# Improvement on Flux Weakening Control Strategy for Electric Vehicle Applications
###### Abstract  
This paper proposes an optimized flux weakening (FW) control strategy for interior permanent-magnet synchronous electric motor to address the critical issues that could occur under torque setpoint transition in flux weakening region, due, for example, to an emergency braking. This situation is typical in electric vehicles where the electrical machines operate over a wide speed range to reach high power density and avoid gearboxes. Two modified traditional flux weakening strategies are proposed in this paper to improve torque control quality during high speed torque transition. The proposed modified control strategies were validated both by Matlab/Simulink simulations, modeling the power train of a light vehicle application, and extensive experimental tests on a dedicated test bench. interior permanent magnet synchronous electrical machine; electric vehicle; flux-weakening; torque control loop +
Footnote †: journal: Applied Sciences  
optimal permanent magnet quantity needed to obtain an optimal flux weakening behavior, the main results of these studies can be synthesized in a relation between the inductance on the d-axis and a the permanent magnet flux linkage that place the characteristic current close to the edge of the current limit circle in the \(i_{sd}-i_{sq}\) plane. This design approach allows the maximum exploitation of the electric power system and avoids the MTPV region [2; 3; 4] Thus, machines which avoid MTPV operation could be also considered for electric vehicle applications  
Other control design approaches that implement all the three different control strategies were developed by different authors [5], this control scheme could be useful when the characteristic current of the electric machine falls inside the current limit circle. In recent years, other different approaches were developed based on low coercive force of permanent-magnets [6], but their application is still uncommon. Some authors propose also mechanical solutions to reduce the permanent-magnets flux at high speed creating a different mechanical gap between rotor and stator in the axial direction as the speed increases [7], in this way it is possible to obtain flux weakening without any control strategy implemented on the drive. Figure 1: Constant torque and power regions for the reference motor under test. Figure 2: \(i_{d}-i_{q}\) plane, MTPA, FW and MTPV control strategies. Other works try to develop flux weakening algorithms to avoid the need of any magnetic machine model [8]. There are also some examples of control schemes based on different state variables (linkage flux instead of stator currents [9], or other works focused on loss minimization strategy [10]. In any case, when a wide-speed range is required and rare-earth PMs are employed, the current vector at maximum speed is very close to the \(i_{sd}\) axis. In the case of electric power train there are different current limit circles for the different duty types. In the case of continuous duty type (S1), the current limit circle is typically limited by the thermal behaviour of the electrical machine, while in short time over-current, or over-torque, (duty type--S2) the current limit circle is typically given by the inverter current limit, therefore a trade-off for the characteristic current is necessary. In this study, the characteristic current of the electric motor is chosen in such way that it falls in the middle of the two current limits corresponding to the continuous duty type (S1) and the short-time duty (S2). The choice of the PMs volume must take into account not only the characteristic current, but also the demagnetization issues and the requirements linked to the torque density and the efficiency of the system. These latter considerations imply a design with a high PM flux that requires high negative d-axis current component at high speed to counteract the PMs back--electromotive force (Back-EMF). This corresponds to a current vector with an angle close to 180\({}^{\circ}\) and a high amplitude, even if a low torque setpoint is required.