Control of synchronous reluctance machines using differential flatness theory

The article uses differential flatness theory to solve the nonlinear control and estimation problems of synchronous reluctance machines. By exploiting the differential flatness properties of the state-space model of the synchronous reluctance machine it is shown that a state-variables transformation (diffeomorphism) can be applied to it. This finally brings the model to an input-output linearized form, or equivalently to the so-called linear canonical Brunovsky state-space form. For the the transformed state-space description of the model the solution of the feedback control problem becomes possible after applying a linear feedback controller and the pole placement concept. Moreover, to solve the state-estimation problem and to implement state estimation-based feedback control through the measurement of specific state variables, the Derivative-free nonlinear Kalman Filter is used as a state observer. This is a new nonlinear filtering method, which consists of (i) the Kalman Filter recursion applied on the aforementioned linearized model of the synchronous reluctance machine, (ii) an inverse transformation based again on differential flatness theory which allows for computation of estimates of the state variables of the initial nonlinear model. Furthermore, to improve the robustness of the flatness-based control scheme and to compensate for model uncertainty or additive input disturbances that affect its dynamics, the Derivative-free nonlinear Kalman Filter is redesigned as a disturbance observer. The proposed control method is of proven global asymptotic stability and its efficiency is further confirmed through simulation experiments.