# Improvement on Flux Weakening Control Strategy for Electric Vehicle Applications
## 4 Traditional Flux Weakening Control Scheme in Vehicle Applications  
Many authors developed FW methods and control schemes based on the detection of the current error or of voltage saturation. The FW control schemes proposed in [15; 16; 17] have been investigated in this paper because of their simplicity and effectiveness. Figure 4 shows the scheme proposed in [16] where MTPA strategy is carried out calculating the \(i_{sd}^{*},i_{sq}^{*}\) set points, following an equation or a LUT (to take into account magnetic saturation). The FW control is achieved with the \(i_{sd}\) error (\(\Delta i_{sd}\)) between the d-axis current setpoint \(i_{sd}^{*}\) and the actual value \(\vec{i}_{sd}\). The \(\Delta i_{sd}\) represents a valuable detection feedback. If d-axis current error \(\Delta i_{sd}\) grows, the q-axis current setpoint \(i_{sq}^{*}\) will be reduced, releasing voltage in order to compensate the error on \(i_{sd}\). In this way, the current vector is kept inside the voltage limit ellipse and it is moved toward the \(i_{sd}\) axis. Figure 5 shows the FW control scheme proposed in [17]. In this paper, the setpoint of MTPA torque is transformed into the corresponding current setpoints \(i_{a\_sp}\) in the d-q axis reference frame by function blocks. Then, \(i_{a\_sp}\) setpoint is transformed from polar to rectangular coordinates: \(i_{d\_sp}\) and \(i_{q\_sp}\). Both methods allow to take advantage of the flux weakening potential of the IPM electrical machine, at least in acceleration. In fact, both schemes rely on an integral action that drives the limits of the currents setpoints, thus some issues could appear in deceleration due to the integral dynamic of PI regulators. With the aim to test the FW performance of control schemes in [16; 17], a complete model of the vehicle was developed in Matlab/Simulink environment. Both control schemes have been performed in acceleration and deceleration operations. The simulation results of the [PERSON] control scheme are shown in Figure 7, the MTPA trajectory has been evaluated keeping into account the saturation of the lamination following the \(L_{sd}L_{sq}\) variation reported in Figure 8. The motor parameters used for the simulations are reported in Table 1. As expected, during fast torque transition the currents \(i_{sd}\) and \(i_{sq}\) are far from an ideal situation. Figure 6: Feed forward results under two different battery voltage estimation. Red line actual battery voltage, blue line voltage underestimated of 5%. Figure 8: Motor inductances versus stator phase current. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Description** & **Value** & **Unit of Measure** \\ \hline Motor External Diameter & 140 & mm \\ Motor Stack Length & 120 & mm \\ Motor Nominal Current & 160 & mm \\ Motor Nominal Torque & 15.8 & Nm \\ Motor base speed & 3000 & rpm \\ Motor Phase Resistance & 1.65 & m\(\Omega\) \\ Motor Direct axis Inductance & 0.055 & mH \\ Motor Quadrature axis Inductance & 0.075 & mH \\ Motor Permanent magnet flux Linkage & 0.0128 & Wb \\ System Moment of inertia & 3 & kgm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters for the Simulation. Figure 7: Simulation results with [PERSON] traditional control scheme. Figures 9 and 10 show the experimental results in acceleration and deceleration at high speed of [16; 17], respectively. As expected, both traditional FW control schemes perform quite good in acceleration, but show an unwanted behaviour when the torque setpoint goes to zero at high speed, as a results of the driver setpoint. This is the typical situation of a braking action. In Figures 11 and 12, it can be easily seen that the angle computed by the integrator (orange solid line) approaches the value computed for the MTPA, when torque setpoint goes instantly to zero. In [17], this behavior is due to the fact that the voltage error method changes sign and the integral action reduces it to its minimum angle value (about \(18^{\circ}\)) in braking condition. A similar phenomenon happens with FW control method of [16].