Performance of a Vector-Controlled PMSM Drive without Using Current Sensors

: The current sensorless vector-controlled permanent-magnet synchronous motor (PMSM) drive using a single sensor (i.e., speed sensor) is presented in this work. The current sensors are removed, and the estimated currents are used to close the current loop to minimize the drive cost and make it fault-tolerant against current sensor failure. A classical vector-control PMSM drive requires at least three sensors, i.e., two current sensors and one speed/position sensor. This paper presents a new current estimation technique that is free from inverter switching states, an integrator, and differentiator terms. The drive is suitable for retroﬁt applications, as it does not require any additional hardware. The reference voltages ( v ds and v qs ) are used to estimate the rotor reference frame currents (i.e., i qs and i ds ). The presented algorithm depends on the stator resistance (


Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in ntrolled permanent-magnet synchronous motor (PMSM) nsor) is presented in this work. The current sensors are used to close the current loop to minimize the drive cost sensor failure. A classical vector-control PMSM drive rerent sensors and one speed/position sensor. This paper e that is free from inverter switching states, an integrator, table for retrofit applications, as it does not require any ges ( and ) are used to estimate the rotor reference ented algorithm depends on the stator resistance (Ɍ ). The r compensation to overcome the effect of the Ɍ on the is for the currents against the speed is verified and preal speed information, which will try to maintain the refe proposed current sensorless PMSM drive was validated d on a hardware prototype. The presented technique was and some of the extensive results are presented. Ɍ or; PMSM; vector control chronous machines) have been gaining a strong ine characteristics meet the electric vehicle drive opinertia ratio and minimum copper losses with high uccessfully at the required speed and load [1]. A other machines [1]. Vector-control drive has an exspeed/position data are accessed from a sensor atlling the drive. In general, a three-phase PMSM rerotor position information to compute the rotating tion can be caused by sensor parameters, such as in poorer performance [3]. The failure of the sensor ns and high ambient temperature, which results in

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in drive instability. The decrease in the sensors in the drive will lower the failure rate, increase the reliability, and reduce the cost of the drive. This paper mainly concerns the reduction of the sensor's dependability (i.e., current sensors), increasing the drive reliability, and making it fault-tolerant. In the literature, current sensor reduction/elimination is discussed. This section starts with a brief overview of the various current estimating techniques for current sensor reduction, and then it is carried out with the proposed estimation technique.
In the literature, there are a few single-current sensor-based drive approaches. Based on the placement of the current sensor in the inverter, the reconstruction of three-phase currents is divided into a DC-link current measurement, measuring multiple branch current measurements with a single current sensor, and a single-phase current measurement [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Three-phase currents are reconstructed based on the DC-link current, voltage, and inverter switching information [8,10,[19][20][21][22]. Although DC-link current measurement is a common strategy, it has certain drawbacks: low modulation index, active-switching states at the sector boundary/short duration, and phase variation in the estimated currents, which are all factors to consider. A few solutions for enhancing the phase current accuracy in the reconstruction in all four-quadrant regions have been given in the literature. Under the zero-voltage vector sampling zone, an isolated current sensor technique is used to detect phase currents matching the DC-link current [4]. The measurement vector insertion approach was adopted to overcome the difficulty of switching states in a short period [23]. In [16], it shows how to measure phase currents in a low-modulation index or a near-sector boundary region. These approaches rely on the DC-link current and inverter switching states to reconstruct the phase currents and require an extremely complicated analysis.
A current sensor is used to measure the current passing through multiple branches [4][5][6]9,10,12]. The three-phase currents are reconstructed using the advantage of switching states and the sum of the branch currents. In this method, a current sensor is employed to measure more than the rated current [12], which increases the current sensor's cost.
The estimation of the current without using a DC-link current sensor is presented in [21,[24][25][26][27][28][29][30][31]. These methods use either a speed encoder/voltage sensor/single-phase current measurement and an accurate machine model to estimate the currents. The current sensor detects the single-phase current, and using an observer design approach, the remaining phase currents are estimated [32]. The PMSM drive current sensorless procedure makes the drive more robust, cost effective, and reliable. References [25,33] present a PMSM drive prediction approach based on a current sensorless extended Kalman-filtered operation. This approach is mostly machine-dependent and involves both the initial conditions and filters.
A new technique is presented for current estimation with a low precession speed/ position sensor for a PMSM drive. In the d and q axes frame, the current estimation was constructed on machine formulae. The dead-time was employed to make the delay caused by the machine and inverter in real time. This process was simulated in MATLAB/Simulink and verified for various conditions and verified for a four-quadrant operation.
To overcome the drawbacks in the existing methods, the paper presents a new method for a current sensorless approach. The proposed method has several advantages. As it does not require any additional sensors or hardware, it makes the drive suitable for retrofit applications. The current estimation technique can be used to monitor the status of current sensors by implementing them in the existing PMSM drive. A speed sensor was employed to perform the drive operation, and the current estimation technique reduces the drive cost and complexity. The reliability and immunity to signal noise are increased, as a single sensor is used, i.e., speed/position sensor. The proposed drive is independent of the switching states, an integrator, and differentiator terms.
A current sensorless algorithm for a PMSM drive; An algorithm that is independent of an integrator and differentiator terms; The algorithm can be applied with a low-resolution speed sensor; The overall drive cost can be reduced for low-precession applications; Has a reduced current sensor dependency; The proposed current estimation method can be used to make the existing PMSM drives (which use all of the current sensors) fault-tolerant against failure of the current sensors.
The following is a summary of the structure of the paper. In Section 2, the modeling of the PMSM is discussed. Section 3 explains the mathematical model of the current estimating scheme. In Section 4, a sensitivity analysis is performed and presented. In Section 5, the proposed drive is validated using the MATLAB/Simulink platform, and the results are provided to show the performance under various conditions. On the dSPACE 1104-based laboratory prototype, the current sensorless PMSM drive is validated, and the results are presented in Section 6. Finally, in Section 7, this work is concluded.

