Formal derivation of direct torque control for induction machines

Direct torque control (DTC) is an induction motor control technique that has been successful because it explicitly considers the inverter stage and uses few machine parameters, while being more robust to parameter uncertainty than field-oriented control (FOC). This paper presents a formal derivation of DTC based on singular perturbation and nonlinear control tools. The derivation elaborates an explicit relationship between DTC performance and machine characteristics; low-leakage machines are expected to per form better under DTC. It is shown that DTC is a special case of a sliding-mode controller based on the multiple time-scale properties of the induction machine. The known troublesome machine operating regimes are predicted and justified. Explicit conditions to guarantee stability are presented. DTC is shown to be a suboptimal controller because it uses more control effort than is required for flux regulation. Finally, compensation strategies that extend DTC are discussed. The derivation does not require space vector concepts thus, it is established that the traditional link between DTC and space vectors is not fundamental.