Modified Predictive Direct Torque Control ASIC with Multistage Hysteresis and Fuzzy Controller for a Three-Phase Induction Motor Drive

This paper proposes a modified predictive direct torque control (MPDTC) applicationspecific integrated circuit (ASIC) with multistage hysteresis and fuzzy controller to address the ripple problem of hysteresis controllers and to have a low power consumption chip. The proposed MPDTC ASIC calculates the stator’s magnetic flux and torque by detecting three-phase currents, three-phase voltages, and the rotor speed. Moreover, it eliminates large ripples in the torque and flux by passing through the modified discrete multiple-voltage vector (MDMVV), and four voltage vectors were obtained on the basis of the calculated flux and torque in a cycle. In addition, the speed error was converted into a torque command by using the fuzzy PID controller, and rounding-off calculation was employed to decrease the calculation error of the composite flux. The proposed MDMVV switching table provides 294 combined voltage vectors to the following inverter. The proposed MPDTC scheme generates four voltage vectors in a cycle that can quickly achieve DTC function. The Verilog hardware description language (HDL) was used to implement the hardware architecture, and an ASIC was fabricated with a TSMC 0.18 μm 1P6M CMOS process by using a cell-based design method. Measurement results revealed that the proposed MPDTC ASIC performed with operating frequency, sampling rate, and dead time of 10 MHz, 100 kS/s, and 100 ns, respectively, at a supply voltage of 1.8 V. The power consumption and chip area of the circuit were 2.457 mW and 1.193 mm × 1.190 mm, respectively. The proposed MPDTC ASIC occupied a smaller chip area and exhibited a lower power consumption than the conventional DTC system did in the adopted FPGA development board. The robustness and convenience of the proposed MPDTC ASIC are especially advantageous.


Introduction
The use of direct torque controllers in three-phase induction motor (IM) drives is common because of the fast torque and flux control of these controllers [1,2]. Nevertheless, the traditional hysteresis controller is the most frequently used controller in such drives. Conventional direct torque control (DTC) is a simple and robust method that is associated with the disadvantages of high torque, flux ripples, and switching losses [3]. After considerable research effort, the performance of the conventional DTC method was improved. In DTC space vector modulation (SVM), torque ripples and switching losses are reduced using a predictive controller, which increases the complexity of DTC [4]. DTC SVM with an imaginary switching time requires low memory and does not require sector determination; the torque and flux ripples induced by the limited vector voltages and low speed response in a traditional DTC [22]. A modified DTC ASIC not only improves the stability of the motor control system, but also reduces power consumption.
In this paper, we propose a modified PDTC (MPDTC) ASIC with fuzzy seven-stage hysteresis and a fuzzy PID controller. Fuzzy controllers and round-off calculations can significantly improve the performance of three-phase IM drive systems. The remainder of this paper is organized as follows. Section 2 describes the circuit design of the proposed MPDTC ASIC for an IM drive system, and Section 3 presents the simulation and experimental results for functional verification. Lastly, Section 4 presents the conclusions of this study. Figure 1 depicts the block diagram of the proposed MPDTC ASIC with fuzzy sevenstage hysteresis and a fuzzy PID controller for a three-phase IM drive system. This ASIC contains a three-to two-phase transformation block, voltage calculation block, flux calculation block, torque calculation block, sector selection block, speed feedback block, predictive calculation block, fuzzy PID controller, torque error fuzzy controller, flux error fuzzy controller, five-stage hysteresis controller, seven-stage hysteresis controller, modified discrete multiple-voltage vector (MDMVV) switching table, and short-circuit prevention block. All the functional blocks were designed using the Verilog hardware description language (HDL) and verified using an FPGA development board. Lastly, the proposed ASIC was fabricated with a TSMC 0.18 µm 1P6M CMOS process to reduce power consumption, and enhance the robustness and convenience of the three-phase IM drive. All symbols used in Figure 1 are shown in Appendix A to enhance the reading.