Modeling of PMSM
Reference [1] was used to model the PMSM machine. The stator currents (i.e., "d" and "q" axes) in the rotor-reference frame for the PMSM are shown in (1).  The overall drive cost can be reduced for low-precession applications;  Has a reduced current sensor dependency;  The proposed current estimation method can be used to make the existing PMSM drives (which use all of the current sensors) fault-tolerant against failure of the current sensors.
The following is a summary of the structure of the paper. In Section 2, the modeling of the PMSM is discussed. Section 3 explains the mathematical model of the current estimating scheme. In Section 4, a sensitivity analysis is performed and presented. In Section 5, the proposed drive is validated using the MATLAB/Simulink platform, and the results are provided to show the performance under various conditions. On the dSPACE 1104based laboratory prototype, the current sensorless PMSM drive is validated, and the results are presented in Section 6. Finally, in Section 7, this work is concluded.

Modeling of PMSM
Reference [1] was used to model the PMSM machine. The stator currents (i.e., " " and " " axes) in the rotor-reference frame for the PMSM are shown in (1).
The electromagnetic torque is expressed as shown in (2). The electromechanical dynamics equation is shown in (3). Þ = derivative − term (d/dt); ω = P ω ; and the machine was a nonsaliency type with a sinusoidal back-EMF waveform, where Ƭ and Ƭ are the electric-torque and load-torque, respectively. Table 1 shows the PMSM machine's parameters.

Current Sensorless Methodology
In the " " and " " axes frame, the proposed method estimates the currents using the machine modeling in Equation (1). In the rotor reference frame, the stator voltages were defined as in (4) and (5), where and show the actual and axes stator currents; and show the estimated and axes stator currents; and * and * represent the and axes reference currents.
Under a steady-state operation, the differential terms are considered as zero.
The electromagnetic torque is expressed as shown in (2). The electromechanical dynamics equation is shown in (3). = derivative − term (d/dt); ω s = P ω r ; and the machine was a nonsaliency type with a sinusoidal back-EMF waveform, where T e and T L are the electric-torque and load-torque, respectively. Table 1 shows the PMSM machine's parameters. , and ). The presented algorithm depends on the stator resistance (Ɍ ). The ation algorithm is used for compensation to overcome the effect of the Ɍ on the nts. The sensitivity analysis for the currents against the speed is verified and preed loop is closed with actual speed information, which will try to maintain the refder any circumstances. The proposed current sensorless PMSM drive was validated /Simulink and also verified on a hardware prototype. The presented technique was ous operation conditions, and some of the extensive results are presented. Ɍ ent estimation; speed sensor; PMSM; vector control n permanent-magnet synchronous machines) have been gaining a strong inpast decades. Its unique characteristics meet the electric vehicle drive op-, with a higher torque/inertia ratio and minimum copper losses with high the PMSM operates successfully at the required speed and load [1]. A ller in size compared to other machines [1]. Vector-control drive has an exic performance [2]. The speed/position data are accessed from a sensor atachine shaft for controlling the drive. In general, a three-phase PMSM retwo phase currents and rotor position information to compute the rotating e currents [1,2]. ipple in the drive operation can be caused by sensor parameters, such as ift, and offset, resulting in poorer performance [3].

Current Sensorless Methodology
In the "d" and "q" axes frame, the proposed method estimates the currents using the machine modeling in Equation (1). In the rotor reference frame, the stator voltages were defined as in (4) and (5), where i ds and i qs show the actual d and q axes stator currents; i e ds and i e qs show the estimated d and q axes stator currents; and i * ds and i * qs represent the d and q axes reference currents.  The overall drive cost can be reduced for low-precession applications;  Has a reduced current sensor dependency;  The proposed current estimation method can be used to make the existing PMSM drives (which use all of the current sensors) fault-tolerant against failure of the current sensors.
The following is a summary of the structure of the paper. In Section 2, the modeling of the PMSM is discussed. Section 3 explains the mathematical model of the current estimating scheme. In Section 4, a sensitivity analysis is performed and presented. In Section 5, the proposed drive is validated using the MATLAB/Simulink platform, and the results are provided to show the performance under various conditions. On the dSPACE 1104based laboratory prototype, the current sensorless PMSM drive is validated, and the results are presented in Section 6. Finally, in Section 7, this work is concluded.

