Fuzzy-based estimation of reference flux, reference torque and sector rotation for performance improvement of DTC-IM drive

In this study, the fuzzy-based reference flux estimator (RFE), reference torque estimator (RTE) and sector rotation strategy called fuzzy logic estimator are proposed to direct torque control of induction motor (DTC-IM) drive for performance improvement. The basic DTC-IM drive with conventional RFE, RTE and sector division causes large torque ripple, variable switching frequency and uneven voltage vector contribution in stator flux. The torque and speed responses of the proposed system are investigated with load variations. The simulation results of the proposed DTC-IM drive are compared with the basic DTC-IM drive. The assessment of the proposed system shows improved performance. A hardware is developed using Xilinx Spartan-6XC6SLX45-Field Programmable Gate Array (FPGA) Kit for experimental verification of the results. Moreover, sinusoidal pulse width modulation and space vector pulse width modulation techniques are applied to reduce the torque ripples. The performance of the drive is investigated for various speed ranges. The comparison of the simulated and experimental results proves that the proposed fuzzy-based DTC-IM drive provides better performance than the basic DTC-IM drive.


Introduction
In advanced motor drive applications, direct torque control of induction motor (DTC-IM) drives have been used widely owing to their instantaneous torque and flux control with simple structure. The DTC drive system is identified for its robustness and dependency on motor parameter variations [1,2]. However, DTC control scheme uses hysteresis comparators for torque and flux control which causes variable switching frequency and torque ripple. Hence, it requires high sampling rate for experimental validation. DTC scheme applies voltage vectors to IM based on the switching table which is developed based on hysteresis comparators output and stator flux angle. The instantaneous requirements of variation in stator flux and torque are accomplished by the switching table. The stator flux plot has been separated into six equal sectors with respect to stator flux angle, and DTC scheme is developed using the induction machine model [3,4].
The literature survey indicates that the stator flux control and torque control of DTC-IM are enhanced by employing soft computing control strategies like fuzzy logic controller (FLC), neural networks and genetic algorithm [5]. The bandwidth of the torque hysteresis comparator is adjusted using FLC to reduce torque and flux ripples [6]. The virtual voltage vectors as well as model predictive control methods are proposed for improving the performance of DTC [7,8]. Using intermediate voltage vectors by synthesizing the conventional full voltage vectors, an altered switching table was proposed for preventing the demagnetization of stator flux in DTC. However, the synthesizing of voltage vectors and computation of flux and torque ripples becomes complex [9].
The reference value of stator flux is significantly influencing the torque ripples in DTC. Nominal value of stator flux is not suitable for all load variations. Hence, the reference flux is optimized as a function of torque to reduce the torque ripple [10]. In Ref. [11], fuzzy logic is used as stator flux optimizer for selfregulating the value of reference flux in DTC. However, the fuzzy membership functions are asymmetric across the operating range. Some ranges do not come under any membership functions. The reference flux is optimized by torque variations with the aid of fuzzy logic, Artificial Neural Network (ANN) and Adaptive Neuro Fuzzy Inference System [12]. The symmetrical membership functions are used for fuzzy logic in Ref. [12]. On the other hand, the results are investigated only through simulation [11,12].
The DTC scheme uses Proportional Integral (PI) controller in speed control loop to produce the reference torque by tracking speed error as input. The fine tuning of PI controller helps to improve the dynamic speed response of the DTC-IM drive [12,13]. Soft computing techniques are used to tune the PI controller [14]. The fuzzy gain scheduling (FGS) decides the gain values of the PI controller through online tracking of the speed error [12][13][14]. The input membership functions are seven and output membership functions are only two, so that optimum speed control is not attained [13]. Seven membership functions are used for input and output of FGS [12,14]. However, the results are validated only through simulation [12][13][14].
In basic DTC scheme, the stator flux drooping at low speeds near flux sector boundaries have been investigated [15]. By rotating the sectors of the stator flux plot based on the states of torque and flux hysteresis comparators output, the performance of the DTC system is improved. Gated sector rotation in DTC is introduced in Ref. [15]. The sector rotation angle has to modify every time whenever the system condition changes. The decoupling of the stator flux amplitude and angle for selecting reference stator voltage vectors to avoid the flux droop during sector transition is discussed in Ref. [16].
The flux and torque hysteresis band magnitudes are varied and the effect of variation on the dynamic performance of DTC-IM drive is investigated [17]. The existing DTC techniques for inverter fed IM and permanent magnet synchronous motors together with soft computing controllers are presented [18]. The performance of the drive in low speed regions can be improved by the model reference adaptive system-based direct flux magnitude estimation technique [19]. Conventional PI controller is made adaptive to improve the reference torque in DTC [20,21]. A comparative study between DTC based on fuzzy and DTC based on sinusoidal pulse width modulation (SPWM) is performed [22]. The variation of stator resistance at low speeds in DTC-IM drive is investigated [23].
This paper contributes to DTC majorly by (i) Proposing a DTC scheme with fuzzy-based reference flux estimator (RFE), FGS-based PI speed controller, and fuzzy-based sector rotation. (ii) The fuzzy-based sector rotation scheme has not been tried by any other researchers. (iii) The proposed fuzzy DTC scheme and basic DTC scheme are developed in hardware setup. The experimental results are correlated with simulation results. (iv) The developed DTC scheme is validated by changing the reference speed to medium and low speed ranges to prove the high performance. (v) SPWM and space vector pulse width modulation (SVPWM) are applied to improve the performance of the DTC-IM drive.
All the three fuzzy logic estimator (FLE) are developed to operate together adaptively according to the instantaneous system conditions. Hence, the proposed fuzzy DTC-IM drive will be better than the basic DTC-IM drive for reducing torque ripples and adaptive speed control.
In this paper, Section 2 describes the basic DTC with fixed angle sector rotation. Section 3 discusses about SPWM, SVPWM as well as the three FLE, namely, fuzzy-based RFE, fuzzy-based reference torque estimator (RTE) (FGS-based PI speed controller) and fuzzybased sector rotation. In Section 4, the development of the experimental setup for the basic DTC and fuzzy DTC is described in detail. Section 5 investigates the simulation and experimental results as well as the performance indices of the basic DTC, SPWM-DTC, SVPWM-DTC and proposed fuzzy DTC. The proposed schemes are validated by various reference speeds like nominal, medium and low speeds to prove the high performance. In Section 6, it is found that the proposed fuzzy DTC is performing superior to the basic DTC based on simulation and experimental results.

