Formal Derivation of Direct Torque Control for Induction Motors using the Singular Perturbation Method

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 the singular perturbation method (SPM). The derivation elaborates a link between DTC and feedback linearization and presents an explicit relationship between DTC performance and machine characteristics. It is shown that DTC can be considered a special case of a continuous-time feedback law under quantization of the flux angle and the flux magnitude and torque errors. In addition, the feedback law from which DTC is derived is shown to have equivalent performance and similar information requirements as DTC, while being more robust to parameter uncertainty than FOC. From the analysis, it is shown that low-leakage machines are expected to perform better under both DTC and the SPM controller. The derivation does not require space vector concepts; therefore the traditional link between DTC and space vectors is shown not to be a fundamental one