Modeling of PMSM
Reference [1] was used to model the PMSM machine. The stator currents (i.e., " " and " " axes) in the rotor-reference frame for the PMSM are shown in (1).
The electromagnetic torque is expressed as shown in (2). The electromechanical dynamics equation is shown in (3). Þ = derivative − term (d/dt); ω = P ω ; and the machine was a nonsaliency type with a sinusoidal back-EMF waveform, where Ƭ and Ƭ are the electric-torque and load-torque, respectively. Table 1 shows the PMSM machine's parameters.

Current Sensorless Methodology
In the " " and " " axes frame, the proposed method estimates the currents using the machine modeling in Equation (1). In the rotor reference frame, the stator voltages were defined as in (4) and (5), where and show the actual and axes stator currents; and show the estimated and axes stator currents; and * and * represent the and axes reference currents.
Under a steady-state operation, the differential terms are considered as zero. Under a steady-state operation, the differential terms are considered as zero.
taking from * in for (6) and in for (7). The currents on the and axes are calculated and presented as and . Figure 1 shows a flow chart for the proposed current estimation method. From Figure  1, the outer speed loop from the motor speed sensor maintains the voltage gains to maintain the estimated currents in a closed loop.

Sensitivity Analysis
In this secession, the sensitivity [34] of the estimated currents against variation was performed. The taking i qs from i * qs in i e ds for (6) and i e ds in i ds for (7). The currents on the d and q axes are calculated and presented as i e ds and i e qs . Figure 1 shows a flow chart for the proposed current estimation method. From Figure 1, the outer speed loop from the motor speed sensor maintains the voltage gains to maintain the estimated currents in a closed loop. athematics 2022, 10, x FOR PEER REVIEW V = Ɍ i − ω = Ɍ + + ω λ taking from * in for (6) and in for (7). The currents on the are calculated and presented as and .
= * + * = * − − Figure 1 shows a flow chart for the proposed current estimation method 1, the outer speed loop from the motor speed sensor maintains the voltage g tain the estimated currents in a closed loop.

Sensitivity Analysis
In this secession, the sensitivity [34] of the estimated currents against was performed. The

Sensitivity Analysis
In this secession, the sensitivity [34] of the estimated currents against ω r variation was performed. The Let, These r n (n = 1,2,3&4) are the transfer functions of the PI controllers of the speed loop and the q axes and d axes current loops.

PI-current
∆v * ds is expressed as As i * ds = 0 From (17) and (18) ∆v * qs is expressed as Using a small-signal analysis, the expressions for ∆i e ds and ∆i e qs become: ∆i e ds is expressed as where ∆i e qs is expressed as Mathematics 2022, 10, 4623 The sensitivity plot for the estimated currents is shown in Figure 3 for the ω r variation.

Figure 3a presents
∆i e qs ∆ω r with respect to the ω r variation. Figure 3b presents ∆i e ds ∆ω r with respect to the ω r variation. The performance of the estimated current is presented with the speed (ω r ). The sensitivity is shown for the motoring and regenerating mode operation range with a 10 N·m load. The outer loop was closed with the actual speed information from the sensor; thus, the drive stabilized itself to maintain the shaft speed at the reference speed. from the sensor; thus, the drive stabilized itself to maintain the shaft speed at the reference speed.

Simulation Results
This work presents a position or speed sensor-based vector-controlled PMSM drive for the current sensorless scheme. A schematic diagram is shown in Figure 2. References [1,2] present the switching sequence, vector-control, and mathematical model for the PMSM drive. Under various operating speeds/loads, the PMSM drive with the current sensorless algorithm was modeled and tested in MATLAB/Simulink, and some of the results are demonstrated to show the performance of the PMSM drive. The speed loop was closed using data acquired from the speed sensor, while the currents were closed with the estimated quantities. Table 1 shows the machine's parameter obtained from a laboratory prototype of the PMSM machine.
The actual currents axes and the estimated currents axes are shown in the rotor-reference frames. = 0 denotes a successful vector-control operation, whereas denotes the torque-producing current component. The simulation plots the shaft speed ( ) against the reference speed ( * ), and the position is displayed. The drive performance is presented for the various reference speed commands, and the simulation results confirmed the performance of the proposed method. The drive was verified for the ramp speed command, step speed command, and four-quadrant operation. To check the accuracy of the estimated values, the actual currents, reference currents, and estimated currents are shown on the same graph in the simulation results.