Circuit Design of the Proposed MPDTC ASIC
Electronics 2022, 10, x FOR PEER REVIEW 3 of 19 trol of the stator flux and instantaneous torque without a complex algorithm [21]. A modified DTC ASIC with five-stage fuzzy hysteresis and a fuzzy PID speed controller was used to reduce the torque and flux ripples induced by the limited vector voltages and low speed response in a traditional DTC [22]. A modified DTC ASIC not only improves the stability of the motor control system, but also reduces power consumption.
In this paper, we propose a modified PDTC (MPDTC) ASIC with fuzzy seven-stage hysteresis and a fuzzy PID controller. Fuzzy controllers and round-off calculations can significantly improve the performance of three-phase IM drive systems. The remainder of this paper is organized as follows. Section 2 describes the circuit design of the proposed MPDTC ASIC for an IM drive system, and Section 3 presents the simulation and experimental results for functional verification. Lastly, Section 4 presents the conclusions of this study. Figure 1 depicts the block diagram of the proposed MPDTC ASIC with fuzzy sevenstage hysteresis and a fuzzy PID controller for a three-phase IM drive system. This ASIC contains a three-to two-phase transformation block, voltage calculation block, flux calculation block, torque calculation block, sector selection block, speed feedback block, predictive calculation block, fuzzy PID controller, torque error fuzzy controller, flux error fuzzy controller, five-stage hysteresis controller, seven-stage hysteresis controller, modified discrete multiple-voltage vector (MDMVV) switching table, and short-circuit prevention block. All the functional blocks were designed using the Verilog hardware description language (HDL) and verified using an FPGA development board. Lastly, the proposed ASIC was fabricated with a TSMC 0.18 μm 1P6M CMOS process to reduce power consumption, and enhance the robustness and convenience of the three-phase IM drive. All symbols used in Figure 1 are shown in Appendix A to enhance the reading.

Coordinate Transformation and Calculation Formulas
Coordinate transformation from three phases (ABC axes) to two phases (DQ axes) was performed to reduce the calculation burden and increase the speed response. This transformation can be completed using the following trigonometric function [23]:

Coordinate Transformation and Calculation Formulas
Coordinate transformation from three phases (ABC axes) to two phases (DQ axes) was performed to reduce the calculation burden and increase the speed response. This transformation can be completed using the following trigonometric function [23]:   (2) where v s as (= V as ) and v s bs (= V bs ) are three-phase voltages, i s as (= I as ) and i s bs (= I bs ) are three-phase currents, v s ds (= V ds ) and v s qs (= V qs ) are two-phase voltages, and i s ds (= I ds ) and i s qs (= I qs ) are two-phase currents.
Next, two-phase voltages V ds and V qs can be calculated using the three up-arm voltages of the U-, V-, and W-phases (S a , S b , and S c , respectively). DC voltage V dc is measured at the output terminal of the inverter as follows: The flux (ϕ) can be expressed in terms of the single-phase stator winding resistance R s as follows: According to the Laplace transform, variable p is defined as complex s, and T is the sampling period. The two fluxes ϕ s ds and ϕ s qs can then be expressed as follows [23]: The torque (T e ) is calculated on the basis of DTC theory by using (7), in which P is the number of motor poles.
when two magnetic fluxes λ ds and λ qs are obtained, the synthetic flux λ dqs can be calculated using a square root circuit, round-off calculation circuit, and D-type flip-flop (DFF) circuit.
The square root is obtained using the shadow tree algorithm [1], and the DFF circuit is employed to complete synchronization using the clock signal (clk). The round-off calculation is used to reduce the calculation error of the square rooting circuit. Figure 2 illustrates the calculation blocks of the synthetic flux λ dqs , namely, the square root, round-off calculation, and DFF circuits.
The flux (φ) can be expressed in terms of the single-phase stator w Rs as follows: According to the Laplace transform, variable p is defined as comp sampling period. The two fluxes φ s ds and φ s qs can then be expressed as The torque (Te) is calculated on the basis of DTC theory by using (7 number of motor poles. The square root is obtained using the shadow tree algorithm [1], a is employed to complete synchronization using the clock signal (clk). culation is used to reduce the calculation error of the square rooting cir trates the calculation blocks of the synthetic flux λdqs, namely, the squa calculation, and DFF circuits.  To complete the round-off calculation, a calibration constant (Cal) is used to modify the output code of the rounding-down calculation (RD) with the input code IN. If Cal is less than or equal to 0, the output digital code (RO) does not change and is equal to RD. If the Cal is greater than 0, the output digital code (RO) is equal to the rounding-down code (RD) + 1. Cal can be defined as follows: The decision formula can be expressed as follows:

