is the mass of the first particles and M is the mass of the second particles; and R is the distance between the first and second particles. According to Newton’s second law, acceleration a is directly proportional to force and inversely proportional to mass M [13] as follows:

3





4

1

,

Fig. 1 shows the effect of forces between the mass with other masses and the process of extracting the net force and acceleration. GSA-based optimal fuzzy speed controller The numerical values of the membership functions are difficult to determine in FLC design. Therefore, in this study, the fuzzy membership functions were fixed with the parameters tuned by GSA to obtain the optimal numerical values of the membership function limits. The detail of the operating flow of the GSA-based optimal fuzzy speed controller is shown in Fig. 2. The positions of the N number of the initialization agents are initialized (i.e., the masses are randomly selected within the given search interval).

5

,……,

,……,

,

1,2, … ,



where X is the position of i-th agent in the d-th dimension and n is the space dimension. RMSE was employed to compute the fitness objective for each agent and determine the best and the worst fit for each iteration. The computation, which aims to minimize problems and determine the masses of each agent, is as follows [15]:

1

6

7



∈ ,…,

8



∈ ,…,











9 10



∑

where e ω . ω is the error and n is the number of samples. Gravitational constant G at iteration t was computed as follows: ⁄

11



The total force computation in different directions in the i-th agent, the acceleration and velocity computation, and the position of the agents in the next iteration are as follows:



12



13 ∈

Fig. 1. Mass effect with other masses.

Gravitational constant G t was calculated as the initial value of the gravitational constant, G t , multiplied by the ratio between the initial time t and actual time t [13] as follows:



14 15 16

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,



1 1

1

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The GSA parameters for all test cases were selected, as illustrated in Table 2. The models stated above were implemented in the GSA-based optimal fuzzy speed controller, as shown in the flow chart in Fig. 2. Table 2. GSA parameters Parameters Gravitational constant, G User specified constant, α Number of agents, N Maximum number of iterations

Values 100 20 30 200

START

Results and discussion The results were obtained by implementing the control scheme to validate the proposed GSAF optimization method and the performance of the overall system. The scalar-controlled TIM drive with the proposed fuzzy speed controller was simulated according to the TIM data shown in Table 1. The SVPWM voltage-source inverter is a six-IGBT diode bridge inverter with a switching frequency of 20 kHz. The parameters of the fuzzy speed controller were tuned with the methods of GSA for optimal fuzzy GSAF and PSO for optimal fuzzy (PSOF) for the purpose of comparison and to determine the GSA optimization robustness.

Initialize values for the position of parameters for the membership functions X with N agent and d dimension by using Eq. (5) Yes

No Evaluate the fitness for each agent using RMSE Eq.(6) Update G, best and Worst of the population by using Eq.s (7), (8) and (11). Calculate the masses (M) for each agent by using Eq.s (9) and (10) Calculate the force and total force by using (12) and (13) Calculate the acceleration for each agent by using (14) Evaluate the velocity by using Eq. (15)

Parameters specified No

Agent ≤ N

Yes Run the simulation Defining input variables (error and change of error) to fuzzy speed controller

0.0667

GSA PSO

0.0664

Fuzzification Control Rules Calculate µe and µce

0.0659

RMSE

K ≤ Iteration

peak voltage for SVPWM. The GSA–Mamdani fuzzy controller was used for the speed controller system for simplicity. The task of this controller is to allow the actual speed to track the commanded or reference speed. The speed controller provides the required slip speed to reach the reference speed (synchronous speed). The slip speed is then added to the feedback signal is the rotor speed to produce the required frequency to the inverter then to TIM. A V/f relationship is required to fix the machine at its rated flux linkage.

Calculate the crisp value using Eq.(1)

0.0654

Agent = Agent +1

0.0649

Update the position by using Eq. (16) K=K+1

0.0644 0

END

25

50

75

Fig. 2. GSA-based optimal fuzzy speed controller flow diagram.

125

150

175

200 Fig.

4.

Fitness function curve.

