Imperialist Competitive Algorithm (ICA)-Optimized Fuzzy Logic Speed Control of DTC Induction Motor

Drives Mohammad Reza Ghadiri

Electrical Engineering Department Islamic Azad University, Qazvin Branch

Qazvin, Iran m.r.ghadiri@qiau.ac.ir

S.Hamid Shahalami Electrical Engineering Department

Islamic Azad University, Qazvin Branch Qazvin, Iran

shahalami@qiau.ac.ir

Mahdi Tahbaz Electrical Engineering Department

Islamic Azad University, Qazvin Branch Qazvin, Iran

m.tahbaz@qiau.ac.ir

Mansor Khaksaran Electrical Engineering Department

Islamic Azad University, Qazvin Branch Qazvin, Iran

m. khaksaran@qiau.ac.ir

Abstract— In this paper, Imperialist Competitive Algorithm (ICA) is employed to optimize Fuzzy Logic Controller (FLC) as the speed controller of an Induction Motor (IM) in the Direct Torque Control (DTC) method. In order to achieve better control performance, the ICA optimizes the parameters of the FLC consisting of input and output membership functions (MFs) and normalization factors. Since, the proposed FLC speed controller has a few rules, it requires less computation. Simulation results show that optimizing the fuzzy logic speed controller of IM through ICA is the better performance compared to FLC-based drive.

Keywords- Induction Motor (IM); Direct Torque Controller (DTC); Fuzzy Logic Controller (FLC); Imperialist Competitive Algorithm (ICA)

I. INTRODUCTION Induction motors (IMs) are widely applied in the industry

because they are cheap, simple, robust, and easy to maintain [1]. Since, the IMs are nonlinear systems, the time-varying parameters cause an extra complexity during the controller design [2]. For such these reasons, some methods are applied to get better control performance for IM. Two significant control strategies for IM drives are Field–Oriented Control (FOC) [3, 4] and Direct Torque Control (DTC) [5, 6].

DTC method was proposed in 1980s [7]. DTC is a suitable alternative control strategy for the FOC because the complicated coordinate transformation is not required and also, the current control loop and Pulse Width Modulation (PWM) modulator are not needed [6, 8]. DTC is based on controlling directly the stator flux and the torque by selecting the proper switching states [9].

Also, this method has advantages such as robustness against machine parameter variations, accurate torque response in steady state and transient operation condition, and simplicity in implementation [10, 11].

Generally, conventional controllers like PI, PID are extensively used in the DTC as the speed controller [8]. But, the performance of conventional controllers is dependent on the exact machine model and accurate gains [12]. Also, the factors such as motor saturation, load disturbance, and thermal change machine parameters. These nonlinearities disrupt the performance of the conventional controllers [8].

To overcome these problems, advantage can be made of artificial intelligence techniques such as Neural Networks (NN), Genetic Algorithm (GA), and Fuzzy Logic Controller (FLC) [13-18].

FLC is an intelligent but computationally simple controller. The advantages of FLC over conventional controllers are that it is able to handle nonlinearities and that its design is independent of system parameters [19, 20].

However, there is no systematic procedure for designing and tuning the FLC. It is takes time and requires the designer to be particularly experienced and skillful for the tedious task of fuzzy tuning [21, 22].

In this paper, a computationally simple FLC is proposed in order to control the speed of an IM in the DTC method. To avoid the lengthy computation and to achieve a better control performance, the Imperialist Competitive Algorithm (ICA) is used to tune the parameters of the FLC, which are MFs and normalization factors. Also presented is assessment of simulation results obtained using the proposed technique in comparison with FLC-based drive.

II. MODEL OF IM The electrical dynamics of an IM in the synchronous

coordinate system (d- and q-axis) can be given in matrix form as follow [23]:

VV00 (1)

The mechanical equation of IM can be expressed as: T (2)

where ω , ω electrical and rotor angular frequency ω slip angular frequency (ω ω ) i , i d- and q-axis stator current i , i d- and q-axis rotor current v , v d- and q-axis stator voltage R , R stator and rotor resistant L , L , L stator, rotor, and mutual inductance p laplace operator P number of poles T electromagnetic torque T load torque J inertia moment B friction coefficient

III. DIRECT TORQUE CONTROL (DTC) STRATEGY Fig. 1 shows the block diagram of IM drive system based

on DTC scheme. As shown in this figure, DTC scheme constitutes of flux and torque estimation block, flux and torque hysteresis comparators, switching table, and Voltage Source Inverter (VSI) [23].