Various Speed Operations
The current sensorless PMSM drive was evaluated for various speed operations, and the simulation results are presented in Figure 4. The current sensors were used to observe the actual currents and verify the estimation technique performance. The estimated current followed the actual currents observed from the simulation results presented in Figure  2. To demonstrate the accuracy of the current estimation technique, the and axes estimated and the actual currents are plotted on the same scale in Figure 4.

Simulation Results
This work presents a position or speed sensor-based vector-controlled PMSM drive for the current sensorless scheme. A schematic diagram is shown in Figure 2. References [1,2] present the switching sequence, vector-control, and mathematical model for the PMSM drive. Under various operating speeds/loads, the PMSM drive with the current sensorless algorithm was modeled and tested in MATLAB/Simulink, and some of the results are demonstrated to show the performance of the PMSM drive. The speed loop was closed using data acquired from the speed sensor, while the currents were closed with the estimated quantities. Table 1 shows the machine's parameter obtained from a laboratory prototype of the PMSM machine.
The actual currents dq axes and the estimated currents dq axes are shown in the rotorreference frames. i ds = 0 denotes a successful vector-control operation, whereas i qs denotes the torque-producing current component. The simulation plots the shaft speed (w r ) against the reference speed (w * r ), and the position is displayed. The drive performance is presented for the various reference speed commands, and the simulation results confirmed the performance of the proposed method. The drive was verified for the ramp speed command, step speed command, and four-quadrant operation.
To check the accuracy of the estimated values, the actual currents, reference currents, and estimated currents are shown on the same graph in the simulation results.

Various Speed Operations
The current sensorless PMSM drive was evaluated for various speed operations, and the simulation results are presented in Figure 4. The current sensors were used to observe the actual currents and verify the estimation technique performance. The estimated current

Drive Performance for the Ramp Speed Command
The drive was verified and tested for the ramp command, and the results are shown in Figure 5 under varied load and speed circumstances. The tracking performance was tested for the ramp-type speed (i.e., slow zero crossings). The reference speed was changed in a slow ramp command with +10 to −10 rad/s. The PMSM was connected with the DC generator-type load (i.e., load). The was maintained at zero, reflects the q-axes vector-control operation. The estimated and actual torque-producing stator current components are presented on the same scale. The current estimation technique's performance is shown in Figure 5 for the ramp speed command and slow zero crossings.

Drive Performance for the Ramp Speed Command
The drive was verified and tested for the ramp command, and the results are shown in Figure 5 under varied load and speed circumstances. The tracking performance was tested for the ramp-type speed (i.e., slow zero crossings). The reference speed was changed in a slow ramp command with +10 to −10 rad/s. The PMSM was connected with the DC generator-type load (i.e., Kω r load). The i ds was maintained at zero, reflects the q-axes vector-control operation. The estimated and actual i qs torque-producing stator current components are presented on the same scale. The current estimation technique's performance is shown in Figure 5 for the ramp speed command and slow zero crossings.

Drive performance for Step Speed Command
The simulation results for the proposed technique for the step speed command are illustrated in Figure 6. Initially, the reference speed was set at ten rad/s, and the speed was altered between ±10 rad/s. The DC generator-type load (i.e., Kω r load) was acting on the PMSM. It was observed that the estimated and actual dq axes stator currents were comparably similar. The estimated currents and actual currents are shown on the same scale to demonstrate the accuracy of the proposed current estimation technique.

Drive performance for Step Speed Command
The simulation results for the proposed technique for the step speed command are illustrated in Figure 6. Initially, the reference speed was set at ten rad/s, and the speed was altered between ±10 rad/s. The DC generator-type load (i.e., load) was acting on the PMSM. It was observed that the estimated and actual axes stator currents were comparably similar. The estimated currents and actual currents are shown on the same scale to demonstrate the accuracy of the proposed current estimation technique.  Figure 7 shows a four-quadrant operation. The machine was initially set to +10 rad/s and 8 N·m. The reference speed was changed from +10 to 0, −10, and +10 rad/s at t = 2, 3, and 6 s. The load was changed within ±8 N·m at t = 4 and 7 s.  Figure 7 shows a four-quadrant operation. The machine was initially set to +10 rad/s and 8 N·m. The reference speed was changed from +10 to 0, −10, and +10 rad/s at t = 2, 3, and 6 s. The load was changed within ±8 N·m at t = 4 and 7 s. Figure 6. The drive was tested for the forward motoring and reverse motoring operations for the ramp step commands Figure 7 shows a four-quadrant operation. The machine was initially set to +10 rad/s and 8 N·m. The reference speed was changed from +10 to 0, −10, and +10 rad/s at t = 2, 3, and 6 s. The load was changed within ±8 N·m at t = 4 and 7 s.  The PMSM was coupled with a DC motor, and for the first two seconds, the torque and speed were both positive, resulting in the first quadrant operation. The DC motor produced the torque in the same direction as the PMSM. In the simulation results, a zero-speed operation with a positive load was demonstrated.

