Development of ANFIS-based reference flux estimator and FGS-tuned speed controller for DTC of induction motor

Thispaperdiscussesaboutself-regulatingthereferencefluxininductionmotor(IM)directtorquecontrol(DTC)drivebyfuzzylogic.Self-regulationisimprovedbyusing“ArtificialNeuralNetwork (ANN)”and“AdaptiveNetworkBasedFuzzyInferenceSystem(ANFIS)”basedreferencefluxesti-mators.Furthermore,PIspeedcontrollerisinvestigatedtodeveloptheperformanceofthedrive. TwodifferentPIspeedcontrollertuningstrategies,manualandFuzzyGainScheduling(FGS),arecomparedforloadtorquedisturbance.TheresultsclearlyshowthatthemodifiedDTCofIMwith “ANFIS-basedreferencefluxestimatorandFGS-tunedPIspeedcontroller”ismostsuitablefortorqueripplereductionandspeedcontrol.


Introduction
Induction motors (IMs) are extensively used in industry due to their cost-effectiveness, reliability and robustness to load variations [1][2][3][4][5].The field-oriented control (FOC) is applied to regulate the IM like a DC Motor.FOC became complicated due to the involvement of Concordia transformation, current regulator and pulse width modulation signal generator [5].In the late 1980s, M. Depenbrock, Takahashi and T. Noguchi introduced a new concept of IM mechanism called direct torque control (DTC) [6,7].It is simple in structure and avoids coordinate transformation and current regulator.It is robust to the variations of machine parameters.DTC directly controls the torque and stator flux of the IM by adjusting the inverter switching signals.The inverter switching signals are taken from a predefined look-up table.The look-up table was created by the output of the three-and two-level comparators using hysteresis loop, stator flux position [8].
Many researchers have tried to involve artificial intelligence (AI) techniques to modernize the DTC.In DTC, the AI techniques have been applied for generating switching signals to voltage source inverter.The AI techniques like ANN, fuzzy and neuro-fuzzy can also be applied to hysteresis comparator, reference flux estimator and PI speed controller [9][10][11][12].Increasing the sector division in the locus of the flux [13] is also tried.
Control algorithms have been developed by the authors [14,15] for computing the stator flux reference by command torque to reduce the ripples in torque.But these control algorithms are based on mathematical approximations relating the stator flux reference value and the command torque.The stator flux reference value is computed based on command torque by using fuzzy logic [16].The estimated flux of stator is named as the modified reference flux.The fuzzy logic controller inputs are error in torque, stator flux reference value and the output is the modified reference flux.Still, the stator flux reference value and the modified reference flux membership functions are not distributed symmetrically and continuously.Hence, the solution obtained may not be global.
The speed control of IM with DTC is normally by a PI speed controller [17][18].A neuro-fuzzy controller (NFC) based on IM speed control is used [19][20][21][22] to replace the conventional PI speed controller [23].NFC uses the benefits of both fuzzy as well as neural network.The PI speed controller can be optimized in DTC using adaptive heuristic search algorithms like genetic algorithm (GA) and particle swarm optimization (PSO) [24][25].The constant gain values obtained may not provide optimum for all changes in system conditions.Adjusting the PI speed controller gain values by an adaptive mechanism for fuzzy inference is presented as Fuzzy Gain Scheduling (FGS) [26][27][28].The adaptation is based on error in speed and derivative of error in speed.The error in speed and derivative of error in speed membership functions were divided into seven membership functions but the output has only two membership functions.This yields almost the same values of controller gain even for large changes in speed error [26][27].Hence, the fine-tuned controller gain values are not obtained.The reference flux value is not modified according to loading conditions by the researchers [20][21][22][23][24][25][26][27], whereas it is maintained constant from no load to full load.
In this research work, the major contributions are as follows