Sector Selection
The sector can be selected through the calculation of the two-phase magnetic fluxes λ ds and λ qs and synthesis magnetic flux λ dqs . In general, the voltage space vector can be divided into six sectors, with each sector covering an angle of 60 • . To simplify the analysis, the first quadrant of the coordinate plane is examined. If λ ds and λ qs are positive, the first quadrant includes the sectors S 1 and S 2 , which extend from 0 • to 30 • and from 30 • to 90 • , respectively. In trigonometry, a relational equation can be expressed as follows: If magnetic fluxes λ ds and λ qs are positive, the result of (11) is negative (<0) for sector S 1 and positive (>0) for sector S 2 . Table 1 summarizes the sector selection for the proposed MPDTC ASIC. The output sector can be easily selected using this table [21].

Predictive Calculation Circuit
An MPC system is used to provide decoupled flux and torque control, and to reduce the torque and flux ripples in a three-phase IM drive system. The advantages of an MPC system include its retention of the benefits of the conventional DTC architecture and its light calculation burden in rapidly computing the motor's position [24]. Figure 3 presents the block diagram of an MPC system for stator flux error (λ e ), torque error (T e ), and speed error (ω e ) calculations. The proposed MPC DTC architecture can improve the control performance of an IM drive with high speed and high-precision motor control. As depicted in Figure 3, the delay (z −1 ) block is implemented with a DFF circuit, and the subtraction block (−) is used to obtain the deviation between the present data D[k] and previous data D[k − 1]. The input code D[k] comprises the flux (λ e ), torque (T e ), and speed error (ω e ). Moreover, the absolute block (Abs.) provides the magnitude of the deviation. The multiplexer determines the output codes out[k], including λ p , T p , and ω p , according to the control signals C[k] (τ or ϕ), from the hysteresis controllers.

Fuzzy PID Controller
PID controllers are widely used for solving complex control problems, including the speed control problem of an IM drive. The traditional PID controller, which has a simple structure, low cost, and easy repairability, decides the values of Kp, Ki, and Kd by using the Ziegler-Nichols tuning method [25]. The general formula of a PID controller can be expressed as follows: where s is a complex frequency. Parameters KP, Ki, and Kd represent the proportional, integral, and derivative coefficients, respectively, which markedly influence the stability of the PID controller. A fuzzy PID controller can obtain optimal parameters more easily and efficiently than a nonfuzzy linear PID controller can. Figure 4 presents a block diagram of the adopted fuzzy PID controller, which operates with an input error e(t) (expressed as e(t) = ω * r − ωr) and an input error variation Δe(t). The fuzzy controller destination is determined by computing the parameters Kp and Kd by using the membership function and fuzzy rules. Integral coefficient Ki can be calculated using a constant α as follows: The operating principle of the PID controller is to determine the output u(t) with three coefficients, which can be calculated as follows: After u(t) is calculated, a closed-loop control procedure is executed for the IM drive. The self-adjusting mechanism is completed using the speed feedback ωr. The fuzzy PID controller operates with adequate adaptability. The fuzzy rules of KP, Kd, and α are listed in Tables 2-4, respectively [23]. Constant α is restricted to 4-level architecture, which is numbered from 2 to 5, and a minimal constant of 2 was set for PB and NB of input error variation Δe(t). By setting the small constant α of 2, the operational range was restricted to 3 levels, PS, ZE, and NS, at input error variation Δe(t). Input error e(t) was also proportional to constant α. The large error e(t) corresponded a large constant α at the PB or NB of input error e(t). Table 4 can not only speed up the calculation, but also shorten the convergence time.