DTC with sector rotation
The block diagram of basic DTC-IM drive is presented in Figure 1. The IM of DTC is operated by stator flux and torque hysteresis comparators. The inverter switching states are selected by a predefined look-up table [1]. The stator flux of the DTC-IM drive can be defined using voltage space vector (U s ) in Equation (1) by ignoring the stator resistance (R s ) as [2,3] = U s * t.
( 1 ) The stator flux plot is separated as six sectors as given in Figure 2. The stator flux hysteresis comparator (d s), torque hysteresis comparator output (dT) and the sector number α[i]of stator flux angle (α) are used for selecting the switching voltage vectors. The look-up table is furnished in Table 1 [4].
The drawback in basic DTC is that while the stator flux vector changes from beginning of a sector to the end, the effect of the voltage vectors is not the same throughout the sector as shown in Figure 3. When the stator flux has to be improved and torque has to be reduced in sector I, the voltage vector U6 has to be applied based on Table 1. The activeness variation of U6 at the beginning and end of the sector I is shown in Figure 3(a). In the same way, when U5 is applied, activeness variation is given in Figure 3(b).
It shows that at the beginning of sector I, the lookup table gives U6. However, U5 is also compatible at the beginning of sector I, suggested by the look-up table for sector VI. In the same way, at the end of sector I, instead of U6 the voltage vector U1 is compatible, suggested by the look-up table for sector II. The change of stator flux decides the effectiveness of voltage vector to meet the desired output. If the sectors of stator flux plot based on stator flux angle (α) are slightly rotated by an angle, then the performance improvement in the DTC scheme can be achieved [15]. The proposed sector rotation is implemented using Equations (2) and (3) for modified stator flux angle (α m ): where α rot is the angle by which the sectors are shifted from original position, d s and dT are the outputs from flux and torque hysteresis comparators. In this paper, in basic DTC, sector rotation is performed at a particular angle to improve the performance.

