Tristan Braun

In-depth evaluations of an electric drive's behavior typically result from co-simulation, combining models of motor, power electronics and control software. This approach can be used to evaluate pulse patterns for a given operating point, e.g., for electric vehicle applications, preventing real-world experiments. Here, the co-simulation model is fed with offline calculated optimized pulse patterns (OPPs) that are used to increase, among others, the drive's efficiency. Due to the large motor time constant compared to the fundamental wave period, reaching steady state using a simple open-loop control requires unnecessary long simulation times. Hence, a model predictive closed-loop control implementation of the OPPs is proposed which reduced the overall computational effort significantly. However, it turns out that the OPP evaluation using a finite-element-method-based co-simulation for a permanent magnet synchronous motor remains largely uncertain in terms of the predicted power losses which led to the development of a semi-analytical model to further reduce the required computational time. As none of the approaches was able to deliver a suitable trade-off between model accuracy and calculation time, this investigation highlights the remaining challenges of evaluating OPPs based on drive co-simulations motivating further research towards the surrogate-assisted or direct experimental OPP optimization in the future.

In this article, a high-frequency (HF) six-port delta- and star-connected three-phase induction motor model is proposed. The model consists of multistage RLC circuits, which include the mutual inductances between the phases. The three-phase HF motor model is derived from common-mode (CM) and differential-mode (DM) equivalent circuits, which are extracted from CM and DM measurements on the motor. A methodology is developed to consider the nonlinear DM inductance effect in the low-frequency (LF) range. The per-phase circuit is symmetric concerning the begin and end points. This symmetry allows us to connect a star configuration into a delta configuration by simply changing the phase connections of the proposed three-phase circuit without recalculating the parameters and vice versa. The three-phase motor model is eventually combined with external circuitry and simulated by a standard circuit solver. The proposed model allows impedance predictions with good accuracy up to 100 MHz. The method is verified with two induction machines, which have 3- and 11-kW rated powers. The proposed HF six-port three-phase motor model can be used for decoupled CM and DM noise predictions as well as for six-port mixed-mode noise prediction.

A feedback-systems-based approach for real-time copper-loss minimization of nonlinear anisotropic permanent magnet synchronous motors (PMSMs) considering saturation and cross coupling is proposed. The procedure is based on a feedback systems formulation of the underlying optimization problem for maximum torque per current (MTPC) control. A nonlinear dynamical system is derived that describes the scalar product of the tangent of the torque curve and the gradient of the current circle. By a suitable feedback design, a closed expression of the control input of the nonlinear current dynamics in the direct-quadrature ( $dq$ )-axis is obtained. As a result, the solution of the differential equations of the nonlinear current dynamics yields the desired optimal setpoint $d/q$ currents. The stability of the designed feedback system for MTPC control is thoroughly examined by Lyapunov’s direct method. Comparative studies for measured data as well as an analysis of computational runtimes confirm the effectiveness of the proposed method.

A nonlinear mathematical model for the dynamics of permanent magnet synchronous machines with interior magnets is discussed. The model of the current dynamics captures saturation and dependency on the rotor angle. Based on the model, a flatness-based field-oriented closed-loop controller and a feed-forward compensation of torque ripples are derived. Effectiveness and robustness of the proposed algorithms are demonstrated by simulation results.

A constructive method for the design of nonlinear observers is discussed. To formulate conditions for the construction of the observer gains, stability results for nonlinear singularly perturbed systems are utilised. The nonlinear observer is designed directly in the given coordinates, where the error dynamics between the plant and the observer becomes singularly perturbed by a high-gain part of the observer injection, and the information of the slow manifold is exploited to construct the observer gains of the reduced-order dynamics. This is in contrast to typical high-gain observer approaches, where the observer gains are chosen such that the nonlinearities are dominated by a linear system. It will be demonstrated that the considered approach is particularly suited for self-sensing electromechanical systems. Two variants of the proposed observer design are illustrated for a nonlinear electromagnetic actuator, where the mechanical quantities, i.e., the position and the velocity, are not measured.

A constructive nonlinear observer design for self-sensing of digital (ON/OFF) single coil electromagnetic actuators is studied. Self-sensing in this context means that solely the available energizing signals, i.e., coil current and driving voltage are used to estimate the position and velocity trajectories of the moving plunger. A nonlinear sliding mode observer is considered, where the stability of the reduced error dynamics is analyzed by the equivalent control method. No simplifications are made regarding magnetic saturation and eddy currents in the underlying dynamical model. The observer gains are constructed by taking into account some generic properties of the systems nonlinearities. Two possible choices of the observer gains are discussed. Furthermore, an observer-based tracking control scheme to achieve sensorless soft landing is considered and its closed-loop stability is studied. Experimental results for observer-based soft landing of a fast-switching solenoid valve under dry conditions are presented to demonstrate the usefulness of the approach.