Spinning Internal Permanent Magnet motors with sensored Field Oriented Control using Altair FluxMotor™ and real-time embedded software Altair Embed®
Spinning Internal Permanent Magnet motors with sensored Field Oriented Control using Altair FluxMotor™ and real-time embedded software Altair Embed®
Prof. Dr. Ir. Duco W. J. Pulle
Chief electrical drive consultant for Altair
Yichen Zhang
Project Engineer for Altair
Summary
Internal Permanent Magnet (IPM) motors provide high torque density and high efficiency provided by the permanent magnet torque and the reluctance torque. They are widely used for traction motors, machine tools in general and EVs in particular. At higher current values, magnetic saturation has a significant nonlinear effect on the electromagnetic torque. The ability to model this behavior and design a drive system to control the motor efficiently subject to this behavior is the topic of this blog.
Introduction
So called magnetic saturation effects occur in ferromagnetic materials used for electrical machines and the toroid shown in figure 1a. Central to this phenomenon is the non-linearity of said ferromagnetic materials, which is present in the form of a flux-density (B) versus magnetic field (H) characteristic known as a B-H curve. For flux density values which approach the saturated value 
,the linearity boundary is reached and magnetic field values increase significantly that leads to a non-linear flux-linkage/current characteristic 
(see figure 1b). Within this curve a linear range is present, that defines the inductance of the toroidal example namely 
. The behavior of the toroid illustrates the impact that magnetic saturation has on the current. For example, assume the unit is connected to a sinusoidal voltage source, which drives the flux-linkage of the coil as depicted by the simulation model shown below (figure 2). In the linear case the relationship 
holds, which leads to the results shown below for current. However, if the inverse model of the flux-linkage curve is used in the simulation model the results are dramatically different as apparent below (figure 3). The reason being that increased flux-linkage values lead to increased flux levels and when the saturated flux density values are reached or exceeded the magnetic field density increases, which in turn leads to higher coil magneto-motive Force (MMF) values that causes the ‘peaks’ shown in the ‘saturation’ current plot (figure 3).
Machines with rotors that utilize ‘interior’ (buried) permanent magnets, as shown below (figure 4) for an electrical vehicle (EV) application, are prone to magnetic saturation effects and this is clearly shown by finite element plots where the ‘red’ areas reflect high flux density levels that can significantly affect the behavior of the machine. This also means that control of said machine must be adapted to accommodate saturation effects.
Fig. 4 – FE model of IPM [ref Altair FluxMotor]
Figure 5, below shows the shaft torque of the EV motor considered here for the linear and saturated case. Both are calculated using the out-product of the flux-linkage and current based on the Ideal Rotating Transformer (IRTF) model [3].
Fig. 5 – IPM shaft torque as function of id, iq: linear and saturation (generated using Altair Compose and FluxMotor)
IPM model with magnetic saturation
The IRTF model shown below [2], [3] (figure 6) is designed to accommodate either linear or magnetic saturation. Input to this model is the amplitude invariant representation 
of the 3 phase voltages that are converted to the two phase equivalent vector 
. The IRTF model generates the two-phase current vector 
, that in turn generates the current 
for the controller. In addition, its value is combined with the stator resistance 
namely 
, that is used together with to generate the differential of the stator flux vector 
. Output of the IRTF is the flux in d,q coordinates 
, with components 
used by the non-linearity module. For linear models the currents are found using 
, where 
are the d-axis and quadrature axis inductance values of the linear model respectively and 
the PM flux.
Output for the IRTF unit is the electrical torque 
that is multiplied by the pole pair number 
to find the mechanical torque 
. The mechanical load equation 
is used to determine the mechanical shaft angle 
, which in turn leads to the electrical angle 
, for the IRTF unit. When considering modelling saturation in IPM machines the situation is similar to that discussed for the toroidal example discussed above, namely the need to use the flux-linkage/current characteristics generated using the FE method FluxMotor) as shown below. This implies that inversion of the flux-linkage characteristics is required, which leads to the results shown below. For a user defined set of flux reference stator fluxes 
the algorithm example (figure 7) determines the flux values generated by the non-linear flux modules (as depicted in the flux plots shown below, (figures 8a,8b) that have as output the desired 
value. The inverse flux results (figures 9a, 9b), also shown, are those that can be generated by this algorithm using Compose.