Output

GSA-based Fuzzy Speed Controller Simulation Model The developed GSAF speed controller simulation model for the TIM drive model is shown in Fig. 3. SVPWM switching technique was utilized to control the TIM drive with the V/f control fuzzy speed controller. The TIM model is a stationary reference frame in which rotor speed is measured depending on the feedback signal. Therefore, the sensor speed needs to be measured. All possible sudden changes in the speeds and mechanical torques were applied in the simulation model to generate a robust TIM controller. The developed controller was also utilized to tune the parameters and determine the best values for the membership function parameters through GSA optimization.

100

Iteration

6 4 2 0 -2 -4 -6 2

1

0

de

-1

-2

-2

-1

0

1

2

e

Fig. 5. Slip speed output surface



Fig. 3. block diagram of the proposed GSA-based fuzzy speed controller for TIM.

As shown in Fig. 3, SVPWM technique receives three and produces switching input values ( V , V , and V signals for the IGBT of the inverter to provide three-phase AC voltages to TIM. The V/f control strategy generates the

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Fig. 4 shows the relationship between the flatness function curve and the number of iterations performed by the two optimization methods (GSA and PSO); the same number of population was applied in both methods. The access of the GSA curve to the target is faster than that of the PSO curve. The simulation results are presented in two test cases to determine the effectiveness and robustness of the proposed fuzzy speed controller. The two test such as speed constant with torque variation and torque constant with speed variation are considered. Fig. 5 shows the relationship between two inputs are error, change of error with GSAF speed controller output.

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Speed constant with mechanical load variation The first test for TIM involves constant speed and mechanical torque variations. This test aims to determine the system performance and robustness. The performance of the proposed controller at full rotor speed with changes in mechanical torque was evaluated. The results are shown in Fig. 6 as indicated by the speed response and its zoomed locations in Fig. 6a, the estimated speed is consistent with the actual speed with good accuracy. In terms of the steady-state error between the reference and actual speeds and damping minimization, the GSAF controller is better than the PSOF controller. Fig. 6b shows the stator currents; the constant frequency and variable peak values were changed by the variation in load duration because of fixed speed and mechanical load variation. Table 3 shows the mechanical load, which is varing according to to specific time durations, and the overshoot (%) values. The overshoot has been calculated by the following define OS % 100%. As can be shown in

PSOF

GSAF

1000

Mech. load

40 30

750

20

500

Time (sec)

10

250

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Time (sec)

Stator currents (A)

(b)12

(b)12 Stator currents (A)

50 800 40 700 600 30 500 PSOF GSAF Mech. load 400 20 300 200 10 100 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Mechanical load (N.m)

1250

50

Mechanical load (N.m)

Speed (rpm)

(a)1600 1500

(b)900 Speed (rpm)

Table 3, the GSAF has been succeed to achieve best result compared with the PSOF according to the overshoot values.

Table 3. Change in mechanical load when full speed constant Overshoot (%) at FullPeriod Mechanical load speed (sec) (N.m) GSAF PSOF 0 – 0.1 No-load 5.594 7.342 0.1 – 0.2 6.8 2.237 2.477 0.2 – 0.3 13.5 2.167 2.376 0.3 – 0.4 20.2 1.958 2.097 0.4 – 0.5 27 1.818 1.958 0.5 – 0.6 20.2 2.797 3.076 0.6 – 0.7 13.5 2.937 3.286 0.7 – 0.8 6.8 3.076 3.496 0.8 – 0.9 No-load 3.216 3.636 0.9 – 1 6.8 2.307 2.447 1 – 1.1 No-load 3.216 3.636 1.1 – 1.2 13.5 5.664 6.363 1.2 – 1.3 No-load 6.433 7.342 1.3 – 1.4 20.2 5.524 5.734 1.4 – 1.5 No-load 11.258 12.027 1.5 – 1.6 27 7.412 9.230

10 5 0

10 5 0 -5

-10 -12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-5

Time (sec)

-10 -12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Time (sec)

1 1.1 1.2 1.3 1.4 1.5 1.6

Fig. 7. Half-speed constant with torque variations: (a) speed response and (b) stator currents. 1

1.1 1.2 1.3 1.4 1.5 1.6

Fig. 6. Full-speed constant with torque variations: (a) speed response and (b) stator currents.