Drive Performance for the Four-Quadrant Operation
From t = 2 to 3 s, the DC motor pushed the PMSM machine and acted as a generator until the speed was negative and the torque was positive. From t = 4 s to t = 6 s, the torque was negative, and the speed was negative, resulting in the third quadrant reverse motoring action. From t = 6 s to t = 7 s, the torque was negative, and the speed was positive, resulting in a second quadrant operation. The DC motor pushed the PMSM machine, which acted as a generator. The position information provides the accuracy of the presented algorithm for a zero-speed and four-quadrant operation. e current sensorless vector-controlled permanent-magnet synchronous motor (PMSM) a single sensor (i.e., speed sensor) is presented in this work. The current sensors are d the estimated currents are used to close the current loop to minimize the drive cost fault-tolerant against current sensor failure. A classical vector-control PMSM drive rest three sensors, i.e., two current sensors and one speed/position sensor. This paper w current estimation technique that is free from inverter switching states, an integrator, tiator terms. The drive is suitable for retrofit applications, as it does not require any rdware. The reference voltages ( and ) are used to estimate the rotor reference ts (i.e., , and ). The presented algorithm depends on the stator resistance (Ɍ ). The timation algorithm is used for compensation to overcome the effect of the Ɍ on the rrents. The sensitivity analysis for the currents against the speed is verified and prepeed loop is closed with actual speed information, which will try to maintain the refunder any circumstances. The proposed current sensorless PMSM drive was validated AB/Simulink and also verified on a hardware prototype. The presented technique was arious operation conditions, and some of the extensive results are presented. Ɍ urrent estimation; speed sensor; PMSM; vector control tion s (permanent-magnet synchronous machines) have been gaining a strong inthe past decades. Its unique characteristics meet the electric vehicle drive opria, with a higher torque/inertia ratio and minimum copper losses with high and the PMSM operates successfully at the required speed and load [1]. A aller in size compared to other machines [1]. Vector-control drive has an examic performance [2]. The speed/position data are accessed from a sensor ate machine shaft for controlling the drive. In general, a three-phase PMSM re-s ) The method was tested for the parameter change, and the simulation results are displayed in Figure 8. The current loop was closed with the estimated d and q axes current quantities. The machine resistance was varied with +0.2 ohms from t =10 s to t = 12 s. The effect of the parameter variation was observed on the vector-control (as i ds = 0), and the simulation results are given in Figure 8 sensorless vector-controlled permanent-magnet synchronous motor (PMSM) ensor (i.e., speed sensor) is presented in this work. The current sensors are mated currents are used to close the current loop to minimize the drive cost ant against current sensor failure. A classical vector-control PMSM drive reensors, i.e., two current sensors and one speed/position sensor. This paper estimation technique that is free from inverter switching states, an integrator, s. The drive is suitable for retrofit applications, as it does not require any The reference voltages ( and ) are used to estimate the rotor reference , and ). The presented algorithm depends on the stator resistance (Ɍ ). The algorithm is used for compensation to overcome the effect of the Ɍ on the e sensitivity analysis for the currents against the speed is verified and prep is closed with actual speed information, which will try to maintain the ref- ., speed sensor) is presented in this work. The current sensors are rrents are used to close the current loop to minimize the drive cost st current sensor failure. A classical vector-control PMSM drive re-., two current sensors and one speed/position sensor. This paper n technique that is free from inverter switching states, an integrator, rive is suitable for retrofit applications, as it does not require any ence voltages ( and ) are used to estimate the rotor reference ). The presented algorithm depends on the stator resistance (Ɍ ). The is used for compensation to overcome the effect of the Ɍ on the ity analysis for the currents against the speed is verified and prewith actual speed information, which will try to maintain the reftances. The proposed current sensorless PMSM drive was validated lso verified on a hardware prototype. The presented technique was onditions, and some of the extensive results are presented. Ɍ speed sensor; PMSM; vector control s compensation to avoid the impact of the machine's parameters.

Effect of the Stator Resistance (Ɍ )
The method was tested for the parameter change, and the simulation results are displayed in Figure 8. The current loop was closed with the estimated d and q axes current quantities. The machine resistance was varied with +0.2 ohms from t =10 s to t = 12 s. The effect of the parameter variation was observed on the vector-control (as ≠ 0), and the simulation results are given in Figure 8. The estimated and the actual currents were affected from t = 10 s, with the Ɍ variation effect. Therefore, the drive requires the estimation algorithm with Ɍ compensation to avoid the impact of the machine's parameters. Figure 8. The drive was tested for the stator-resistance variation.

