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

Abstract

This paper proposes a modified predictive direct torque control (MPDTC) application-specific 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.

1. 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; thus, this method retains the simplicity of conventional DTC and produces the same results as DTC SVM with predictive controllers [5].

Compared with conventional proportional–integral–derivative (PID) controllers, the fuzzy PID controller exhibits a more favorable dynamic response and static deviation in a DTC system [6]. In [7], a novel predictive DTC (PDTC) scheme was proposed that maintains the motor torque, stator flux, and inverter’s neutral-point potential within the set hysteresis bounds and minimizes the switching frequency of the inverter to reduce the torque and flux ripples. The complexity of the aforementioned PDTC model results from the computation of the stator flux reference and the prediction of the stator flux in the next cycle. The inverter switching frequency of the aforementioned scheme is on average 16.5% lower than that of a traditional DTC scheme [8]. Computational control solutions are becoming computationally and economically feasible, with versatile and flexible control algorithms being developed for electric motor drives. In comparison with a traditional PID regulator, a fuzzy PID regulator is more effective in improving the speed response and stability of a DTC system. In [9], an alternative control strategy that involved using a permanent-magnet synchronous-motor (PMSM) drive was proposed on the basis of the model system, prediction components, and optimization problem [10,11]. This strategy can improve speed tracking and strengthen robustness against disturbance and uncertainties when the suggested DTC controller is employed.

In [12], a DTC scheme was presented for a matrix-converter-fed IM drive system. A matrix converter is a single-stage AC–AC power conversion device without DC-link energy storage elements. Because of the properties of matrix converters, the pseudo DC-link provides three voltages, namely, high, middle, and low voltages. Three states are observed at each space vector location according to the SVM generated using a matrix converter. By selecting a suitable switching table, the electromagnetic torque ripple of the IM was effectively reduced, and a satisfactory servo drive was achieved. Moreover, no complicated computation was involved in the aforementioned scheme, and the matrix converter constituted a precise servo-drive control system. Next, the hysteresis band (HB) controller was used to enhance dynamic performance. Although the HB controller is extensively used in voltage source inverters and inverter-based drive systems, it is rarely used in matrix converters or matrix-converter-based motor drives [13]. The sinusoidal-band hysteresis controller generated low harmonic content at a high average switching frequency. The aforementioned scheme is simple and has a low computation burden. This scheme can be applied to IMs and other machines, such as PMSMs. A design method was presented for variable structure system control in [14] based on a differential geometric approach, and it was intended to deal with the class of nonlinear systems in the control with uncertainties and disturbances. The main goals of this method are robustness, tuning simplicity, chattering reduction, and reaching mode control. A robust controller was designed for the wind subsystem of an electricity generating hybrid systems (EGHS) [14]. A wind power system under failures was presented in the lubricant system, and a procedure was provided to detect the failure. A model-based fault detection filter was designed to detect DC/DC converter failure in a wind system [15].

A tariff plan is recommended for completely eliminating round-off error and reducing the operations on floating-point numbers [16,17]. Two round-off error models are used in fixed-point arithmetic: a generic model with no assumptions on the predicted system or weight matrices and a parametric model that exploits the Toeplitz structure of the linear model predictive control (MPC) problem for a Schur stable system. The experimental results of these models indicate that the resource usage, computational energy, and execution time vary significantly with the adopted field-programmable gate array (FPGA) [18,19]. Next, the feasibility condition for the design parameters was verified, and the optimized design parameters were rounded off to the nearest feasible design values [20]. Lastly, an application-specific integrated circuit (ASIC) was used to enable the direct control 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.

2. Circuit Design of the Proposed MPDTC ASIC

Figure 1 depicts the block diagram of the proposed MPDTC ASIC with fuzzy seven-stage 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.