The speed of the TIM response under the condition of changing mechanical torque in the second stage at the same mechanical loading is shown in Fig. 7. Fig. 7a shows the motor response speed in the GSAF and PSOF control systems. The obtained results show that the GSAF control system is better in controlling motor speed than the PSOF control system. In Fig. 7b, the stator currents varied because of the high speed under variation in mechanical torque; this condition also caused a change in the peak of current waves and fixed frequency. Table 4 shows the mechanical load, which is varing according to to specific time durations, and the overshoot (%) values. Again the GSAF has been achive the lowest overshoot values compare with PSOF which lead to beat response.

Table 4. Change in mechanical load when half speed constant Mechanical Overshoot (%) at half-Speed Period load (sec) GSAF PSOF (N.m) 0 – 0.1 No-load 3.076 4.615 0.1 – 0.2 6.8 4.616 5.034 0.2 – 0.3 13.5 4.195 4.615 0.3 – 0.4 20.2 3.776 4.195 0.4 – 0.5 27 3.496 3.636 0.5 – 0.6 20.2 5.454 6.153 0.6 – 0.7 13.5 5.874 6.713 0.7 – 0.8 6.8 6.153 6.993 0.8 – 0.9 No-load 6.433 7.412 0.9 – 1 6.8 4.615 5.174 1 – 1.1 No-load 6.433 7.412 1.1 – 1.2 13.5 9.230 10.069 1.2 – 1.3 No-load 13.146 14.825 1.3 – 1.4 20.2 13.846 15.244 1.4 – 1.5 No-load 23.076 24.615 1.5 – 1.6 27 18.461 19.580

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Table 5. Change in reference speed Ref. speed Period (sec) Period (sec) (rpm) 0 – 0.2 1430 1.2 – 1.4 0.2 – 0.4 1073 1.4 – 1.6 0.4 – 0.6 715 1.6 – 1.8 0.6 – 0.8 358 1.8 – 2 0.8 – 1 715 2 – 2.2 1 – 1.2 1073 -

(a)

0 0 0 0 0

Ref. speed (rpm) 1430 715 1073 358 715 -

Speed (rpm)

1700 1500

PSOF GSAF

1250 1000 750 500 250 0 0

0.2

0.4

0.6

0.8

1

1.2

Time (sec)

1.4

1.6

1.8

2

2.2

1.6

1.8

2

2.2

0 0 0 0 0

(b)15 10 5 0 -5

-15 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (sec)

Fig. 9. Full-load constant with speed variations: (a) speed response, (b) stator currents.

0

(a)

PSOF GSAF

1500

1250

1250

Speed (rpm)

1000

1000

750 500 250 0 0

0 0 0 0 0

(a)

-10

0

1700 1500

Speed (rpm)

The second test was performed under 100% of the nominal torque for the speed variation in the TIM drives (Fig. 9). Fig. 9a shows the speed response and stabilization after each change in speed to demonstrate the controller performance. The settling time and damping of the GSAF controller is better than that of the PSOF controller. Fig. 9b shows the peak stator currents, which are nearly 11.5 A.

Stator currents (A)

Torque constant with speed variation The second test involves increasing or decreasing the reference speed with the torque constant. This case study aims to evaluate the performance of the proposed fuzzy speed controller and estimate the reference speed variation with the torque constant of TIM controlled by the V/f ratio. The performance of the TIM drive during the step response change was determined under the effect of the load torque constant being applied to the TIM rotor shaft. The torque constant was obtained from many cases. In the first case, the no-load condition was applied on TIM with the speed variable in short times (Fig. 7). The best or robust structure generally keeps the TIM performance unchanged. This robust structure shows the speed responses of GSAF and PSOF control with optimal speed change. The performance of TIM changed only a few times (Table 4). GSAF control achieved better results than PSOF control by minimizing the overshoot, settling time, steady-state error, and damping ratio after change and exhibiting rapid stability after each speed change (Fig. 7a). Fig. 7b shows that the stator current signal at the start-up of TIM involved a high-current pull and then stable signals. It also shows that the changes in frequency with the peak value were fixed in the duration of sudden changes in speed according to the system requirements because speed change control corresponds a change in supply frequency.