In this system, hysteresis comparators are applied to calculate the stator flux error (∆ ) and electromagnetic torque error (∆ . According to these errors and the position of the stator flux appropriate voltage vector can be selected based on table I. The switching table generates pulses , , and to control the power switches in the Voltage Source Inverter (VSI). VSI generates the eight available space voltage vectors in order to keep the stator flux and electromagnetic torque within the limits of two hysteresis bands.

Also, the equation of stator flux in d-q coordinate system can be estimated by V (3) V (4)

where and are d- and q-axis stator flux, respectively.

Figure 1. Block diagram of DTC

TABLE I. DTC SWITCHIG TABLE

Flux Sector Torque

1 2 3 4 5 6

∆ =1

∆ =1 ∆ =0 ∆ =-1

∆ =0

∆ =1 ∆ =0 ∆ =-1

The equation of electromagnetic torque can be obtained as: (5)

IV. THE PROPOSED CONTROL SCHEME The schematic representation of the proposed controller is

shown in Fig. 2. This figure gives the way the ICA is applied to optimize the proposed FLC speed control of the IM using DTC method. As it is illustrated in the figure the ICA is utilized to optimize the parameters of controllers so as to satisfy the design criteria. As it can be seen, the reference electromagnetic torque T is generated by the ICA-optimized FLC.

Figure 2. DTC of an IM using ICA-FLC

A. FLC Fig. 3 depicts proposed configuration of the FLC that is

applied as speed controller. The inputs of FLC are the error signal e and the derivative of the error signal e. Then these inputs have to be fuzzified. The fuzzy control algorithm includes a set of fuzzy control rules that are related through the concept of MFs and the composition rule of inference. Fuzzy control sets have to be defuzzified because the plant cannot respond directly to these control sets. On the other hand, the controller output ΔU is summed or integrated in order to generate the actual control signal U as torque . Moreover, input variables of FLC have to be normalized over a range specified for MFs and also, output variable of FLC has to be normalized over a range specified for plant. Therefore, the gains , ∆ , and ∆ are applied as normalization factors. An appropriate normalization has a direct impact on efficiency of the controller [24, 25].

The performance of a FLC depends on the control rules, MFs, and normalization factors. To account for this, the optimization algorithm ICA is utilized to optimize the MFs and the normalization factors.

Figure 3. Block diagram of FLC

B. Imperialist Competitive Algorithm (ICA) ICA is a recently introduced optimization algorithm.

Optimization through this algorithm has basis on the concept of imperialistic competition. Fig. 4 portrays the flowchart of ICA. ICA takes advantage of the assimilation policy adopted by imperialistic countries since the 19th century. According to this policy, the imperialists seek to improve the economical, cultural, and political situation of their respective colonies so as to win their loyalty. This theory uses the term “empire” to refer an imperialist and its colonies. The power of an empire depends on the power of its imperialist and its colonies. In imperialistic competitions, weaker imperialists lose their colonies to more powerful empires. After dividing all colonies among imperialists and creating the initial empires, these colonies start moving toward their relevant imperialist state. This movement is a simple model of assimilation policy that was pursued by some imperialist states.

Figure 4. Flowchart of Imperialist Competitive Algorithm

Figure 5. Motion of colonies toward their relevant imperialist

Fig. 5 shows the movement of a colony towards the imperialist.

In this movement, x and θ are random numbers with uniform distribution as shown in equations (4) and (5), respectively, and d is the distance between a colony and its imperialist. x ~ U 0, β d (4) θ ~ U γ, γ (5)

where β and γ are arbitrary numbers that modify the area around the imperialist which colonies randomly search.

The weak empires, once they lose all their colonies, will be the colonies of other empires. Eventually, all the weak empires will collapse, leaving only one powerful empire. Fig. 5 portrays the flowchart of ICA [26].

V. OPTIMIZING FLC USING ICA Table II shows the nine fuzzy if-then rules of FLC speed

controller. To design such a controller, the input variables of speed error e and derivative of speed error Δe are considered to have three MFs: N (Negative), ZE (Zero), and P (Positive) as shown in Fig. 6 and Fig. 7, respectively. The MFs of the output are NB (Negative Big), N, ZE, P, and PB (Positive Big) are shown in Fig. 8.