Stator Resistance Compensation
The procedure was verified for the Ɍ variation with online estimation [34] and compensation. The algorithm failed to estimate the actual − currents under Ɍ variation. The online Ɍ estimation algorithm was used to estimate and compensate for the current estimation algorithm. The machine was loaded with the load. The speed command was changed in a ramp form and maintained constant at five rad/s. The Ɍ was

Stator Resistance Compensation
The procedure was verified for the 390 troduction PMSMs (permanent-magnet synchronous machines) have been gaining a strong inst over the past decades. Its unique characteristics meet the electric vehicle drive opion criteria, with a higher torque/inertia ratio and minimum copper losses with high iency, and the PMSM operates successfully at the required speed and load [1]. A M is smaller in size compared to other machines [1]. Vector-control drive has an exnt dynamic performance [2]. The speed/position data are accessed from a sensor ated to the machine shaft for controlling the drive. In general, a three-phase PMSM rees at least two phase currents and rotor position information to compute the rotating rence frame currents [1,2]. Torque ripple in the drive operation can be caused by sensor parameters, such as errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor rs under heavily loaded conditions and high ambient temperature, which results in s variation with online estimation [34] and compensation. The algorithm failed to estimate the actual dq-axes currents under Mathematics 2022, 10, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/mathematics

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in  tor-controlled permanent-magnet synchronous motor (PMSM) ed sensor) is presented in this work. The current sensors are s are used to close the current loop to minimize the drive cost rrent sensor failure. A classical vector-control PMSM drive reo current sensors and one speed/position sensor. This paper hnique that is free from inverter switching states, an integrator, is suitable for retrofit applications, as it does not require any voltages ( and ) are used to estimate the rotor reference presented algorithm depends on the stator resistance (Ɍ ). The sed for compensation to overcome the effect of the Ɍ on the nalysis for the currents against the speed is verified and preh actual speed information, which will try to maintain the refes. The proposed current sensorless PMSM drive was validated erified on a hardware prototype. The presented technique was ions, and some of the extensive results are presented. Ɍ sensor; PMSM; vector control t synchronous machines) have been gaining a strong innique characteristics meet the electric vehicle drive opque/inertia ratio and minimum copper losses with high tes successfully at the required speed and load [1]. A ed to other machines [1]. Vector-control drive has an ex-. The speed/position data are accessed from a sensor atontrolling the drive. In general, a three-phase PMSM res and rotor position information to compute the rotating operation can be caused by sensor parameters, such as lting in poorer performance [3]. The failure of the sensor ditions and high ambient temperature, which results in s estimation algorithm was used to estimate and compensate for the current estimation algorithm. The machine was loaded with the kw r load. The speed command was changed in a ramp form and maintained constant at five rad/s. The

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in . Figure 9 confirms the satisfactory results for the Ɍ estimation and compensation to the current estimation algorithm. Figure 9. The drive was tested for the online stator-resistance estimation and compensation.

Hardware Validation
The presented method was validated experimentally on a laboratory prototype using dSPACE 1104 (shown in Figure 10). The drive consisted of the DC generator, PMSM, inverter, driver and protection circuit, and dSPACE 1104. The current sensorless PMSM drive was verified for various conditions; some are presented to show the performance of the proposed algorithm. The experimental results show the shaft speed ( ), reference speed ( ) , actual and axes stator currents ( and ), and estimated and axes stator currents ( and ), and axes reference currents ( * and * ), and Figure 9. The drive was tested for the online stator-resistance estimation and compensation.

Hardware Validation
The presented method was validated experimentally on a laboratory prototype using dSPACE 1104 (shown in Figure 10). The drive consisted of the DC generator, PMSM, inverter, driver and protection circuit, and dSPACE 1104. The current sensorless PMSM drive was verified for various conditions; some are presented to show the performance of the proposed algorithm. The experimental results show the shaft speed (ω r ), reference speed (ω re f ), actual d and q axes stator currents (i ds and i qs ), and estimated d and q axes stator currents (i e ds and i e qs ), d and q axes reference currents (i * ds and i * qs ), and the position.
The dSPACE-based laboratory interface is more flexible for verifying the alg and advantageous for testing in various applications, such as robotics and electri The dSPACE 1104 is more suitable for a laboratory interface with a cost-effect time processor with an I/O interface. The dSPACE is user friendly with MATL ulink (the Realtime Interface provides Simulink with blocks for the I/O config Using the DS1104, the Simulink block was interfaced with the I/O graphically, code was generated for the Realtime Interface (RTI). The model was compiled a into the DS1104 controller board connected with the PC.
The I/O signals were accessed via an adapter cable from the CP1104 (connect to the DS1104 controller board. The CP1104 had eight ADCs and eight DACs, I/O, a slave I/O PWM, two incremental encoders, and serial communication: RS RS485. For the IPMSM drive, two ADCs were used: one for speed information other for the current sensor information. The controller board computed the cont rithm, and three-pulse width modulation (PWM) signals with 5 V were generate CP1104 (slave I/O PWM). Three PWM pulses were sent to the driver circuit boa the dSPACE-1104 PWM I/O board. Six PWM pulses of 15 V (three inverting a noninverting PWMs) were generated using three PWM pulses. The pulses were g with a dead band of 2 µsec to the SKYPER 32 R (SEMIKRON) driver circuit in the The dSPACE-based laboratory interface is more flexible for verifying the algorithms and advantageous for testing in various applications, such as robotics and electric drives. The dSPACE 1104 is more suitable for a laboratory interface with a cost-effective, real-time processor with an I/O interface. The dSPACE is user friendly with MATLAB/Simulink (the Realtime Interface provides Simulink with blocks for the I/O configuration). Using the DS1104, the Simulink block was interfaced with the I/O graphically, and the code was generated for the Realtime Interface (RTI). The model was compiled and built into the DS1104 controller board connected with the PC.
The I/O signals were accessed via an adapter cable from the CP1104 (connector panel) to the DS1104 controller board. The CP1104 had eight ADCs and eight DACs, a digital I/O, a slave I/O PWM, two incremental encoders, and serial communication: RS232 and RS485. For the IPMSM drive, two ADCs were used: one for speed information and the other for the current sensor information. The controller board computed the control algorithm, and three-pulse width modulation (PWM) signals with 5 V were generated on the CP1104 (slave I/O PWM). Three PWM pulses were sent to the driver circuit board from the dSPACE-1104 PWM I/O board. Six PWM pulses of 15 V (three inverting and three noninverting PWMs) were generated using three PWM pulses. The pulses were generated with a dead band of 2 µsec to the SKYPER 32 R (SEMIKRON) driver circuit in the inverter. The Semikron driver circuit could control the IGBT (SKM75GB12T4) switching in the inverter.