Fuzzy PID Controller
PID controllers are widely used for solving complex control problems, including the speed control problem of an IM drive. The traditional PID controller, which has a simple structure, low cost, and easy repairability, decides the values of K p , K i , and K d by using the Ziegler-Nichols tuning method [25]. The general formula of a PID controller can be expressed as follows: where s is a complex frequency. Parameters K P , K i , and K d represent the proportional, integral, and derivative coefficients, respectively, which markedly influence the stability of the PID controller. A fuzzy PID controller can obtain optimal parameters more easily and efficiently than a nonfuzzy linear PID controller can. Figure 4 presents a block diagram of the adopted fuzzy PID controller, which operates with an input error e(t) (expressed as e(t) = ω * r − ω r ) and an input error variation ∆e(t). The fuzzy controller destination is determined by computing the parameters K p and K d by using the membership function and fuzzy rules. Integral coefficient K i can be calculated using a constant α as follows: The operating principle of the PID controller is to determine the output u(t) with three coefficients, which can be calculated as follows: After u(t) is calculated, a closed-loop control procedure is executed for the IM drive. The self-adjusting mechanism is completed using the speed feedback ω r . The fuzzy PID controller operates with adequate adaptability. The fuzzy rules of K P , K d , and α are listed in Tables 2-4, respectively [23]. Constant α is restricted to 4-level architecture, which is numbered from 2 to 5, and a minimal constant of 2 was set for PB and NB of input error variation ∆e(t). By setting the small constant α of 2, the operational range was restricted to 3 levels, PS, ZE, and NS, at input error variation ∆e(t). Input error e(t) was also proportional to constant α. The large error e(t) corresponded a large constant α at the PB or NB of input error e(t). Table 4 can not only speed up the calculation, but also shorten the convergence time.     Figure 5 presents a block diagram of the error fuzzy controller. Error et and error variation Δet, which are derived from the speed feedback, are input variables of the error fuzzy controller. The output variable u(t) is obtained when it is input into the error fuzzy controller. Figure 6 illustrates the seven-stage fuzzy membership function, in which two input variables, namely et and Δet, are divided into seven fuzzy sets: negative big (NB), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM), and positive big (PB) fuzzy sets. Table 5 details the rules for the seven-stage fuzzy controller. In the five-stage hysteresis controller, two input variables, namely, et and Δet, are divided into five fuzzy sets: NB, NS, ZE, PS, and PB. The rules for this controller are presented in Table 6.   Figure 5 presents a block diagram of the error fuzzy controller. Error e t and error variation ∆e t , which are derived from the speed feedback, are input variables of the error fuzzy controller. The output variable u(t) is obtained when it is input into the error fuzzy controller. Figure 6 illustrates the seven-stage fuzzy membership function, in which two input variables, namely e t and ∆e t , are divided into seven fuzzy sets: negative big (NB), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM), and positive big (PB) fuzzy sets. Table 5 details the rules for the seven-stage fuzzy controller. In the five-stage hysteresis controller, two input variables, namely, e t and ∆e t , are divided into five fuzzy sets: NB, NS, ZE, PS, and PB. The rules for this controller are presented in Table 6.

MDMVV Switching Table
A major drawback of the traditional DTC hysteresis controller is the inst caused by the large torque and flux ripples generated by it. A five-or seven-stage resis controller can be used to reduce the torque error for speed response or flux respectively. The torque error must be managed by using a fuzzy PID controller be this error requires a long processing time. Moreover, the torque error in a five-stag teresis controller has a synchronous action to the flux error in a seven-stage hys controller. To solve the aforementioned problem, an MDMVV switching table i posed. Figure 7 illustrates the torque error fuzzy controller with five-stage hysteresi trol and the input variables of torque error (dT, which is defined as dT = Te* − Te) and c rate of torque error (ΔdT). The output variable of this controller is the selected tor The input variables of the five-stage hysteresis controller were divided into the P ZE, NS, and NB fuzzy sets for torque error. The aforementioned sets were defined +2, +1, 0, −1, and −2, respectively. Figure 8 depicts the flux error fuzzy controlle seven-stage hysteresis control and the input variables of flux error (dλ, which is defi dλ = λe* − λe) and change rate of flux error (Δdλ). The output variable of the aforemen controller is the selected flux . The input variables of the seven-stage hysteresis con