TABLE II. DECISION TABLE OF FLC

P

ZE

N

eΔ

Output e

P N NBN

P ZE N ZE

PB ZE N P

To apply ICA to optimize the FLC, the parameters of the FLC in the ICA are coded in the form of the array country. In addition, a cost function is defined so as to minimize it with the purpose of satisfying the design criteria.

To optimize the parameters of FLC using ICA, the MFs of the input variable of speed error e specified by means of three points P1, P2, and P3 as shown in Fig. 6. Also, for the MFs of the input variable of derivative of speed error Δe, three points P4, P5, and P6 are used as shown in Fig. 7. Similarly, the MFs of the output variable specified by means of five points P7, P8, P9, P10, and P11 as shown in Fig. 8. Finally, the normalization factors , ∆ , and ∆ can be represented by means of three points P12, P13, and P14.

Figure 6. MFs of speed error before optimization

Figure 7. MFs of derivative of speed error before optimization

Figure 8. MFs of output before optimization

Hence, the problem of finding the parameters of the FLC consisting of MFs and normalization factors is reduced to the problem of determining 14 points (Pi, 1 ≤ i ≤14).The 14 points are put together to form the array country.

Country = [P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13,

P14] The performance of the designed FLC speed controller is

evaluated on the basis of the transient and steady-state responses. In line with this, Settling Time (ts) and Overshoot (Ov) along with the Integral of Absolute Error (IAE) are used to evaluate the designed controller. A good controller causes the output to have low values for ts, Ov, and IAE. By considering a combination of all criteria, the multi-objective design problem is reduced to a problem of a single objective [27]. Therefore the cost function is chosen as follow:

Cost Function = (6) where are the weights which must be determined by the designer. The ICA looks for the best array Country (i.e. the array of Pi's) with a minimal cost function.

In ICA, the initial number of colonies is set at 150, eighteen of which are chosen as the initial imperialists. Also β and γ are set at 2 and 0.6 (Rad) respectively. The maximum number of iterations the ICA put 80.

VI. SIMULATION RESULTS The inputs and output fuzzy MFs optimized through ICA

are shown in Figures 9 to 11.

Figure 9. MFs of speed error after optimization

Figure 10. MFs of derivative of speed error after optimization

Figure 11. MFs of the output after optimization

For assessment purposes, the proposed ICA-optimized FLC is compared with the FLC in MATLAB toolbox. The

performance of the motor was evaluated for a period of 1s against a reference speed of 150 rad/s.

In addition, the validity of the system has been examined with load torque change TL=12 N.m at t=0.7s. The speed response of the FLC and the ICA-optimized FLC are plotted as shown in Fig. 12 and Fig. 13, respectively.

Figure 12. Speed response of IM using FLC

Figure 13. Speed response of IM using ICA-optimized FLC

Also, the torque response of the FLC and the ICA-optimized FLC are plotted as shown in Fig. 14 and Fig. 15, respectively. As shown in these figures the ICA-optimized FLC showed a better performance compare to fuzzy logic speed controller.

Figure 14. Torque response of IM using FLC

Figure 15. Torque response of IM using ICA-optimized FLC

The control criteria of the speed responses of the FLC and the ICA-optimized FLC are compared in Table III. The control criteria used were Settling Time (ts), Rise Time (tr), Overshoot (Ov), Integral of Absolute Error (IAE), and Cost Function (CF). It is obvious from this table that the fuzzy logic speed controller of IM optimized by ICA has a better performance in all criteria than the FLC-based drive.

TABLE III. SIMULATION PERFORMANCE COMPARISON

CF IAE Ov(%) tr(s) ts(s) Criteria

Method

1.02 1.11 0 0.52 0.18 FLC

1 0.62 0 0.2 0.09 ICA-FLC

VII. CONCLUSION In this paper, a fuzzy logic speed controller optimization

using ICA was proposed for an IM in the DTC method. In order to prove the superiority of the proposed controller scheme, a performance comparison with FLC has also been provided. Comparative simulation results indicate that the ICA-optimized FLC speed controller is more efficient than the FLC-based drive.

APPENDIX The specifications of the IM chosen for simulation are as

follows:

Electrical power: 7HP Stator voltage: 460V Rated speed: 1780Rpm Frequency: 60HZ Number of Poles: 4 Stator resistant: 1.8Ω Rotor resistant: 1.34Ω Stator inductance: 0.0014H Rotor inductance: 0.0012H Mutual inductance: 0.369H Moment of inertia: 0.025Kg. m Coefficient of friction: 0.02N. m. s

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