Summary
The optimal control problem that hinges on the Euler‐Lagrange equation can be applied to electric‐machine drives and the necessary and sufficient optimality conditions around the system control and the control variables can be designed in a congruent way. In this paper, a variational problem is proposed to minimize energy consumption by an Induction Motor (IM) under a Rotor Field–Oriented Vector Drive (RFOVD) during torque and speed transients. The optimal stimulus is to take into account real applications, like perturbed load torques, and an abrupt speed input. The approach consists of an off‐line algorithm that minimizes a cost functional or integral of the weighted sum of IM energy/power under the dynamic stress of the rotor flux and of rotation speed. The variational problem leads to a nonlinear differential equation known as the Euler‐Lagrange equation. A new method is suggested to run out an analytical solution and results in a time‐varying rotor flux considered as the optimal state variable of the dynamic IM model that saves energy of the IM drive under RFOVD. This solution provides loss‐minimization in steady‐state operations at an infinite horizon and performs adaptive suboptimal minimum‐energy consumption for torque transients. Simulation and experimental results are fully performed on 1.5‐kW laboratory IM, and prove the validity of the proposed method for both steady‐state and transient‐IM drive operations.