SPWM, SVPWM and fuzzy in DTC
The SPWM, SVPWM and fuzzy logic are applied in this paper to reduce the ripples in torque and better speed control for DTC-IM drive.

SPWM and SVPWM-based DTC
The basic induction machine (Equation (1)) clearly depicts that the stator flux variation is proportional to the applied voltage vector direction and the time period t. The developed electromagnetic torque (T e ) is also dependent on the stator flux [1] as per Equation (4). The block diagram of the DTC-SPWM/SVPWM strategies is shown in Figure 4.
The torque, flux hysteresis comparators as well as the look-up table are replaced by PI controllers and SPWM/SVPWM module. The PI controllers are used to decide the required voltage vectors.
In SPWM, the outputs of the PI controllers are used to construct the reference sinusoidal signals (dq-abc). The constructed reference signals are compared with triangular wave carrier signal to determine the switching states of inverter.
The applied voltage vector and its duration affect the torque and flux. The applied voltage vectors are synthesized using predetermined time intervals by SVPWM technique. Each cycle period is subdivided by computing the voltage space vectors required for torque and flux errors sampled from previous state.

Fuzzy-based estimators for DTC-IM drive
Mamdani-type fuzzy logics are developed for DTC-IM drive. The reference flux value ( * ), gain values for the PI speed controller and the sector rotation angle (α rot ) are decided by the fuzzy logic in this paper.

Fuzzy-based reference flux estimation
The fuzzy logic is used to fine-tune the reference flux ( * ) value estimated by the conventional RFE [11]. In normal DTC operation, the standard RFE gives the reference flux value derived from whether the motor operating at constant flux region or field weakening region [10]. If the flux level is adjusted in proportion to the load, the energy consumed by the drive can be reduced [10][11][12]. The RFE output ( * ) and actual flux ( ) are used to calculate the flux error ( * − ) as shown in Figure 1 [1]. In real-time experimental validation, the actual flux is estimated using Uds, Uqs, Ids and Iqs components with the help of current and potential transducers.
By using torque error (T * − T) and reference flux ( * ) from conventional RFE, FLE calculates the   correction in reference flux ( * ) as presented in Figure 5. To reduce the torque ripple, fuzzy logic gives the correction in reference ( * ) through approximation [11,12]. This correction in reference flux ( * ) is added with reference flux ( * ) to obtain the modified reference flux ( * m ) as per Equation (5). * m = * + * .
The   [12]. The 18 rules of the developed FLE are given in Table 2 [12].
In Ref. [11], the membership functions are distributed discontinuously and irregularly. Hence, in this paper, an attempt has been made to implement the symmetrical membership functions proposed by the authors [12] experimentally.

Fuzzy-based reference torque estimation
The torque ripples can be further reduced by replacing the fixed gain PI speed controllers in basic DTC to adaptive gain PI speed controllers. This is accomplished using fuzzy logic for gain scheduling. Figure 6 shows the PI speed controller with gain scheduler. The attitude is to exploit fuzzy reasoning to develop the control parameters.
In FGS, the gain values are calculated based on speed error (ω * r − ω r ) and its first derivative (ω * r − ω r ) | . The outputs of the FGS are K PFGS and K iFGS from which the gain values of speed PI controller are calculated using Equations (6) and (7). The K PFGS and K iFGS values are assumed with certain ranges [12,13].
where K 1 p and K 1 i are the optimal online tuning gain values. The input and output membership functions are of five symmetrical triangular membership functions {VS = very small, S = small, M = medium, B = big, VB = very big} and two trapezoidal membership functions {XS = extra small, XB = extra big}. The inputs, speed error (ω * r − ω r ) and rate of change of speed error (ω * r − ω r ) | are normalized for 0-1 and −1 to 1, respectively. The outputs K PFGS and K iFGS are in between 0-100 and 0-0.75, respectively. The rule base is furnished in Table 3 [14]. Table 3 is used for load frequency control in hydro thermal system [14], whereas Table 3 is used here for adaptive speed control in DTC.

