Sensorless DTC of IPMSM for embedded systems

Received Apr 19, 2019 Revised Jul 8, 2019 Accepted Nov 14, 2019 The main objective of the present work is to describe the sensorless control of interior permanent magnet synchronous motor (IPMSM) for embeded systems in traction applications using the Model Reference Adaptive System (MRAS) method for speed estimation. The algorithm of this method has been adapted with the mathematical model of the motorized wheels electric vehicle. The command used is the DTC. Sensorless DTC of IPMS in-wheel motor based on MRAS for electric vehicle is simulated by Matlab/Simulink. The simulation results show the effectiveness of this proposed sensorless DTC control used for embedded system applications.


INTRODUCTION
Embedded networks have become increasingly important. This change is not strange to that of power electronics, quite the opposite. The reliability and robustness offered by static converters when combined with electrical machines have naturally led to their massive use.
Nowadays, interior permanent magnet synchronous motors (IPMSM) are expected to be applied to propulsion systems of electric vehicles for their high power and torque density, high efficiency, large constant power operation region, robust mechanical construction and cost-effectiveness. However, their large torque ripple is an obstacle in practical applications of PMSMs to vehicle propulsion. According to the litterature review, [1, 2] gave more attention to reduce the torque ripple in PMS motors for EV traction applications.
For embedded applications, synchronous permanent-magnet motors powered by a converter have good energy efficiency, power density, and high specific torque with the capability to ensure maximum torque from zero speed to base speed and to extend its operation beyond the base speed while ensuring high torque at low ripples thanks to its control. These motors are also known for their low weight and volume. On the other hand, some disadvantages exist such as the high cost of magnets and the demagnetization of permanent magnets at high temperature. The direct torque control for EV-traction means the torque control of a traction motor [3][4][5][6][7][8]. Thus, the DTC strategy for IPMSM drive is the right candidate for the highperformance control to meet the EV-traction requirements. The major advantage of DTC is the fast and accurate torque response with low torque ripple which is used in the embedded systems [9]. Direct torque control (DTC) applied to asynchronous machines appeared in the 1980s [10]. Its principle is to select one of the eight voltage vectors generated by the different possible configurations of the inverter switches in order to maintain the stator flux and the electromagnetic torque inside two hysteresis boundries. Proper application of this principle allows decoupling of the control between the flux and the torque without the need for a coordinate transformation or pulse width modulation for generating the control pulses of the inverter switches [11]. The DTC has a simplified structure, robust with respect to the variations of the parameters of the machine [12,13].
In this paper, we have chosen an NPC (Neutral Point Clamped) distributed-level three-level inverter, which is a very interesting converter for powering high-power machines. This makes it possible to increase the power delivered to the load and to improve the shape of the output voltage so that it is closer to the sinusoid. The general idea of multi-level inverters is to generate a sinusoidal voltage of several voltage levels, typically obtained from DC voltage sources. The increase in the number of levels produces a wave of stairs on the synthesized waveform which approaches the sinusoidal wave with the minimum of harmonics [14,15].
Knowledge of the rotor position of interior permanent magnet synchronous machines (IPMSM) in most variable speed drive systems is required. It is measured by a shaft position sensor or a resolver. Currently, many authors have proposed sensorless control strategies using different control methods for estimating rotor speed and position. [16][17][18][19][20].
In this paper MRAS (Model reference adaptive system) observer is proposed as a sensorless closed loop algorithm to detect speed and position due to their design simplicity and fewer computation requirement compared with other closed-loop model-based methods [21,22].
There are four sections in this paper. The organization is as follows: In section 2, a mathematical model of the interior permanent magnet synchronous motor (IPMSM) is presented. In section 3, a detailed study of the principle of direct torque control (DTC) for IPMSM, which fed by a NPC structure three-level voltage inverter, is carried out based on the analysis of the Switching table, including five level hysteresis controller of torque and three level hysteresis controller of flux. In section 4, an algorithm for the sensorless drive of IPMSM based on MRAS observer is presented. Simulation and discussion of the Simulink waveforms are presented in section 5. In the end, there is a comprehensive conclusion.