Variable Speed Operations
This section shows the experimental results for the current sensorless PMSM drive under various speed commands and slowly zero crossings. The current sensors were used to observe the actual currents and to verify the estimation technique's performance. The estimated current followed the actual currents that can be observed in Figure 11. The actual currents and estimated currents were plotted on the same graph to see the accuracy of the estimated quantities.
R PEER REVIEW 14 of 19 Figure 11. Experimental results for the forward and reverse motoring operations. Figure 12 shows the experimental results for the ramp speed command. The speed command changed between 15 and −15 rad/s in a ramp form. The machine was loaded with a DC generator-type load. The machine was started from a standstill position to 15 rad/s in a ramp form. The drive performance confirmed the ramp speed change with zero crossing also.  Figure 12 shows the experimental results for the ramp speed command. The speed command changed between 15 and −15 rad/s in a ramp form. The machine was loaded with a DC generator-type load. The machine was started from a standstill position to 15 rad/s in a ramp form. The drive performance confirmed the ramp speed change with zero crossing also.

Drive Operation for the
Step Speed Command Figure 13 shows the experimental results for the step speed change. The machine was loaded with a DC generator-type load. The speed command was altered up to ±10 rad/s in a step form. The drive was verified for the step command, and the results confirmed the performance of the presented algorithm.

Drive Operation with Online Rotor Resistance Estimation and Compensation
The dive performance was verified for the Ɍ variation, with online Ɍ estimation and compensation. Figure 14 shows the actual shaft speed and reference speed command,

Drive Operation for the
Step Speed Command Figure 13 shows the experimental results for the step speed change. The machine was loaded with a DC generator-type load. The speed command was altered up to ±10 rad/s in a step form. The drive was verified for the step command, and the results confirmed the performance of the presented algorithm.

Drive Operation for the
Step Speed Command Figure 13 shows the experimental results for the step speed change. The machine was loaded with a DC generator-type load. The speed command was altered up to ±10 rad/s in a step form. The drive was verified for the step command, and the results confirmed the performance of the presented algorithm.

Drive Operation with Online Rotor Resistance Estimation and Compensation
The dive performance was verified for the Ɍ variation, with online Ɍ estimation and compensation. Figure 14 shows the actual shaft speed and reference speed command,

Drive Operation with Online Rotor Resistance Estimation and Compensation
The dive performance was verified for the oi.org/10.3390/xxxxx www.mdpi.com/journal/mathematics presents a new current estimation technique that is free from inverter switching states, an integrator, and differentiator terms. The drive is suitable for retrofit applications, as it does not require any additional hardware. The reference voltages ( and ) are used to estimate the rotor reference frame currents (i.e., , and ). The presented algorithm depends on the stator resistance (Ɍ ). The online Ɍ estimation algorithm is used for compensation to overcome the effect of the Ɍ on the estimated currents. The sensitivity analysis for the currents against the speed is verified and presented. The speed loop is closed with actual speed information, which will try to maintain the reference speed under any circumstances. The proposed current sensorless PMSM drive was validated using MATLAB/Simulink and also verified on a hardware prototype.