Modelling of induction machine and DTC strategy
The basic theory of DTC, shown in Figure 1, is to control directly the stator flux and electromagnetic torque of IM.This is done by applying the suitable voltage vector from the inverter to the motor.The voltage vectors are designated from a standard look-up table (Table 1).The voltage vector rotates the stator flux and produces the required electromagnetic torque in the IM [1].During this operation, stator flux and electromagnetic torque magnitude of the motor are confined using a predefined hysteresis band.The stationary reference frame modelling of IM is done by converting the threephase quantities (V a , V b and V c ) into two-phase, dqaxis quantities (V ds , V qs ) using Clarke's transformation [2][3][4][5].
The induction machine [4,5], dynamic machine model developed in stationary reference frame, establishes  2) α( 3) α( 4) α( 5) α( 6) the relation between voltages and currents in matrix form using equivalent circuit of induction machine as where s is the Laplacian operator.V ds and V qs are the stator dq-axis voltage components.The stator and rotor resistances are referred as R s and R r respectively.Stator, rotor and mutual inductances are referred as L s , L r and L m , respectively.By using Equation (1), the stator and rotor current components for dq-axis i ds , i qs , i dr and i qr can be calculated.The corresponding flux components ds , qs , dr and qr are given by Equations (2) to (5) [5].
The actual torque (Te), stator flux ( s), stator flux angle (α) and actual speed (ω r ) are developed using Equations ( 6) to (9) [5].The torque component is estimated from The IM actual speed (ω r ) in Figure 1 is calculated using where T L is load torque and J represents the inertia.
For the stator flux ( s), The calculated stator flux angle (α) is given by ( 9), The reference torque (T*) is calculated by PI speed controller with input as speed error (ω * − ω r ).The difference between reference torque (T*) and actual electromagnetic torque (Te) is obtained from Equation (6) and applied to the three-level torque comparator in Figure 1 [5][6][7].Sector number is calculated by using the stator flux angle (α) [5].The angle of stator flux (α) is separated into six sectors as −30°to 30°as sector 1, 30°to 90°as sector 2 and similarly till sector 6 as −90°to −30°.
The DTC controls the triggering signals to the voltage source inverter by the outputs from the three-level torque hysteresis comparator (dTe), two-level flux hysteresis comparator (dψs) and sector estimator.Based on the output, the triggering signals to the voltage source inverter are selected from a standard look-up table [5].Due to the hysteresis comparators, the triggering signals not only depend on the amplitude but also on the direction of flux and torque.In this paper, soft computing techniques are applied to reference flux estimator and PI speed controller for better performance of DTC.The usual reference flux estimator is replaced by fuzzy, ANN-and ANFIS-based reference flux estimators.The PI speed controller is tuned using manual and FGS methods.Thus, by using soft computing methods, modified reference flux estimator and PI speed controller are established as shown in Figure 2 for DTC of IM.

Reference flux estimator
In general, IMs are always operated at rated flux to meet the maximum load torque and also during starting conditions.According to Equations ( 2) and ( 3), the stator flux value will change proportional to voltage vector applied.

Fixed reference flux estimator
Normally for DTC, the reference flux is estimated from the reference flux estimator in Figure 1.From the IM characteristics [2] for flux, it is perceived that the motor speed upto rated value operates in constant flux region.Hence, the reference flux estimator shown in Figure 1 gives constant reference flux till the rated speed and after that it transfers to field weakening region.Operating the motor always at constant reference flux is not a suitable idea especially under light load and no load conditions.
In light load conditions, constant flux causes more core loss and poor efficiency [14].In DTC, the amplitude of flux in terms of torque is generally given as The above equation is simple but it does not include the power dissipation of the drive.

