Posted on 22 August 2019

Sensorless Control for Electrical and Hybrid Electric Vehicles

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An Overview and Simulation

For Electrical Vehicles (EV) and Hybrid Electrical Vehicles (HEV) sensorless control of electric machines is a particular relevant topic. There are two main reasons why. Firstly mechanical position sensors are difficult to integrate and to implement into the driveline of the vehicle. Secondly the mechanical sensors are fragile and susceptible to Electro Magnetic Interference (EMI) and signal distortion.

By Peter van Duijsen, Simulation Research, The Netherlands, and Pavol Bauer, TU Delft, The Netherlands


If mechanical position sensors could be minimized or eliminated entirely and replaced by software algorithms, the costs of the driveline would reduce while reliability would increase. The sensorless control would not only be important for a smooth control of the driveline, it would also be independent from signal distortion. Signal distortion would impact on the control of the drive and thereby introduce unbalance on the driving voltage vector causing noise and vibration. The Ideal Rotating TransFormer (IRTF) is introduced for modeling the electrical machines. The advantage of the IRTF based machine models is, that they give better insight in the machine modeling required for observer design.

General model of the AC machine

To study the sensorless control and to design a sensorless control for either the Induction Machine (IM) or the Permanent Magnet Synchronous Machine (PMSM), a machine model is required from which the stator and rotor flux can be identified. Recently the Ideal Rotating TransFormer (IRTF) was proposed to give a better insight into the operation of sinusoidal distributed AC machines [1].

The basic IRTF AC machine model is build around the ideal transformer. In this Caspoc model [3] in Figure 1 the airgap is modeled in the IRTF model. Here the flux and current produce the electromagnetic torque where the IRTF models the position dependent coupling between stator and rotor. On the left side the model of the stator (green) has to be added, on the right side the model of the rotor (blue) has to be added. The electromagnetic torque is exported from this model on the bottom connection. The position of the rotor is fed into the model. An interface block is used to connect the signal oriented IRTF model to a mechanical model. A quadratic load in the figure above represents the mechanical model. Any type of mechanical model can be connected to this interface.

Basic IRTF AC machine model for modeling the Induction

Depending on the machine type, IM, Synchronous Machine (SM), Synchronous Reluctance (SynRel) or PMSM, the stator and rotor models have to be connected to the IRTF model. Since all sinusoidal distributed AC machines have a sinusoidal distributed stator winding the model for the stator is for almost all machine types equal. The rotor is depending on the type of machine. A PMSM has a constant rotor flux and is simply modeled by a constant rotor flux connected on the right side of the IRTF. The IM with squirrel cage has no constant rotor flux but an equivalent winding that has to be modeled. For the IM the rotor circuit with the rotor time constant Tr=Lr/Rr has to be modeled.

The Caspoc models in Figure 2 [3], give insight in the functioning of the machines and can easily be interchanged. Not only is it visually better understandable how the machine model is build, it also gives insight in how the stator and rotor flux can be constructed from measured voltage and current signals from the machine. The IRTF models allow us to have better insight in creating an observer required for sensorless control. Numerous schemes to build machine and observer models are given in [1] and [2].

Figure 2 - part 1 (images a, b)

Figure 2 - part 2 (images c, d)

Figure 2 caption - IRTF based AC machine models a, b, c, d

All the stator flux estimators described in this article use the stator winding resistance and inductance. These two parameters have to be known in advance. However during the operational time of the drive, due to the losses in the stator yoke and the winding resistance losses, the stator winding resistance increases. This thermal dependency also has to be modeled in the observer.

Because of saturation, the stator and rotor flux are not ideal, but follow the magnetization curve of the lamination. As a result, Ld and Lq vary upon load of the machine.

Sensorless control

The sensorless control can be applied to Field Oriented Control (FOC) and Direct Torque Control (DTC). DTC is actually already a sensorless control method if the control scheme from figure 3 is used. DTC is the most simple to implement sensorless control method [2]. Its disadvantage is however the undetermined switching behavior and its resulting torque ripple.