Fig. 8a – 
generated with FluxMotor Fig. 8b – 
generated with FluxMotor
Fig. 9a – 
generated with Compose Fig. 9b – 
generated with Compose
IPM drive to accommodate magnetic saturation
The objective of the IPM drive is to control the IPM motor in a manner that produces maximum torque for a given current. The electrical drive shown below (figure 10) consists of the processor (MCU) that houses the control algorithms and all the functionality needed to use the measured current/voltages and generate the PWM signals for the converter. The currents, typically measured using in-line sensors (as opposed to shunts) is preferable to maximize the modulation index 
. Low-pass filters (LPF) are used to measure the converter output voltages and eliminate the PWM component. This implies that the average voltage per sample component remains and is not affected by converter dead-time or conductive voltage components of the semi-conductors. Hence, this gives the ability to accurately measure key motor parameters, provided that the LPF characteristics are taken into account, as is the case. Furthermore, access to phase voltages/currents is advantageous as the input power can also be found. The 12 bit ADC unit digitizes the incoming voltages/currents and these are sent to the “Forward Clarke” module that generates the motor current/voltages in 
stationary coordinates. These variables together with the measured DC bus voltage are required for the “Controller” and “FOC data” modules.
The purpose of the FOC Data module is to track the PM rotor flux vector 
and orientate the controller d-q synchronous coordinate system using an encoder input. This requires instantaneous knowledge of the flux speed 
, angle 
and PM flux amplitude.
The controller module consists of a synchronous current and speed controller [3], where use is made of the measured current vector 
and electrical shaft speed. In this case the speed controller sets the reference torque, which is then used by a ‘saliency controller’ [3] that generates the optimum reference 
. This approach underlines the need for e-Drives to fully utilize the e-Motor [4], which effectively means making full use of the various torque production capabilities the machine has. This implies controlling the currents 
to maximize the ratio: shaft torque to current vector amplitude 
. The torque to current ratio for the machine in question, as shown in figure 11, underlines the importance of e-Drive control. For example, ignoring the reluctance torque mechanism by choosing 
, implies that e-Motor operation is not as efficient as can be observed from figure 11. The so called “Maximum torque per Amp (MTPA)” curve shows the optimum combination that is to be used and this corresponds to the highest Torque/current values, as indicated by the black trajectory (see figure 11) shows the optimum combination that is to be used . For machines with magnetic saturation (as is the case here) a LUT approach is needed in combination with FluxMotor to generate the 
data represented by the MTPA curve.
Figure 11: Torque to current amplitude ratio as a function of (id, iq)
Application example
The Embed model shown in figure 13, makes use of the IPM model described above. The user has the option of selecting a linear or saturated IPM model. This affects the control strategy and IRTF topology as mentioned earlier. Sensored FOC control is used and the reference direct/quadrature currents are also shown in this diagram together with the measured input power level and shaft torque. A load torque characteristic is used that provides rated torque 400 Nm at rated speed 1000 rpm. The controller module is already implemented for real-time embedded control, which implies that fixed point representation is used and the generated output file is IPM_PILv1.out.
The compiled output file is downloaded to a Texas Instruments TMSF320F28069M launchpad (figure 12) to allow processor in the loop (PIL) operation, as is used here.
Fig. 12 – TMS320F280xF Launchpad
Fig.13 – Altair Embed IPM simulation with PIL: optional IPM saturation/linear module
Conclusion
Magnetic Saturation is a key concern for engineers faced with the design and control of an IPM of the type considered in this document. The tool-chain that accompanies this process consists of :
- Altair FluxMotor: A finite element design application that models the IPM: figures 4, 5, 8 and generates the data represented by the MTPA curve in figure 11, as required for optimal control.