Fuzzy-based reference flux estimator
The torque ripple is minimized by optimizing the reference flux estimator using fuzzy logic controller as shown in Figure 3.The inputs to the fuzzy logic controller are [16] torque error (T* − Te) and the reference flux ( * ) from the reference flux estimator.The output is the correction in reference flux ( ψ * ) required for modified reference flux (ψ * m ).The FLC membership functions for both input and output are presented in Figures 4(a-c), respectively.
The response of the torque error (T* − Te) of the system, when tried with three membership functions, is very slow.The slow response in three membership functions-based fuzzy is due to the wide range of torque error (T* − Te).This keeps the slope of the membership functions smaller and therefore the system response is very slow.To overcome this issue, in this paper, six membership functions-based fuzzy is used.The torque error variation (T* − Te) during starting, load changes and steady state vary between [−100, 100], [−28, 28] and [−3, 3], respectively.Due to this reason, the membership functions are not regular.Though the membership functions are not regular, the total degree of membership functions for any input value over the universe is one (i.e.symmetrical membership functions are maintained).Since the range for torque error (T* − Te) during starting, load changes and steady state are not in uniform pattern and regular placement of membership functions cannot be used.
The computation inside fuzzy for a three-member ship will be faster than six-membership functions, but it fails to provide required control on all the three stages namely starting, load changes and steady state.
When the number of membership functions is more than six, a large change in output is observed for small change in input.Hence for stable performance,  2 and * is decided by fuzzy inference [15][16].
The triangular and trapezoidal membership functions are chosen for computational simplicity and easy overlapping.The solution offered by symmetrical membership functions is globally applicable, not local.

ANN-based reference flux estimator
The fuzzy logic-based reference flux estimator provides better response than the conventional reference flux estimator.For further improvement, ANN-based reference flux estimator is developed by collecting data from Fuzzy-based reference flux estimator and trained using backpropagation algorithm.Like Fuzzy, the proposed ANN has two inputs and single output.The inputs are torque error (T* − Te) and reference flux ( * * ).The output is correction in reference flux ( * ).Totally 33,408 input-output data are collected for supervised learning.The backpropagation algorithm provides desired convergence characteristics with required goal for a two-layer architecture with 10 neurons in hidden layer.Log-sigmoid and tan-sigmoid activation functions are used for the hidden and output layers, respectively.The Fuzzy-based reference flux estimator explained in Section 3.2 is replaced by the trained ANN to test its performance.

ANFIS-based reference flux estimator
ANFIS provides training of data based on a suitable mixture of ANN and fuzzy logic.Since the fuzzy logic is not completely adaptive, to optimize the response, the membership functions and the rule base of the fuzzy logic have to be tuned.This requires a tedious trial and error procedure.Therefore, fuzzy logic may not be enough to give proper results.The initial structure of ANFIS is built by knowledge base from fuzzy logic and then that structure is improved by neural network.The five-layer ANFIS structure performs normalization of inputs, fuzzification, rule base evaluation and defuzzification.It provides a transparent model, in which a neural network is used to design a fuzzy inference system.
Hence, if the input-output data, input membership functions and rule base are available for a fuzzy system, then neural network training can be used for the adjustment of membership functions and rule base.Due to this transparency, the effects of various weight values with torque error (T* − Te) and reference flux ( * * ) are used to find optimal weights for minimal torque error.ANFIS makes an intelligent choice of antecedent and consequent parameters for torque error (T* − Te) and reference flux ( * * ) membership functions.The adaptive nature of ANFIS incorporates various parameters over a wide range of operating conditions.Therefore, in this paper, the hybrid formulation of Fuzzy and ANN as ANFIS is used to get better system response when compared to fuzzy and ANN alone [19].ANFIS structure with the Sugeno model is trained with 18 rules.Here, ANFIS provides reference flux to the DTC as given in Figure 3 ANFIS structure is composed of a five-layer feed forward neural network as in Figure 5.The gradient descent and least squares estimator [19] are combined in the proposed network.The structure consists of functional blocks as rule base, database, decisionmaking unit, an interface for fuzzification and a defuzzification interface by using five network layers [20][21][22].The proposed ANFIS has two variable inputs namely torque error (T* − Te) and the reference flux ( * ) from reference flux estimator.The output of the ANFIS is the correction required in reference flux ( * ).In the first layer, (T* − Te) and ( * ) are multiplied by the corresponding weights and are mapped using membership functions [12].The second layer is for estimating the input weights for minimum error with firing strength of the rules as, where μ i A1 (T * − Te) and μ i A2 (ψ * ) are the degree of membership function for torque error and reference flux, respectively.The third layer is for normalization of weights.The normalized value of firing strength is given as The fourth layer is for de-fuzzification.The relationship between the input membership functions {μ i A1 (T * − Te), μ i A2 (ψ * )} and the output (O 4 ) can be defined as, where p i , q i and r i are the node consequent parameters and x = μ i A1 (T * − Te) and y = μ i A2 (ψ * ) are inputs.The fifth layer is the weighted output summation of layer 4. The output layer is given as ANFIS is developed by collecting 10,004 data from the fuzzy-based reference flux estimator in this work.Initially, the same membership functions from Figure 4(a,b) are given as input membership functions for ANFIS.The data are loaded in the ANFIS editor and the structure shown in Figure 5 is created.
No clustering methods are used during training of ANFIS.Instead of clustering method, grid partitioning method is used for training the ANFIS.The number of nodes is determined based on fuzzy-based reference flux estimator.The network is trained for 100 epochs in the backpropagation algorithm.Then the trained ANFIS is loaded in the system and tested.Membership functions of the universe of torque error (T* − Te) and reference flux ( * ) are self-tuned to provide the better performance.