Fuzzy-based sector rotation
In Section 2, the sector division is rotated at a fixed angle for performance improvement [15,16], but the rotation angle has to be varied accordingly when the system condition changes. In this section, the sector   Table 4, a systematic algorithm is followed using the torque error (T * − T) values and flux error ( * − ) values. If the product of torque error and flux error is greater than zero, then the sectors have to be rotated in anticlockwise and vice versa. The linguistic values should be selected such that the maximum angle of rotation is 30°.

Experimental setup for basic and fuzzy DTC-IM drive
The experimental setup of the proposed fuzzy DTC-IM drive has been developed to analyse the performance. In this work, the setup is built using "Xilinx Spartan-6XC6SLX45-FPGA Kit in 7G676 package" for verification.
The FPGA program design for DTC control algorithm is performed in PC using Xilinx integral square error (ISE) project navigator (P.40xd) software. The Xilinx Spartan FPGA board is interfaced to the PC through dual port to embed the control algorithm. The basic DTC and fuzzy DTC control algorithms are developed individually in the computer. Based on  The schematic diagram of the developed experimental setup of DTC-IM drive is given in Figure 8. The IM with 1HP power rating is supplied by inverter with switching frequency of 10 kHz. Quadrature encoder pulse (QEP) shaft encoder with 512 pulses per revolution is used to measure the speed of the IM. The encoder output is interfaced to the FPGA using QEP signal processing card. Furthermore, the IM currents are measured by hall-effect sensors and delivered to FPGA using A/D channel.
Only two phase currents are sensed and given to FPGA. The third phase is calculated from the measured two phases. The reference speed (ω * r ) of the IM used is 146.53 rad/s. It is possible to run the IM at 149.67 rad/s but as a safety measure, the reference speed (ω * r ) is kept at 146.53 rad/s. The actual speed of IM is subtracted with reference speed (ω * r ) to obtain error signal. The speed error is fed to PI controller for reference torque. The proportional (K p ) and integral (K i ) gain values of the manual tuned PI controller are 2 and 0.3, respectively. The reference flux ( * ) value is based on the actual speed (ω r ) of the IM.
Based on the actual measurements from sensors and encoders, control algorithms are developed in the FPGA for basic DTC and fuzzy DTC strategies. The actual torque (T), actual flux ( ) and stator flux angle (α) of the IM are estimated using the reconstructed voltages and currents in the control algorithm. If the control algorithm embedded in the FPGA kit is for basic DTC, then the respective PWM pulses are sent to the driver circuit of the inverter. Similarly, the PWM pulses for fuzzy DTC are also sent to the inverter by the corresponding control algorithm. Based on the inverter output, the IM performs. Hence, the individual performance of basic DTC and fuzzy DTC are measured.
The integrated power module (IPM) -PEC16DSM01 -is used as an inverter. The IPM is supplied by three-phase auto transformer, and DC link voltage of the inverter is maintained at 400 V. The timings of the load variations are followed based on Ref. [6]. The motor is loaded by direct step loading at 6, 12 and 16 s with full load (5 N m), half load (2.5 N m) and no load (0 N m), respectively. The torque output is measured from FPGA in terms of voltages from D/A ports with a scaling factor of 1.03 for basic and 1.42 for the fuzzy DTC system. The FPGA output of the speed responses are obtained in terms of voltages with a scaling factor of 25.64 for basic DTC and 38.46 for fuzzy DTC. In Section 5, using scaling factors, the simulation and experimental responses are shown in the same scale for better understanding. The developed experimental setup, peripheral connections of FPGA and shaft encoder are shown in Figure 9. The responses are perceived with a digital storage oscilloscope (DSO) having 70 MHz bandwidth and 2 GSa/s sampling rate and the data saved as Microsoft Excel comma separated values (MECSVs) file.