MDMVV Switching Table
A major drawback of the traditional DTC hysteresis controller is the instability caused by the large torque and flux ripples generated by it. A five-or seven-stage hysteresis controller can be used to reduce the torque error for speed response or flux error, respectively. The torque error must be managed by using a fuzzy PID controller because this error requires a long processing time. Moreover, the torque error in a five-stage hysteresis controller has a synchronous action to the flux error in a seven-stage hysteresis controller. To solve the aforementioned problem, an MDMVV switching table is proposed. Figure 7 illustrates the torque error fuzzy controller with five-stage hysteresis control and the input variables of torque error (d T , which is defined as d T = T e * − T e ) and change rate of torque error (∆d T ). The output variable of this controller is the selected torque τ. The input variables of the five-stage hysteresis controller were divided into the PB, PS, ZE, NS, and NB fuzzy sets for torque error. The aforementioned sets were defined to be +2, +1, 0, −1, and −2, respectively. Figure 8 depicts the flux error fuzzy controller with seven-stage hysteresis control and the input variables of flux error (d λ , which is defined as d λ = λ e * − λ e ) and change rate of flux error (∆d λ ). The output variable of the aforementioned controller is the selected flux. The input variables of the seven-stage hysteresis controller are divided into the PB, PM, PS, ZE, NS, NM, and NB fuzzy sets for flux error. These sets were defined to be +3, +2, +1, 0, −1, −2, and −3, respectively. After torque τ and flux ϕ had been computed, an MDMVV switching table was used to select an approximate output voltage set for four voltage vectors according to torque τ, flux ϕ, and sector S. Table 7 presents the MDMVV  switching table. Electronics 2022, 10, x FOR PEER REVIEW are divided into the PB, PM, PS, ZE, NS, NM, and NB fuzzy sets for flux error. The were defined to be +3, +2, +1, 0, −1, −2, and −3, respectively. After torque τ and flux been computed, an MDMVV switching table was used to select an approximate o voltage set for four voltage vectors according to torque τ, flux φ, and sector S. T presents the MDMVV switching table.       If the MDMVV has a large positive flux (PB) and positive torque (PB) in sector S 1 , the output voltage set was selected to be V 2 V 2 V 2 V 2 , which is denoted as 2222 in Example (1). Each voltage (V 2 ) contributes an increment not only in torque, but also in flux. The total incremental value was +4 in Example (1). In Example (2) of Table 8, ZE was selected for the MDMVV because the flux remains unchanged, whereas NS was selected for the torque to reduce its value. The output voltage set for this example is V 2 V 7 V 5 V 0 , which increases the output toque (T e ) to near the recommend torque value (T * e ). The other examples listed in Table 8 also describe the changing flux and torque. Figure 9 displays the time sequence of the MDMVV for the stator's torque. Four voltage vectors were employed in a sampling cycle T S in this study, whereas only an output voltage vector is used in a traditional DTC sampling cycle. Thus, the proposed scheme is suitable for a heavy load or fluctuating torque and flux. Figure 10 illustrates variation d T in response to sampling time T s , which was equal to four times clock time T C (i.e., T S = 4 × T C and T C = T 1 = T 2 = T 3 = T 4 ). If current torque T e was considerably lower than recommend torque T * e (NB) in sector S 1 , voltage set V 2 V 2 V 2 V 2 was selected to significantly increase the torque (PB), as detailed in Example (1) of Table 8. The status of current torque Te was PS, and an NS status was required to increase the torque to the recommend value for S 1 (T * e ). According to Table 7, the aforementioned condition could be achieved using voltage set V 2 V 7 V 5 V 0 , as illustrated in Figure 10. When this voltage set was used, T e was close to T * e .  Table 8. Rules for the five-state fuzzy controller. Table 8. Rules for the five-state fuzzy controller. Time  T1,T2,T3,T4  T1,T2,T3,T4  T1,T2,T3,T4  T1,T2,T3,T4  Vector V2,V2,V2,V2 V2,V7,V5,V0 V2,V3,V5,V6 V5,V5,V5,V5 Torque