Tuning of PI controller
In DTC, the torque reference is calculated from the speed PI controller as shown in Figure 1.The speed PI controller gain values tuned manually by trial and error method are of fixed values.The values are neither optimum nor adaptive.Hence, fuzzy logic is applied to schedule the PI speed controller gain values adaptively.

Manual tuned PI speed controller
In manual tuning, the proportional gain Kp is acting as a multiplying factor with speed error (ω* − ω r ).If the gain value is large, the actual speed (ω r ) of the system will reach the reference speed (ω*) closely.But for larger values of proportional gain, the oscillations are more.The speed PI controller integral part determines the error under the curve.Hence, the integral part of PI speed controller is eliminated using the steady state error.Initially, Ki is made equal to zero and Kp value is increased till the actual speed (ω r ) oscillates like quarter-amplitude decay around the reference speed (ω*).Then, Ki is increased meticulously to adjust the steady state error (23).The Kp and Ki values are finetuned together to get optimum response.The system is subjected to step load disturbance for tuning.

Fuzzy gain scheduling for speed PI controller
The continuous changes in system parameters and the non-linear effective circumstances make the PI speed controller with fixed gain values incapable of offering essential control.The fuzzy logic approach is capable of handling the changes in parameter and mathematical models are not counted [26][27].The block diagram of the FGS is given in Figure 6.FGS control schemes offer interpolation between the tuning tables based on the instantaneous system conditions.
Equations ( 15) and ( 16) give the mathematical concept of FGS, where K p 1 and K i 1 are the adaptive gain values, which are varying as per the system condition.
K PFGS and K IFGS are the gain values suggested by FGS.The inputs to the FGS are error in speed (ω* − ω r ) and derivative of error in speed (ω* − ω r )' .The universe of discourse of speed error is normalized from 0 to 1 and derivative of error in speed is normalized from −1 to 1.The normalization is performed in FGS using scaling factor as the largest value and no scaling factor for the output.The number of fuzzy sets used for speed error as well as time derivative of speed error is seven.The (ω* − ω r ) and (ω* − ω r )' are fuzzified using triangular and trapezoidal membership functions as shown in Figure 7. Linguistic variables of the input and output membership functions are VVL = Very very low, VL = very low, L = low, M = medium, H = High, VH = very high and VVH = Very very high.The rule base is given in Table 3 [28].The output range for the proportional gain is from 0 to 80 and for integral gain is from 0 to 0.75.