- Altair Compose: A Math, Scripting, Data Analysis, and Visualization application that is used to generate the inverse flux plots (figures 9a, 9b and torque plots (figure 5), maximum torque/Amp plot (figure 11).
- Altair Embed: A simulation and Hardware in the Loop application that is used to design the controller model, generate the control software, and monitor its execution on the target microcontroller. In this application a Texas Instruments TI-F28069M microcontroller is used. The Embed Hotlink high speed monitoring function provides time history plots of any of the control signals at the frame rate of the target microcontroller (figure 12) for linear and saturated case (figure 13).
The importance of using this type of toolchain is apparent by considering how drive behavior is affected by saturation. For example, figure 5 shows shaft torque for the IPM as function of the currents 
with and without magnetic saturation, i.e. linear. The torque output is strikingly different as the synchronous reluctance component 
is a function of the inductance components 
. Under rated conditions the peak current value of the IPM with saturation is doubled, as apparent from figures 14a and 14b. Consequently, the copper losses for the saturated case will be four fold compared to the linear case and iron losses will also increase. The impact of saturation reduces the inductance and this is also apparent from the phase voltage levels for both models (figures 14a, 14b), which in turn affect the maximum operation available for a given DC bus voltage.
Note that the IPM considered in this document is of the “flux-weakening type [3] ”, which implies
as is the case for this EV application. However, “flux-enhancement” type IPM’s with
require a different control strategy, but the toolchain indicated above can also be used here.
When considering sensorless FOC control, inductance changes must also be taken into consideration to ensure that the estimated EMF vector matches that of the actual machine. For example, the EMF is determined by using an impedance network where use is made of the inductance 
and stator resistance 
. The voltage across the inductance is equal to 
where 
is the short-circuit current and 
the EMF vector amplitude. This shows that saturation will affect the 
ratio, which must be programmed in an LUT, as function of the stator current amplitude.
Fig. 14a – Results with linear IPM model Fig. 14b – Results with saturated IPM model
References
- Fundamentals of Electrical Drives, 2nd Veltman A. , Pulle D.W.J. , De Doncker R., Springer 2019,
- Modelling Spatial Harmonics and Switching Frequencies in PM Synchronous Machines and their Electromagnetic Forces, Boesing M., Niessen M., Lange, T.B and De Doncker, R. IEEE 2012
- Advanced Control of Electrical Drives, De Doncker R., Pulle D.W.J. and Veltman A., Springer 2020.
- Bringing Personality to the Automotive e-Motor, Dagg, J. , Altair 2021.
About the author
Prof. Dr. Ir. Duco W. J. Pulle
Chief electrical drive consultant for Altair
Forty years of experience in electrical drives including 25 as a professor at European Universities, including RWTH-ISEA, Germany, which is the world leader in electrical drives. Author/co-author of three books and numerous conference/journal papers
Over the past fifteen years have been working as a consultant in the field of sensorless electrical drives with a wide range of machine types and power.
My vision and passion is to promote the use of real-time embedded control for electrical drive applications using Altair Embed. For this reason a wide range of application examples has been developed, which covers all machine types and control algorithms.
Educational background: Aviation College, B.Sc., M.Sc, Ph.D, Flight engineer and aviator.
Co Author
Yichen Zhang
Project Engineer in Altair since 2019. My job is focused on system modeling and embedded control. Over the past two years, I have been working on a wide variety of mechatronics projects which gave me good understanding of sensors, actuators, different communication protocols, etc. I have great passion for electric drives and their control techniques. And I am glad to share my knowledge in our solution for real-time embedded control, Altair Embed.
Educational background: MS in Mechanical Engineering from Carnegie Mellon University, BS in Automotive Engineering from Wuhan University of Technology.
Comments
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Great post! I really like the use of the Flux generated nonlinear Id,Iq Torque tables in combination with Altair Embed to create a control scheme that gives maximum torque per amp automatically. Cool that you actually implemented the controller on a low cost MCU too.
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