2.1. 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]:

$$\left[\begin{array}{c}{v}_{ds}^s\\ v_{qs}^s\end{array}\right]=\left[\begin{array}{cc}1& 0\\ \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{3}$}\right.& \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\sqrt{3}$}\right.\end{array}\right]\left[\begin{array}{c}{v}_{as}^s\\ v_{bs}^s\end{array}\right]$$

(1)

$$\left[\begin{array}{c}{i}_{ds}^s\\ i_{qs}^s\end{array}\right]=\left[\begin{array}{cc}1& 0\\ \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{3}$}\right.& \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\sqrt{3}$}\right.\end{array}\right]\left[\begin{array}{c}{i}_{as}^s\\ i_{bs}^s\end{array}\right]$$

(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:

$$V_{ds}=\frac{V_{dc}}{3}\left(2S_a-S_b-S_c\right)$$

(3)

$$V_{qs}=\frac{\sqrt{3}}{3}{V}_{dc}\left(S_b-S_c\right)$$

(4)

The flux (φ) can be expressed in terms of the single-phase stator winding resistance R_s as follows:

$$\left[\begin{array}{c}{\phi }_{ds}^s\\ {\phi }_{qs}^s\end{array}\right]=\frac{1}{p}\left\{\left[\begin{array}{c}{v}_{ds}^s\\ v_{qs}^s\end{array}\right]-R_s\left[\begin{array}{c}{i}_{ds}^s\\ i_{qs}^s\end{array}\right]\right\}, p=\frac{d}{dt}$$

(5)

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]:

$$\{\begin{array}{c}{\phi }_{ds}^s\left(z\right)=\frac{1}{z}{\phi }_{ds}^s\left(z\right)+T\times \left[V_{ds}^s\left(z\right)-R_s\times i_{ds}^s\left(z\right)\right]\\ {\phi }_{qs}^s\left(z\right)=\frac{1}{z}{\phi }_{qs}^s\left(z\right)+T\times \left[V_{qs}^s\left(z\right)-R_s\times i_{qs}^s\left(z\right)\right]\end{array}$$

(6)

The torque (T_e) is calculated on the basis of DTC theory by using (7), in which P is the number of motor poles.

$$T_e=\frac{3}{2}\frac{P}{2}\left({\phi }_{ds}^s{i}_{qs}^s-{\phi }_{qs}^s{i}_{ds}^s\right)$$

(7)

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.

$${\lambda }_{dqs}^s=\sqrt{{\lambda }_{ds}^2+{\lambda }_{qs}^2}$$

(8)

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.

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:

$$\begin{array}{c}Cal=\left[IN-R{D}^2\right]-\left[{\left(RD+1\right)}^2-IN\right]\\ =2\times \left[IN-RD\times \left(RD+1\right)\right]-1\end{array}$$

(9)

The decision formula can be expressed as follows:

$$\{\begin{array}{l}RO=RD,\hspace{1em}\hspace{1em} if Cal\le 0\hfill \\ RO=RD+1,\hspace{1em}if Cal>0\hfill \end{array}$$

(10)

2.2. 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 S₁ and S₂, which extend from 0° to 30° and from 30° to 90°, respectively. In trigonometry, a relational equation can be expressed as follows:

$$\sqrt{3}\left|{\lambda }_{qs}\right|-\left|{\lambda }_{ds}\right|=0$$

(11)

If magnetic fluxes λ_ds and λ_qs are positive, the result of (11) is negative (<0) for sector S₁ and positive (>0) for sector S₂.

Table 1. Sector selection of the proposed MPDTC ASIC.

$\sqrt{3}\left|{\mathit{\lambda }}_{\mathit{q}\mathit{s}}\right|-\left|{\mathit{\lambda }}_{\mathit{d}\mathit{s}}\right|$	λds	λqs	Output Sector
<0	>0	>0	S1
<0	>0	<0	S1
<0	<0	>0	S4
<0	<0	<0	S4
>0	>0	>0	S2
>0	>0	<0	S6
>0	<0	>0	S3
>0	<0	<0	S5

summarizes the sector selection for the proposed MPDTC ASIC. The output sector can be easily selected using this table [21].

