# Improvement on Flux Weakening Control Strategy for Electric Vehicle Applications
## 3 Flux Weakening Implementation  
From an ideal point of view, the driver sets the desired torque by means of the throttle. Thus, during acceleration, the torque and then the acceleration is proportional to the torque setpoint. This relationship is basically true in MTPA region, while in the FW one the torque decreases as the speed increases, even if the amplitude of current space vector is kept constant. An optimal control strategy should seek to approximate the aforementioned behaviour to fully exploit the FW motor capability.  
FW in traction applications allows to extend the constant power region, eliminating the need for mechanical gear boxes, avoiding the volt-ampere over sizing of the power converter and increasing the power density of the system.  
In order to implement FW strategy on an IPM motor, it is necessary to generate an appropriate negative \(i_{sd}\) setpoint. In fact, a negative \(i_{sd}\) current will produce a magnetic flux along the d-axis opposing the rated flux generated by PMs.  
The strategy adopted to compute the \(i_{sd}\) setpoint affects the motor performance and it must be designed considering: on one side the torque generation and on the other hand the voltage and current limitations. As known, an excessive FW action reduces the generated torque and then vehicle performance. On the other hand, a late start or a weak action may result in undesired torque drop according to the PI current regulator saturation.  
The generation of the exact FW profile and consequently the \(i_{sd}\) setpoint is a tough task since different variables (motor parameters, battery state of charge) and the motor operating conditions affect the optimal setpoint and the level of the FW action.  
Strictly speaking, \(i_{sd}\) and \(i_{sq}\) could be evaluated once the desired torque and the flux magnitude are known. This methodology is know as FF and, as evident, it would be quite impossible to obtain optimal performance due to: motor parameters variations under different operation, battery state of charge value, magnetic saturation and ohmic voltage drop.  
In [19], a robust FF FW control algorithm, based on mathematical motor model is proposed. Being \(l_{s}\) the maximum inverter current and \(V_{BUS}\) the actual BUS voltage, from Equations (4) and (6), it is possible to calculate the setpoints of \(i_{sd-safe},i_{sq-max}\) in function of the measured motor voltage and electric speed \(\omega_{e}=p\omega_{m}\) as in Equation (8). The meaning of the chosen name \(i_{sd-safe}\) will be clarify in the following.  
\[\begin{cases}i_{sd-safe}=\frac{-\Lambda_{Pm}L_{sd}+\sqrt{\Lambda_{Pm}^{2}t_{sd }^{2}-\left(t_{sd}^{2}-L_{sq}^{2}\right)(L_{sq}^{2}t_{max}^{2}+\Lambda_{PM}^{2 }-\frac{V_{BUS}^{2}}{\omega_{m}^{2}})}}{L_{sd}^{2}-L_{sq}^{2}}\end{cases} \tag{8}\]  
Figure 6 reports the results obtained by FF technique generation of \(i_{sd}\) command. The results, in case of a FF calculated from rated motor parameters and measured battery pack voltage, are shown in red. While the results obtained in case of a 5% voltage underestimation are reported in blue. As expected, in FW region, torque and power values drop.  
In both cases an open-loop FW strategy leads to results that are distant from those that could be got in an ideal situation, since the mechanical power is a long way off the constant trend.  
In conclusion, some closed-loop corrections are necessary to fully exploit the power limit of IPM motors.