Introduction
PMSMs (permanent-magnet synchronous machines) have been gaining a strong interest over the past decades. Its unique characteristics meet the electric vehicle drive operation criteria, with a higher torque/inertia ratio and minimum copper losses with high efficiency, and the PMSM operates successfully at the required speed and load [1]. A PMSM is smaller in size compared to other machines [1]. Vector-control drive has an excellent dynamic performance [2]. The speed/position data are accessed from a sensor attached to the machine shaft for controlling the drive. In general, a three-phase PMSM requires at least two phase currents and rotor position information to compute the rotating reference frame currents [1,2].
Torque ripple in the drive operation can be caused by sensor parameters, such as gain errors, drift, and offset, resulting in poorer performance [3]. The failure of the sensor occurs under heavily loaded conditions and high ambient temperature, which results in  Figure 14 shows the actual shaft speed and reference speed command, which was maintained at 5 rad/s. The machine was loaded with a constant load (DC generator load). The www.mdpi.com/journal/mathematics d currents are used to close the current loop to minimize the drive cost against current sensor failure. A classical vector-control PMSM drive rers, i.e., two current sensors and one speed/position sensor. This paper mation technique that is free from inverter switching states, an integrator, he drive is suitable for retrofit applications, as it does not require any reference voltages ( and ) are used to estimate the rotor reference d ). The presented algorithm depends on the stator resistance (Ɍ ). The rithm is used for compensation to overcome the effect of the Ɍ on the nsitivity analysis for the currents against the speed is verified and preclosed with actual speed information, which will try to maintain the refcumstances. The proposed current sensorless PMSM drive was validated and also verified on a hardware prototype. The presented technique was ion conditions, and some of the extensive results are presented. Ɍ tion; speed sensor; PMSM; vector control t-magnet synchronous machines) have been gaining a strong inades. Its unique characteristics meet the electric vehicle drive opigher torque/inertia ratio and minimum copper losses with high SM operates successfully at the required speed and load [1]. A compared to other machines [1]. Vector-control drive has an exance [2]. The speed/position data are accessed from a sensor athaft for controlling the drive. In general, a three-phase PMSM ree currents and rotor position information to compute the rotating s [1,2]. he drive operation can be caused by sensor parameters, such as fset, resulting in poorer performance [3]. The failure of the sensor aded conditions and high ambient temperature, which results in s was estimated using [34] and compensated to the current estimation technique. The drive performance confirmed the current sensorless algorithm under stator resistance variation.
FOR PEER REVIEW 16 of 19 which was maintained at 5 rad/s. The machine was loaded with a constant load (DC generator load). The Ɍ was estimated using [34] and compensated to the current estimation technique. The drive performance confirmed the current sensorless algorithm under stator resistance variation.  Figure 15 shows the experimental results for the high-speed reference command. The machine was connected with a DC generator-type load (i.e., -type load). The machine was initially at the rest position. The reference speed was changed from 0 to 150 rad/s in a ramp form. At 13s, the load on the machine was varied by changing the load resistance connected to the DC motor. The estimated and actual currents were plotted on the same scale to show the accuracy of the proposed technique.  Figure 15 shows the experimental results for the high-speed reference command. The machine was connected with a DC generator-type load (i.e., kω r -type load). The machine was initially at the rest position. The reference speed was changed from 0 to 150 rad/s in a ramp form. At 13 s, the load on the machine was varied by changing the load resistance connected to the DC motor. The estimated and actual currents were plotted on the same scale to show the accuracy of the proposed technique.

Conclusions
In this paper, a current sensorless PMSM motor with a position/speed sensor was presented. The currents were estimated from the reference voltages. In the d and q axes rotating reference frame, the stator currents were calculated and closed in the loop to perform an all four-quadrant operation. No additional sensors or hardware is required to implement the proposed method, which makes the drive suitable for retrofitting applications. The current sensorless algorithm can be applied to various PMSM motor types. The current estimation technique can be used to monitor the status of the current sensors by implementing them in the existing PMSM drive. A speed sensor is employed to perform the drive operation with the current estimation technique, which reduces the drive cost and complexity. The reliability and immunity to signal noise is reduced by using a single sensor, i.e., speed or position sensor. The proposed drive is independent of the switching states, integrator, and differentiator terms. The sensitivity of the estimated currents is also performed with speed information. The algorithm was tested on the MATLAB/Simulink platform and also verified on a laboratory prototype. Finally, the current sensorless for PMSM was experimentally validated, and the system's good performance at a variety of speeds and loading circumstances was confirmed.

Conclusions
In this paper, a current sensorless PMSM motor with a position/speed sensor was presented. The currents were estimated from the reference voltages. In the d and q axes rotating reference frame, the stator currents were calculated and closed in the loop to perform an all four-quadrant operation. No additional sensors or hardware is required to implement the proposed method, which makes the drive suitable for retrofitting applications. The current sensorless algorithm can be applied to various PMSM motor types. The current estimation technique can be used to monitor the status of the current sensors by implementing them in the existing PMSM drive. A speed sensor is employed to perform the drive operation with the current estimation technique, which reduces the drive cost and complexity. The reliability and immunity to signal noise is reduced by using a single sensor, i.e., speed or position sensor. The proposed drive is independent of the switching states, integrator, and differentiator terms. The sensitivity of the estimated currents is also performed with speed information. The algorithm was tested on the MATLAB/Simulink platform and also verified on a laboratory prototype. Finally, the current sensorless for PMSM was experimentally validated, and the system's good performance at a variety of speeds and loading circumstances was confirmed.