2.3. 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.

2.4. 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:

$$\frac{U\left(s\right)}{E\left(s\right)}=K_p+\frac{K_i}{s}+s{K}_d,$$

(12)

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 Δe(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:

$$K_i=\frac{K_p^2}{\alpha \times K_d}$$

(13)

The operating principle of the PID controller is to determine the output u(t) with three coefficients, which can be calculated as follows:

$$u\left(t\right)=K_{p}e\left(t\right)+K_i{\displaystyle {\int }_o^{t}e\left(\tau \right)}d\tau +K_d\frac{de\left(t\right)}{dt}$$

(14)

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

Table 2. Fuzzy rules of K_P.

	Δe	PB	PS	ZE	NS	NB
e
PB		PB	PB	PB	PB	PB
PS		PS	PB	PB	PB	PS
ZE		PS	PS	PB	PS	PS
NS		PS	PB	PB	PB	PS
NB		PB	PB	PB	PB	PB

,

Table 3. Fuzzy rules of K_d.

	Δe	PB	PS	ZE	NS	NB
e
PB		PS	PS	PS	PS	PS
PS		PB	PB	PS	PB	PB
ZE		PB	PB	PB	PB	PB
NS		PB	PB	PS	PB	PB
NB		PS	PS	PS	PS	PS

and

Table 4. Fuzzy rules of α.

	e	PB	PS	ZE	NS	NB
Δe
PB		2	2	2	2	2
PS		4	3	2	3	4
ZE		5	4	3	4	5
NS		4	3	2	3	4
NB		2	2	2	2	2

, 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.

2.5. Error Fuzzy Controller

Figure 5 presents a block diagram of the error fuzzy controller. Error e_t and error variation Δe_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 Δe_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. Rules for the seven-stage fuzzy controller.

	et	PB	PM	PS	ZE	NS	NM	NB
Δet
PB		NB	NB	NM	NM	NS	NS	ZE
PM		NB	NM	NM	NS	NS	ZE	PS
PS		NB	NM	NS	NS	ZE	PS	PM
ZE		NM	NS	NS	ZE	PS	PS	PM
NS		NM	NS	ZE	PS	PS	PM	PB
NM		NS	ZE	PS	PS	PM	PM	PB
NB		ZE	PS	PS	PM	PM	PB	PB

details the rules for the seven-stage fuzzy controller. In the five-stage hysteresis controller, two input variables, namely, e_t and Δe_t, are divided into five fuzzy sets: NB, NS, ZE, PS, and PB. The rules for this controller are presented in

Table 6. Rules for the five-stage fuzzy controller.

	et	PB	PS	ZE	NS	NB
Δet
PB		NB	NS	NS	ZE	ZE
PS		NB	NS	NS	ZE	PS
ZE		NS	NS	ZE	PS	PS
NS		NS	ZE	PS	PS	PB
NB		ZE	ZE	PS	PS	PB

.

2.6. 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 (Δd_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 (Δd_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. MDMVV switching table.