Short Circuit Prevention
For a 0.75 hp IM, a dead time of 100 ns is essential for preventing short-circuit burning in the inverter of the IM control system. Figure 11 depicts the proposed short-circuit prevention scheme, which includes negative edge (Negedge) and positive edge (Posedge) control states, in the control signal [24]. In the Negedge state (1  0), the "Up" signal changes from high (1) to low (0) when the control signal is turned off (1  0). Moreover, the "Down" signal changes from low (0) to high (1) after the dead time (ΔT) is completed. In the Posedge state (0  1), the "Down" signal changes from high (1) to low (0) when the control signal is turned on (0  1). If the dead time (ΔT) is completed, the "Up" signal changes from low (0) to high (1). The proposed short-circuit prevention scheme is simple, and the dead time can be easily adjusted using the control signal.

Simulation and Measurement Results
A functional simulation was conducted using the Simulink package in MATLAB software (MathWorks, Natick, MA, USA). Figure 12 presents the functional simulation chart

Short Circuit Prevention
For a 0.75 hp IM, a dead time of 100 ns is essential for preventing short-circuit burning in the inverter of the IM control system. Figure 11 depicts the proposed short-circuit prevention scheme, which includes negative edge (Negedge) and positive edge (Posedge) control states, in the control signal [24]. In the Negedge state (1 → 0), the "Up" signal changes from high (1) to low (0) when the control signal is turned off (1 → 0). Moreover, the "Down" signal changes from low (0) to high (1) after the dead time (∆T) is completed. In the Posedge state (0 → 1), the "Down" signal changes from high (1) to low (0) when the control signal is turned on (0 → 1). If the dead time (∆T) is completed, the "Up" signal changes from low (0) to high (1). The proposed short-circuit prevention scheme is simple, and the dead time can be easily adjusted using the control signal.

Short Circuit Prevention
For a 0.75 hp IM, a dead time of 100 ns is essential for preventing short-circuit burning in the inverter of the IM control system. Figure 11 depicts the proposed short-circuit prevention scheme, which includes negative edge (Negedge) and positive edge (Posedge) control states, in the control signal [24]. In the Negedge state (1  0), the "Up" signal changes from high (1) to low (0) when the control signal is turned off (1  0). Moreover, the "Down" signal changes from low (0) to high (1) after the dead time (ΔT) is completed. In the Posedge state (0  1), the "Down" signal changes from high (1) to low (0) when the control signal is turned on (0  1). If the dead time (ΔT) is completed, the "Up" signal changes from low (0) to high (1). The proposed short-circuit prevention scheme is simple, and the dead time can be easily adjusted using the control signal.

Simulation and Measurement Results
A functional simulation was conducted using the Simulink package in MATLAB software (MathWorks, Natick, MA, USA). Figure 12 presents the functional simulation chart of the proposed MPDTC system for a three-phase IM drive. Input parameters Meas, Motor, and Ctrl were used to generate the voltage bus (V_bus). In the estimation module, the Figure 11. Proposed short-circuit prevention scheme.