0.2

0.4

0.6

0.8

1

1.2

Time (sec)

1.4

1.6

1.8

2

750 500

0.4

0.5

0.6

0.7

0.8

Ref. w PSOF GSAF 0.9 1

0.4

0.5

0.6

0.7

0.8

0.9

250

2.2

0 0

0

0.1

0.2

0.3

Time (sec)

0 04

0 41 0 42

06

(b)10

0 62

Stator currents (A)

Stator currents (A)

(b) 10 7.5 5 2.5 0 -5

0 -5

-7.5

-7.5

-10 0

0.2

0.4

0.6

0.8

1

1.2

Time (sec)

1.4

1.6

1.8

2

2.2

Fig. 8. No-load constant with speed variations: (a) speed response, (b) stator currents.

204

5 2.5

-2.5

-2.5

-10 0

7.5

0.1

0.2

0.3

Time (sec)

1

Fig. 10. No-load constant with speed variations: (a) speed response, (b) stator currents.

The tracking performance of the TIM drive was evaluated in terms of speed response to a ramp speed command (Fig. 10a). In many cases, the reference speed of

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the ramp response of TIM initially increased and then decreased for a certain duration under the condition of fixed torque. The reference speed increased from 715 rpm to 1430 rpm in 0.1 s and then decreased to 715 rpm at 0.2 s. These increase and decrease in speed continued until 0.9 s and then became stable at 1430 rpm. Fig. 10 shows the scenario where no load torque was applied to TIM. In Fig. 10a, the obtained results reveal the good performance of TIM in terms of ramp speed response. The comparison of GSAF and PSOF controllers shows that the GSAF controller achieved better results in terms of minimizing overshoot, settling time, and steady-state error and exhibiting rapid stability after a change in speed. The stator currents and the effect of ramp response on TIM produced the same result because of the changes in frequency and the fixed peak value of speed change (Fig. 10b). Fig. 11a shows the ramp speed response and mechanical torque constant at 100% nominal load. The difference between rotor and reference speeds is very small, which indicates that the GSAF controller is better than the PSOF controller because of the former’s proximity to the reference speed. Fig. 11b shows how the stator current changes with the change in speed at fixed peak values.

controller is better than that of the PSOF controller in terms of robustness, damping capability, and improvement of the transient responses. The developed GSAF controller reduced the maximum overshoot, steady state error, and settling time of the TIM. Acknowledgment The authors are grateful to Ministry of Science, Technology and Innovation, Malaysia for supporting this research financially under grant 06-01-02-SF1060. Authors Jamal A. Ali is a PhD student in the Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia (UKM), E-mail:[email protected]. Mahammad A. Hannan is a professor in the Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia (UKM), E-mail: [email protected]. Azah Mohamed is a professor in the Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia (UKM), E-mail: [email protected].

REFERENCES [1]

0

(a)

[2]

0 0

1500

[3]

Speed (rpm)

1250 1000

[4]

750 500 250 0 0

0.1

0.2

0.3

0.4

0.5

0.6

Time (sec)

0.7

0.8

Ref. w PSOF GSAF 0.9 1

Stator currents (A)

(b)15

[5]

[6] [7]

10 5

[8]

0

[9]

-5

-10 -15 0

[10] 0.1

0.2

0.3

0.4

0.5

0.6

Time (sec)

0.7

0.8

0.9

1

Fig. 11. Full-load constant with speed variations: (a) speed response, (b) stator currents.

[11]

Conclusion This paper presented an FLC-based optimization approach for TIM using the GSA. The proposed method is formulated to automatically change the MF of the FLC used in the speed controller. To effectively tune the MFs of the proposed FLC used in the TIM applications, a suitable objective function is developed to minimize the RMSE of the speed response. The developed GSAF optimization method is helped to avoid the traditional trial and error procedure in obtaining MFs. The TIM drive is modelled with SVPWM technique and V/f control at different speeds. The performances of GSAF and PSOF were compared. The obtained results confirm that the GSAF controller increases the robustness of the controller and the speed of the rotor responses under the conditions of load and speed variations. Moreover, the results show that the GSAF

[12]

[13] [14] [15]

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