Validation of simulation and experimental responses of DTC
The simulation model is created with MATLAB/Simulink R environment for basic DTC and fuzzy DTC. The experimental setup of the DTC-IM drive is developed as explained in the previous section for validation. The simulation and experimental results are compared for different loading conditions. The parameters furnished in Appendix used for simulation are obtained from actual experimental setup. This paper mainly focusses on torque ripples and speed control at various speed ranges for varying loads than voltages and currents.   reference torque is followed closely in fuzzy DTC than basic DTC.

Comparison of speed responses
Like torque response, the speed response variations are also compared for the basic DTC with the proposed fuzzy DTC system. The starting speed characteristics are given in Figure 11 for basic DTC as well as fuzzy DTC. At starting, the speed characteristics of basic DTC has less rise time with no overshoot and quick settling time than fuzzy DTC in simulation. Similar behaviour is reflected in experiment for rise time, but the overshoot is less and the settling time is compatible. The FLE takes a small time deviation to get settled in the system. Since no soft computing estimators are involved in basic DTC, it takes less rise time. The reference speed (ω * r ) is followed closely in fuzzy DTC than basic DTC. The speed responses of the proposed fuzzy DTC-IM drive are related with basic DTC-IM drive for full load, half load and no load variations as presented in Figure 12. The simulation responses indicate that the drop in speed for the same load is more in basic DTC than fuzzy DTC. When the load is reduced, the speed is recovered nearer to the reference speed (ω * r ) in fuzzy DTC than basic DTC. The experimental responses prove that the fuzzy DTC is superior to basic DTC for all load variations.

Comparison of speed and torque responses at medium and low speeds
In high performance drives like DTC, the drive should be able to perform even at medium and low speed ranges. Hence, the developed control strategies are verified for medium (146.53 * 0.4 rad/s) and low speed ranges (146.53 * 0.06 rad/s).
It is perceived that the torque ripples are more in the proposed DTC schemes, and to validate the performance, SPWM and SVPWM techniques are introduced in DTC [17][18][19][20][21][22]. The speed responses of the SPWMand SVPWM-based DTC are given in Figure 13 for nominal, medium and low reference speeds. It is seen that SPWM performs at nominal and medium speed ranges but for low speed range, the performance of SPWM is not satisfactory. The SVPWM performs at nominal speed range but for medium and low reference speeds, the performances are not satisfactory. In nominal speed range, the SVPWM performs better than SPWM.
The DTC-IM drive is independent of all the machine parameters except stator resistance (R s ) of the IM. At  nominal speed range, stator resistance drop (I s R s ) is negligible when compared to input voltage. In medium and low speed ranges, the input voltage becomes proportionately less. Hence, the value of stator resistance drop (I s R s ) is acute while related to input voltage as shown in Equation (8). Moreover, during the operation of the drive, the stator resistance (R s ) changes due to temperature. The change in stator resistance (R s ) causes the change in stator current (I s ). It causes incorrect stator flux estimation, consequently the developed electromagnetic torque (T e ) as in Equation (4) and position of stator flux [23]. When the developed electromagnetic torque (T e ) is not proper and load torque remains same, the speed control becomes difficult [12]. Hence, no major improvements are observed in speed responses at medium and low speed ranges.
The torque responses of the SPWM-and SVPWMbased DTC schemes for the various speed ranges are shown in Figure 14. The SVPWM improves the torque response prominently for nominal speed range (146.53 rad/s) than SPWM. On the other hand, for medium (58.612 rad/s) and low (8.7918 rad/s) speed ranges, the torque performance is not satisfactory for SVPWM when compared to SPWM.
In SPWM and SVPWM, the torque error (T * − T) and flux error ( * − ) are given to the PI controllers. The reference torque (T * ) is the output of another PI controller which is taking speed error (ω * r − ω r ) as input. Hence, when the reference speed (ω * r ) changes to medium and low ranges, the proportionate changes are reflected in the reference signals of the SPWM.
Based on the output of these PI controllers, the reference voltage is calculated for SVPWM [17]. The DC bus voltage (U dc ) and the sector angle (α) are used to determine the duty cycles of the voltage vectors. The soft computing controllers are not effective in SPWM as well as SVPWM for the reason that the conventional look-up table as well as the hysteresis comparators is removed. In Figure 15, the reference speed is kept as 146.53 rad/s, and the responses clearly prove that the fuzzy DTC (3fuzzy) which consists of fuzzy-based RFE, fuzzy-based RTE and fuzzy-based sector rotation performs better than other control strategies. The fuzzybased RFE (1fuzzy) performs better than basic DTC. The fuzzy-based RFE with fuzzy-based RTE (2fuzzy) performs better than fuzzy-based RFE alone.
In Figure 16, the reference speed is reduced to 58.612 rad/s; here also the 3fuzzy DTC and 2fuzzy are   Similarly, Figure 17 depicts the speed responses for the reference speed of 8.7912 rad/s. The responses show the similar performance as Figure 16, and the 3fuzzy DTC performs better than other strategies.
From Figures 15-17, it is inferred that the fuzzy DTC (3fuzzy) performs better than other strategies. The torque responses of nominal speed (146.53 rad/s), medium speed (51.612 rad/s) and low speed    Figure 18. The ripples are comparatively less for low speed operating region. During starting time, speed error is equal to reference speed and it approaches to zero at settling time. Hence, speed PI controller output during starting is high (reference torque). It is controlled by adding saturator at the output of the speed PI controller.

