Physically Derived Weight for an Exact Torque Penalty in Loss-Minimizing Model Predictive Control of Induction Motor Drives

In loss-minimizing model predictive control of induction motor drives, the torque reference is often enforced by a quadratic penalty. Since every newton-meter costs loss, it leaves a steady torque error, and its weight has no physical basis. The error is shown to equal \( λ_M/(2q_M M^* ) \), where \( λ_M \) is the marginal loss per unit torque of the loss-optimal steady state, and a penalty on the absolute torque error removes it once its weight, in W/(N·m), exceeds the largest \( λ_M \)below the reference. The closed form of \( λ_M \) is derived from a temperature-dependent machine and inverter loss model. For a 7.5 kW drive at 36 simulated operating points, the closed-loop threshold equaled the marginal loss at fixed flux, which coincides with \( λ_M \) except on the voltage-limit boundary (up to 15% lower). The nominal quadratic weight left errors of 0.46–3.88%; with exact measurements the absolute-value penalty kept them below 10-4%, also on pump and conveyor cycles, while the loss per unit of work changed by at most 0.6%. Without flux reservation it lowers and delays the torque during a current-limited flux rebuild, unlike a combined absolute-value and quadratic term. Field-orientation mismatch, measurement noise and dead time cause errors that the penalty does not remove.