Optimal torque trajectories minimizing loss of induction motor under given condition of rotational angle

In order to improve the efficiency of the motor drive systems, the optimal torque should be discussed in order to minimize the total loss energy during the operation. The optimal torque trajectory for a squirrel-cage induction motor under the given two constraint conditions with respect to the operation time period and the rotating speed range have already reported. In these reports, however, the rotational angle is not taken into account as one of constraint conditions. In applications, such as electric trains, elevators, conveyer, and cranes, the rotational angle should be considered. This paper proposes a design methodology of an optimal torque trajectory to minimize the energy loss for IM drive by means of the variational method when the operation time period, rotating speed range, and total rotational angle are given as constraint conditions.