Direct Torque Control with stator speed estimation

For FOC the sensorless control can be implemented by replacing the position and or speed sensors with an observer. The main problem to be solved is in designing a good observer that replaces the position and speed sensor. The rest of the FOC remains equal to the FOC with mechanical position and speed sensor. Various control structures are given in literature and the reader is suggested to have an overview in [4],[6],[7],[2].

Requirements on speed and position estimation for vehicles

Eliminating the position sensor basically leaves us with the question, how accurate the position estimation should be. The accuracy of position estimation is dependent on the type of machine. For a PMSM, accurate position estimation is required, in order to keep the stator current in an optimal angle with regard to the rotor flux angle. The rotor flux angle is fixed and given by the position of the magnets in or on the rotor. For nominal speed control the stator current has to be in quadrature with the rotor flux. For field weakening the stator current has to be positioned more in advance of the rotor flux in order to have the optimum torque within the current and speed limiting cycles [2]. This requires an absolute position sensor that resolves the rotor flux position to approximately less than 0.2 degrees mechanical [8]. Machines with higher pole count would even require a higher resolution. To resolve angles less than 0.176 degrees mechanical also requires an 11bit encoder. In case of high angular speed, these position measurements have to be transferred to the control system at a fairly high speed, requiring a high bandwidth resolver with high bandwidth data transfer. Sensorless control would eliminate the transfer of these measurements, since the actual measurement is taking place in the inverter itself. However the accurate position estimation remains even in sensorless control.

For induction machine drives the position estimation is less stringent in Field Oriented Control (FOC). The observer has to estimate the rotor flux and the slip of the induction machine. Especially estimating the slip in the induction machine is prone to errors because most observers are based on machine parameters that vary due to temperature and non-linearity. The task of the observer is to predict the speed and position of the rotor without any mechanical sensor [5]. The only inputs to the observer are the stator voltages and stator currents. There are two types of observers that are commonly employed; the first type is based on the basic harmonic model of the machine and the second model is based on the anisotropy of the machine. Both methods are discussed in [5].

Practical application of the basic harmonic model

Figure 3 already showed the DTC application. In figure 4 the PMSM modeled in Caspoc [3] using the IRTF is shown. The driving voltage vector us feeding the PMSM model, which is the output from the inverter leads the rotor flux by 90 degrees electrical. The rotor is modeled by a constant flux of 0.995wb, as shown by the yellow block on the right side of the model.

Figure 4 - part 1

Fig 4 - PMSM start up showing the agreement between simulated and estimated rotor angular-speed and position

The observer tracks the rotor position based on the voltage and current of the PMSM and is represented by the block diagram in figure 4. Instead of using the measured rotor position ?r in for controlling the supply voltage, the estimated rotor position ?est is used. As shown in the last scope of figure 4, the estimated rotor position ?est agrees very well with the actual rotor position ?r.


Choosing the right simulation method allows the user to study effectively various sensorless drives used in hybrid and electrical vehicles. Using the new IRTF model as described in [1] inside Caspoc [3], the machine can be modeled in detail and it also gives insight in how to create an observer model suitable for sensorless operation. In reference [1] numerous Caspoc simulations are given, describing AC machine modeling. In reference [2] FOC and observer models in Caspoc are explained in detail.



1) Veltman A., Pulle D., De Doncker R.W., Fundamentals of Drives, Springer 2007, ISBN-13: 978-1402055034.
2) De Doncker R.W., Pulle D., Veltman A., Advanced Electrical Drives, Springer 2010.
3) Simulation Research, Caspoc 2007,
4) Novotny D., Lipo T., Vector Control and Dynamics of A Drives, Oxford Uni. Press, 1996.
5) Vas P., Sensorless Vector and Direct Torque Control, Oxford Uni. Press, 1996.
6) Krishnan, Electric Motor Drives, Prentice Hall, 2001.
7) Boldea, Electric Drives, CRC Press, 2005.
8) Miller J.M., Propulsion Systems for Hybrid Vehicles, IET Press, 2004.



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