Numerical optimal vector control for torque control of interior permanent magnet synchronous motor by poincare map and averaging theory

The permanent magnet synchronous motor (PMSM) is very useful in applications. Vector control of PMSM is popular kind of its control .But nonlinearity of PMSM and existence of inverter in its control circuit caused that optimal gains with conventional optimal control theory can not be found. In this paper first the complete vector control of PMS (including flux leakage model) is modeled with poincare map then the time variant model with averaging theory is converted to time invariant. Finally the system is converted to linear form with jacobian of resultant model. At the end in the numerical simulation result of this model can be seen.