Simulation results
The conventional DTC scheme given in Figure 1 is established in MATLAB/Simulink ® environment.The developed scheme is computer-generated with a 2.2 kW IM.The parameters of the IM are given in the Appendix.The starting of the motor is with no load to a reference speed of 149.67 rad/s from t = 0 s to t = 0.5 s.The effect of load disturbance is observed with a sudden load of 3.65 Nm applied at 0.5 s to the motor and then another step load of 10.95 Nm applied at 1.0 s.After that, at 1.5 s, 7.3 Nm load is removed from the motor.The timing diagram for load variations are chosen based on Uddin [20] and Hafeez [21].Uddin has analysed the system for 1.0 s with 3 HP machine and Hafeez has simulated for 0.7 s with 50-75% load variation at 0.3 s.The performance of the DTC is upgraded in the following five control strategies, as shown in Figure 2.
• Conventional DTC with fixed reference flux estimator and manual tuned speed PI controller (Fixed-Manual).The PI speed controller is tuned manually by trial and error method as given in Section 4.1, and the gain values are shown in Table 4.
The gain values given in Table 4 are fixed.In order to make the controller to be adaptive for the system condition variations, an FGS-tuned PI speed controller is proposed in Section 4.2.FGS gives variable gain PI speed controller in order to be robust against parameter variations and load disturbances.

Speed response
The DTC drive has started under no load condition for a reference speed of 149.67 rad/s till t = 0.5 s. Figure 8 shows the speed response of different control strategies for load disturbance.Figure 8 (a-c) show the zoom-in view during adding and removal of loads.The combined response for all the control strategies is shown in Figure 8(d).The responses show that the conventional DTC with fixed reference flux estimator and modified DTC with fuzzy-based reference flux estimator perform slowly to overcome the disturbance rejection.However, the "modified DTC with ANFIS-based reference flux estimator and FGS-tuned PI speed controller" performs with quick load disturbance rejection than the other control strategies.Though load disturbance rejection is fast, still there is a small steady state error even in ANFIS-based control strategy.
The speed response of DTC IM during starting and loading conditions are analysed.Figure 9 shows the speed response of five control strategies for load variations.In Figure 9, the fixed reference flux estimator has low settling time during no load whereas the fuzzy, ANN and ANFIS take some time to adapt to system conditions.After that (0.32 s), for all other load variations, the ANFIS performs better for transient as well as steady-state conditions than fixed and fuzzy control strategies.This is validated using performance indices.
The starting speed responses alone are given in Figure 10 from t = 0.15 s to t = 0.4 s.The "conventional DTC with fixed reference flux estimator" and "modified DTC with fuzzy-based reference flux estimator" reach reference speed faster than the other two ANFIS-based control strategies.The "modified DTC with ANN-based reference flux estimator" reaches the reference speed slower than all the control strategies.

Torque response
The torque response characteristics for no load, load disturbance and steady state of DTC drive are given in Figure 11.The transient period of ANFIS-based control strategies is slightly larger than fixed and fuzzybased control strategies.The transient response of ANN-based control strategy is poor than ANFIS control strategy.The similar behaviour is observed for speed response also as discussed earlier and shown in Figure 10.
The ANN-and ANFIS-based control strategies reach the reference torque with less ripples than fixed and fuzzy-based control strategies.However, when ANN and ANFIS are compared, ANFIS provides better performance.It is clearly shown in Figure 11 that the "modified DTC with ANFIS-based reference flux estimator and FGS-tuned PI speed controller" reduces the torque ripple than other control strategies.

Flux response
The reference flux is maintained at 0.8 Wb from no load to full load in conventional DTC with fixed reference

Performance indices
The performance of speed, torque and flux responses are computed using the performance index Integral Square Error (ISE), Integral time absolute error (ITAE) and Integral time square error (ITSE) using Equations ( 17), ( 18) and (19).In these equations, the e(t) stands for error in speed, torque and flux.Control systems specified to minimize ISE will tend to eliminate the large errors quickly.For both transient and steady state, ISE is valid.
Hence, overshoot and rise time are taken into account while evaluating the performance using the performance index ISE.The performance indices are  tabulated in Table 5.
Table 5 gives the variation of performance index values for speed error, torque error and flux error for five control strategies.The bold values of performance index in Table 5 show that ANFIS-based reference flux estimator together with FGS-tuned PI speed controller yields minimal conditions for speed error as well as for torque error.The bar chart from Table 5 for ISE alone is given in Figure 13.ITAE and ITSE will also be the same like ISE.The proportional reflections could be verified clearly for flux error.
The improvement in speed control and torque ripple reduction is achieved with the reduction of flux for all the five cases.Also in the fuzzy-and ANFIS-based reference flux estimator, the modified reference flux (ψ * m ) is instantaneous with respect to torque error as well as reference flux from reference flux estimator ( * ).
The performance indices clearly show that the "modified DTC with ANFIS-based reference flux estimator and FGS-tuned PI speed controller" is the most suitable one for speed control and torque ripple reduction for DTC IM drive.