Simulation and Measurement Results
A functional simulation was conducted using the Simulink package in MATLAB software (MathWorks, Natick, MA, USA). Figure 12 presents the functional simulation chart of the proposed MPDTC system for a three-phase IM drive. Input parameters Meas, Motor, and Ctrl were used to generate the voltage bus (V_bus). In the estimation module, the estimated flux (Flux_est) and estimated torque (Torque_est) were obtained, and used to generate the flux error (Flux_error) and torque error (Torque_error) by using the referenced flux (Flux_Ref) and referenced torque (Torque_Ref), respectively. A set of four voltage vectors were generated within a sampling time that comrpised four clock times, namely, T 1 , T 2 , T 3 , and T 4 , after passing through the fuzzy controller, fuzzy hysteresis, and MDMVV switching table. nics 2022, 10, x FOR PEER REVIEW 12 Figure 12. Functional simulation chart of the proposed MPDTC system for a three-phase IM According to the simulation results, the proposed MPDTC system exhibited sm ripples in the stator's flux and torque than a conventional DTC system did with a h resis controller [23]. Figure 13 presents a comparison of the simulated flux errors o proposed MPDTC and traditional DTC systems between 0 and 2 s, and Figure 14 pre According to the simulation results, the proposed MPDTC system exhibited smaller ripples in the stator's flux and torque than a conventional DTC system did with a hysteresis controller [23]. Figure 13 presents a comparison of the simulated flux errors of the proposed MPDTC and traditional DTC systems between 0 and 2 s, and Figure 14 presents a comparison of the two systems' simulated torque errors. The simulated flux and torque errors of the designed MPDTC system were smaller than those of conventional DTC system. The flux trajectories of the MPDTC and conventional DTC systems are depicted in Figure 15a,b, respectively. The aforementioned figure indicates that the proposed MPDTC system operated with a smaller flux border than the conventional DTC system does. The IM also operated smoothly with the proposed MPDTC system. Figure 16 illustrates the simulated line voltages in the U-V-phase, V-W-phase, and W-U-phase (V ab , V bc , and V ca , respectively) for a three-phase IM drive.       After the functional simulations had been completed, the designed modules were implemented using the Verilog HDL. Figure 17 depicts the simulated voltage waveforms of six-arm signals in the inverter at a clock frequency of 10 MHz and a basic frequency of 1800 rpm (≈33.33 ms). The up-arm (USi) and down-arm (DSi) moved according to the inverse waveforms in each phase, with i = a, b, and c. Parameters USa, USb, and USc represent the up-arm output voltages of the U-, V-, and W-phases, respectively. The behavioral simulation verified that the designed functions operate correctly within the ModelSim software. After the functional simulations had been completed, the designed module implemented using the Verilog HDL. Figure 17 depicts the simulated voltage wav of six-arm signals in the inverter at a clock frequency of 10 MHz and a basic frequ After the functional simulations had been completed, the designed modules were implemented using the Verilog HDL. Figure 17 depicts the simulated voltage waveforms of six-arm signals in the inverter at a clock frequency of 10 MHz and a basic frequency of 1800 rpm (≈33.33 ms). The up-arm (US i ) and down-arm (DS i ) moved according to the inverse waveforms in each phase, with i = a, b, and c. Parameters US a , US b , and US c represent the up-arm output voltages of the U-, V-, and W-phases, respectively. The behavioral simulation verified that the designed functions operate correctly within the ModelSim software.  An FPGA development board was used to verify the designed functions, and a logic analyzer was used to analyze the measured digital signals. Figure 18 illustrates the measured waveforms of the six-arm voltage signals of the inverter. These waveforms were measured using the logic analyzer at a clock frequency of 10 MHz and a sampling frequency of 100 kHz. The generation of a dead time between the up-arm and the down-arm was essential for preventing the short-circuit burning of the three-phase IM. As illustrated in Figure 19, dead time of 100 ns that was measured in the W-phase with the logic analyzer was suitable for the adopted 0.75 hp IM.  An FPGA development board was used to verify the designed functions, and a logic analyzer was used to analyze the measured digital signals. Figure 18 illustrates the measured waveforms of the six-arm voltage signals of the inverter. These waveforms were measured using the logic analyzer at a clock frequency of 10 MHz and a sampling frequency of 100 kHz. The generation of a dead time between the up-arm and the down-arm was essential for preventing the short-circuit burning of the three-phase IM. As illustrated in Figure 19, dead time of 100 ns that was measured in the W-phase with the logic analyzer was suitable for the adopted 0.75 hp IM.           (2), I as and I bs can be transformed into two-phase stator currents i s ds and i s qs , respectively, through trigonometric calculation. Figure 21 illustrates the measured up-arm voltages in the U-phase and V-phase (US a and US b , respectively). The proposed MPDTC ASIC and three-phase IM drive operated correctly, with the IM drive producing small ripples. Figure 22 presents a photomicrograph of the proposed MPDTC ASIC, which is fabricated by TSMC (Taiwan Semiconductor Manufacturing Company) and contains 35 pins.