φ	τ	S1	S2	S3	S4	S5	S6
PB	PB	V2V2V2V2	3333	4444	5555	6666	1111
	PS	V2V2V2V6	3331	4442	5553	6664	1115
	ZE	V2V2V6V6	3311	4422	5533	6644	1155
	NS	V2V6V6V6	3111	4222	5333	6444	1555
	NB	V6V6V6V6	1111	2222	3333	4444	5555
PM	PB	V2V2V2V2	3333	4444	5555	6666	1111
	PS	V2V2V2V7	3330	4447	5550	6667	1110
	ZE	V2V2V6V7	3310	4427	5530	6647	1150
	NS	V2V6V6V7	3110	4227	5330	6447	1550
	NB	V6V6V6V7	1110	2227	3330	4447	5550
PS	PB	V2V2V2V3	3334	4445	5556	6661	1112
	PS	V2V2V2V5	3336	4441	5552	6663	1114
	ZE	V2V6V7V7	3300	4477	5500	6677	1100
	NS	V6V6V6V3	1114	2225	3336	4441	5552
	NB	V6V6V6V5	1116	2221	3332	4443	5554
ZE	PB	V2V2V3V3	3344	4455	5566	6611	1122
	PS	V2V7V3V7	3040	4757	5060	6717	1020
	ZE	V2V3V5V6	3461	4512	5623	6134	1245
	NS	V2V7V5V0	3067	4710	5027	6730	1047
	NB	V6V5V0V0	1677	2100	3277	4300	5477
NS	PB	V3V3V3V2	4443	5554	6665	1116	2221
	PS	V3V3V3V6	4441	5552	6663	1114	2225
	ZE	V3V3V0V0	4477	5500	6677	1100	2277
	NS	V5V5V5V2	6663	1114	2225	3336	4441
	NB	V5V5V5V6	6661	1112	2223	3334	4445
NM	PB	V3V3V3V0	4447	5550	6667	1110	2227
	PS	V5V3V3V0	6447	1550	2667	3110	4227
	ZE	V5V5V3V0	6647	1150	2267	3310	4427
	NS	V5V5V5V0	6667	1110	2227	3330	4447
	NB	V5V5V5V5	6666	1111	2222	3333	4444
NB	PB	V3V3V3V3	4444	5555	6666	1111	2222
	PS	V3V3V3V5	4446	5551	6662	1113	2224
	ZE	V3V3V5V5	4466	5511	6622	1133	2244
	NS	V5V5V5V3	6664	1115	2226	3331	4442
	NB	V5V5V5V5	6666	1111	2222	3333	4444

presents the MDMVV switching table.

If the MDMVV has a large positive flux (PB) and positive torque (PB) in sector S₁, the output voltage set was selected to be V₂V₂V₂V₂, which is denoted as 2222 in Example (1). Each voltage (V₂) 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. Rules for the five-state fuzzy controller.

Example	(1)	(2)	(3)	(4)
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	↑↑↑↑ (+4)	↑↓↓↓ (−2)	↑↑↓↓ (+0)	↓↓↓↓ (−4)
Flux	↑↑↑↑ (+4)	↑-↓- (+0)	↑↓↓↑ (+0)	↓↓↓↓ (−4)

, 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 V₂V₇V₅V₀, 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 = T₁ = T₂ = T₃ = T₄). If current torque T_e was considerably lower than recommend torque T^*_e (NB) in sector S₁, voltage set V₂V₂V₂V₂ 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 S₁ (T^*_e). According to Table 7, the aforementioned condition could be achieved using voltage set V₂V₇V₅V₀, as illustrated in Figure 10. When this voltage set was used, T_e was close to T^*_e.

2.7. 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.

3. 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, T₁, T₂, T₃, and T₄, after passing through the fuzzy controller, fuzzy hysteresis, and MDMVV switching table.

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 (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.

Table 9. System specifications of proposed MPDTC ASIC.

Items	Specifications
Technology	0.18-μm 1P6M CMOS
Supplied Voltage	1.8 V
Test Coverage	95.64%
Fault Coverage	93.28%
Operating Frequency	10 MHz
Sampling rate	100 kS/s
Power Consumption	2.457 mW
Gate Counts	99,188
Chip Size	1.193 mm × 1.190 mm
Pins	35

summarizes the system specifications of the proposed MPDTC ASIC. According to the simulation results, the proposed MPDTC had a test coverage of 95.64%, a fault coverage of 93.28%, and a power consumption of 2.457 mW at an operating frequency of 10 MHz and a supply voltage of 1.8 V. The gate count and chip area of this circuit (inclusive of the pads) were 99,188 and approximately 1.193 mm × 1.190 mm, respectively.

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.

Figure 20 depicts measured line currents I_as and I_bs at a sampling frequency of 100 kHz and a rotation frequency of 1200 rpm for a three-phase, 0.75-kW IM. As presented in (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.

4. 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.