IPMSM MATHEMATICAL MODEL
The mathematical model of IPMSM in the  - coordinate system can be written as follows;   (4):   Figure 6 shows the block diagram of direct torque control of an IPMSM powered by a two-level voltage inverter. The estimated value of the stator flux is compared to its desired value and the estimated value of the electromagnetic torque is compared to the control torque generated by the speed controller. The resulting flux and torque errors are used by two hysteresis comparators shown in Figure 1 and Figure

PRINCIPLES OF DIRECT TORQUE CONTROL
Module of flux is: where s R is stator resistance and are voltage and current  , components.IPMSM stator winding currents are measured by hall current sensors, and its voltages are calculated by inverter switch state. The actual stator flux and torque are calculated by flux and torque estimator. The actual stator flux and torque are compared with the reference values in two separate hysteresis controllers:

Three level hysteresis controller of flux
This case, for flux control, the error is located in the three associated intervals that are fixed by the constraints:

Five level hysteresis controller of torque
The electromagnetic torque is the most important variable for the electromagnetic considerations. Therefore, high performances for torque control are required. To improve the control of the torque, we associate with the error of the torque five regions defined by the following constraints: The torque control is then performed by a hysteresis comparator with five levels or two upper bands(

Inverter switching table
Depending on the outputs of the hysteresis controllers and the sector where the stator flux is located, the voltage vectors delivered at the output of the inverter are chosen to maintain the flux and the torque inside the hysteresis bands. The Figure 3 shows an inverter arm. The 3 states possible switching sequences are summarized in the following Table 1.  Figure 4.
In order to achieve the direct control of the stator flux and the electromagnetic torque of the machine controlled by a NPC structure 3-level voltage inverter, we have to develop a switching table optimizing the possibilities of the inverter to deliver the necessary commands to increase or decrease the flux and the electromagnetic torque by choosing the stator voltage vectors to be applied.

SENSORLESS CONTROL SYSTEM BASED ON MRAS OBSERBVER
The need to introduce a speed sensor decreases the reliability of the system. Various solutions have been proposed in the control without speed sensor, model adaptive system (MRAS) estimators, adaptive reference model systems are the most attractive approaches because of their simple design, their operating validity in wide ranges speeds (low speeds, high speeds and their adaptation for both types of machines: smooth poles and salient poles). The algorithm of the adaptive reference model system is well known in the sensorless control of induction motors, and it has been proven effective, it is based on the principle in which the two outputs of the two models are compared: an independent model the rotor speed (reference model) AND another model that depends on it (adjustable model) [1, 17,18,23,24].
With Park's transformation, the equations of voltages and fluxes are expressed in the d-q reference by :  (14) By substitution equations (13) and (14) the current model is given by: The system model can be simplified using equivalent state ' ' , q d i i variables and control variables ' So, equation (15) can be converted to the equation state of the adjustable model of IPMSM with speed angle m  as the adjustable parameter as follows: Where ' ', q d i i are the estimated currents in the d-q axis. The reference model is that of the machine.
The convergence of the estimated speed ˆm  to the measured value m  is carried out by a suitable adaptation mechanism, and the position of the rotor is obtained by integrating the speed. It should be noted that the critical point in this process is to have an adaptation mechanism that ensures the system stability. The adaptation mechanism is a PI given by (18), (7), (6). Or ) 0 ( m   is the initial value of the estimated rotor speed, construction of the MRAS is shown in Figure 5.

SIMULATION RESULTS
In this section, simulations results via Matlab/Simulink will show the validity and the feasibility of the Sensorless DTC of IPMSM using the Model Reference Adaptive System (MRAS) method for speed estimation. The specifications of the IPMSM used in simulation are given in Table 3 [25].  In this simulation study, we consider that all motor parameters are known and constant.The simulation results show that the torque instantaneously responds to the load disturbance at 0.5s and follows its reference. Figure7 (c), Figure 8 (c) and the estimated speed in both directions of rotation perfectly follows the reference without exceeding and without any deformation with a very low observation error Figure7 (a,  b). Figure8 (a, b), The observed current errors show the good estimation of these variables. Figure 7 (d), Figure 8 (d). Figure 7 (e) shows that the two components of the flux are in quadrature and that the satoric flux vector follows its reference. The response of the flux in the phase plane is practically circular Figure 7

CONCLUSION
In this paper, we have used the MRAS technique for speed observation in the sensorless DTC control of the Interior permanent magnet synchronous machine (IPMSM) whose machine model extracts velocity information from measured stator voltages and currents. Using the output of the adjustable model and the reference model the rotor speed and position are estimated. The control of the torque and flux are designed by introducing two multilevel comparators for the flux and the torque to improve the detection of the position of the flux by defining twelve symmetrical sectors in the space of evolution of the flux. Thus, we established a table of commutation with more rules and the voltage vector is more optimal. The simulation results presented have proved the validity of the sensorless DTC control technique with MRAS estimator. Robustness tests are done to highlight the high performance of this proposed strategy.