Conclusion
The modified reference value of flux is computed based on torque error and reference flux from usual reference flux estimator.Self-regulation of reference stator flux value is accomplished with the aid of fuzzy-, ANN-and ANFIS-based reference flux estimators.The control of speed for IM in DTC is accomplished using a PI speed controller.The profound assessment between manual tuning and FGS is performed.The no load and load disturbance rejection characteristics of IM are analysed.The performance indices and responses clearly prove that "modified DTC with ANFIS-based reference flux estimator and FGS-tuned PI speed controller" is most suitable for torque ripple reduction and speed control of DTC IM.

Figure 1 .
Figure 1.The basic DTC scheme of IM drive.

Figure 2 .
Figure 2. Proposed structure of DTC for performance improvement. qs
torque error (T* − Te) and reference flux from reference flux estimator ( * ) are divided into six and three fuzzy subsets with linguistic values {NB = negative big, NM = negative medium, N = negative, P = positive, PM = positive medium, PB = positive big} and {S = small, M = medium, B = big}, respectively.The universe of torque error (T* − Te) and reference flux ( * ) are [−100, 100] and [0, 1], and these ranges are decided by system conditions.The fuzzy inference output is correction in reference flux ( ψ * ), which is divided into seven fuzzy subsets with linguistic values {NB = negative big, NM = negative medium, NS = negative small, O = zero, PS = positive small, PM = positive medium, PB = positive big} with universe [−0.2, 0.2].Since the actual ranges are used in inputs and output, no scaling factor is used before fuzzification and after de-fuzzification.By using knowledge base, the fuzzy rules are developed.The fuzzy rules used are given in Table

Figure 4 .
Figure 4. (a) Input membership functions for torque error.(b) Input membership functions of reference flux.(c).Output membership functions for correction in reference flux.
. It is clearly shown that the modified reference flux (ψ * m ) is computed based on torque error (T* − Te) and the flux from reference flux estimator ( * ) by using ANFIS.

•
Modified DTC with fuzzy-based reference flux estimator and manual tuned speed PI controller (Fuzzy-Manual).• Modified DTC with ANN-based reference flux estimator and manual tuned speed PI controller (ANN-Manual).• Modified DTC with ANFIS-based reference flux estimator and manual tuned speed PI controller (ANFIS-Manual).• Modified DTC with ANFIS-based reference flux estimator and FGS-tuned speed PI controller (ANFIS-FGS).The fixed reference flux value used is 0.8 Wb.The fuzzy-based reference flux estimator explained in Section 3.2 is developed using MATLAB/Simulink ® environment by fuzzy logic toolbox with FIS editor.ANN-based reference flux estimator in Section 3.3 is developed using Neural Network/Data Manager (nntool).ANFIS-based reference flux estimator explained in Section 3.4 is developed in the same

Figure 6 .
Figure 6.Block diagram of fuzzy gain scheduling.

Figure 8 .
Figure 8. Speed responses of all the control strategies for load disturbance rejection.

Figure 9 .
Figure 9. Speed responses of all the control strategies.

Figure 10 .
Figure 10.Starting speed responses of all the control strategies.

Figure 11 .
Figure 11.Torque responses of all the control strategies.

Figure 12 .
Figure 12.Flux responses of all the control strategies.

Figure 13 .
Figure 13.Performance indices of torque, flux and speed error in DTC.

Table 1 .
Look-up table for DTC.

Table 3 .
Rule base for Kp, Ki.

Table 4 .
Tuned values of PI speed controller.

Table 5 .
Performance indices for various reference flux estimators and speed controllers.