Current Minimizing Torque Control of the IPMSM Using Ferrari’s Method

For the torque control of an interior permanent magnet synchronous motor (IPMSM), it is necessary to determine a current command set that minimizes the magnitude of the current vector. This is known as the maximum torque per ampere. In the field-weakening region, current minimizing solutions are found at the intersection with the voltage limits. However, the optimal problem yields fourth-order polynomials (quartic equations), and no attempt has been made to solve these quartic equations online for torque control. Instead, premade lookup tables are widely used. These lookup tables tend to be huge because it is necessary to create separate tables on the basis of the dc-link voltage and motor temperature. In this study, we utilize Ferrari´s method, which gives the solution to a quartic equation, for the torque control. Further, a recursive method is also considered to incorporate the inductance change from the core saturation. A simulation and some experiments were performed using an electric vehicle motor, which demonstrated the validity of the proposed method.