Conclusions
In this study, an MPDTC ASIC with multistage hysteresis and fuzzy controller was proposed to enhance the stability and control of a 0.75-hp three-phase induction motor. ModelSim software was used to conduct functional simulation, and the Verilog HDL was employed to operate all modules of the proposed MPDTC system. After the designed functions had been verified using an FPGA development board, the proposed ASIC was fabricated using a TSMC 0.18 m 1P6M CMOS process. Simulation results indicated that the stator flux trajectory of the proposed MPDTC ASIC was superior to that of a conventional DTC system with a hysteresis controller. In addition, the simulated torque and flux errors of the proposed MPDTC system were smaller than those of the conventional DTC system. The proposed fuzzy multistage hysteresis controller not only exhibited small torque and flux ripples, but also improved the performance of the IM drive by using four voltage vectors in a cycle. Measurement results revealed that the proposed ASIC had a dead time and power consumption of 100 ns and 2.457 mW, respectively, at an operating

Conclusions
In this study, an MPDTC ASIC with multistage hysteresis and fuzzy controller was proposed to enhance the stability and control of a 0.75-hp three-phase induction motor. ModelSim software was used to conduct functional simulation, and the Verilog HDL was employed to operate all modules of the proposed MPDTC system. After the designed functions had been verified using an FPGA development board, the proposed ASIC was fabricated using a TSMC 0.18 m 1P6M CMOS process. Simulation results indicated that the stator flux trajectory of the proposed MPDTC ASIC was superior to that of a conventional DTC system with a hysteresis controller. In addition, the simulated torque and flux errors of the proposed MPDTC system were smaller than those of the conventional DTC system. The proposed fuzzy multistage hysteresis controller not only exhibited small torque and flux ripples, but also improved the performance of the IM drive by using four voltage vectors in a cycle. Measurement results revealed that the proposed ASIC had a dead time and power consumption of 100 ns and 2.457 mW, respectively, at an operating

Conclusions
In this study, an MPDTC ASIC with multistage hysteresis and fuzzy controller was proposed to enhance the stability and control of a 0.75-hp three-phase induction motor. ModelSim software was used to conduct functional simulation, and the Verilog HDL was employed to operate all modules of the proposed MPDTC system. After the designed functions had been verified using an FPGA development board, the proposed ASIC was fabricated using a TSMC 0.18 µm 1P6M CMOS process. Simulation results indicated that the stator flux trajectory of the proposed MPDTC ASIC was superior to that of a conventional DTC system with a hysteresis controller. In addition, the simulated torque and flux errors of the proposed MPDTC system were smaller than those of the conventional DTC system. The proposed fuzzy multistage hysteresis controller not only exhibited small torque and flux ripples, but also improved the performance of the IM drive by using four voltage vectors in a cycle. Measurement results revealed that the proposed ASIC had a dead time and power consumption of 100 ns and 2.457 mW, respectively, at an operating frequency of 10 MHz, a sampling rate of 100 kS/s, and a supply voltage of 1.8 V. Furthermore, the gate count and chip area of the proposed ASIC were 99,188 and approximately 1.193 mm × 1.190 mm, respectively. The objective of this study was to integrate the predictive DTC, fuzzy PID controller, multistage hysteresis, and MDMVV switch table into an ASIC, and have small ripples by using four voltage vectors in a cycle. The proposed ASIC achieved good accuracy and robustness.

Conflicts of Interest:
The authors declare no conflict of interest. Table A1 shows all symbols used in Figure 1 to enhance the reader's understanding. Table A1. All symbols used in the block diagram of the proposed MPDTC ASIC (Figure 1).