Comparison of performance index
To prove the performance precisely, the proposed fuzzy DTC and basic DTC are compared using the ISE as The equation for calculating ISE is given in Equation (9), where e(t) represents the error. The performance indices for speed error and torque error are given in Table 5 for basic DTC and fuzzy DTC. The ISE values of fuzzy DTC are less than basic DTC in both simulation and experiment as given in Table 5. In Table 5, the hardware data are taken from DSO as MECSVs file. The same number of data is collected from simulation also to calculate the ISE values.
The bar charts in Figure 19 pictorially represent that the ISE values are low for fuzzy DTC than basic DTC. Hence, it is proved obviously that the fuzzy DTC system improves the torque and speed control better than basic DTC during loading conditions. The system conditions, i.e. IM parameters, PI controller gain values and inverter DC link voltage, are the same under simulation and experimental studies. The responses derived from simulation and experimental studies differ slightly because of FPGA signal processing, direct loading and other real-time variations. By observing the torque response, speed response and performance indices, it is clear that the proposed fuzzy DTC-IM drive gives improved performance than basic DTC-IM drive.
In Table 6, the ISE values of speed error and torque error for various speed ranges as well as for individual control strategies are furnished. It is seen clearly that individual control strategies show the step by step improvement in the speed and torque ISE values. In Table 6 Figure 19. Bar chart representation of the performance index ISE for speed and torque error from simulation and experimental studies.

Conclusion
The DTC-IM drive is made highly adaptive by fuzzy logic in this work. Fuzzy logic is used for reference flux estimation, reference torque estimation and sector rotation angle in DTC for performance improvement. The proposed DTC system improves torque and speed response than the basic DTC system. In the proposed system, the reference flux is varied continuously according to system conditions, the FGS is applied for adaptive gain values of the speed PI controller and fuzzy-based sector rotation concept is used for stator flux plot sector division. Furthermore, the proposed DTC-IM drive performance is validated by changing the reference speed to medium and low speed ranges. SPWM-based DTC performs at nominal and medium speed ranges. On the other hand, in low speed range, SPWM is not effective. SVPWM technique gives less torque and speed control at nominal speeds than SPWM for DTC. In medium and low speed ranges, SVPWM is not effective. The comparison with basic DTC clearly proves improvement in system performance with the use of fuzzy logic for the proposed RFE, RTE and sector rotation angle. The experimental results validate the simulation responses and clearly prove the superiority of the proposed system. The performance indices also prove that the proposed fuzzy DTC-IM drive provides a better performance compared to basic DTC-IM drive.

Disclosure statement
No potential conflict of interest was reported by the author(s).