This paper deals with discrete-time models and current control methods for synchronous motors with a magnetically salient rotor structure, such as interior permanent-magnet synchronous motors and synchronous reluctance motors (SyRMs). The dynamic performance of current controllers based on the continuous-time motor model is limited, particularly if the ratio of the sampling frequency to the fundamental frequency is low. An exact closed-form hold-equivalent discrete motor model is derived. The zero-order hold of the stator-voltage input is modeled in stationary coordinates, where it physically is. An analytical discretetime pole-placement design method for two-degrees-of-freedom proportional-integral current control is proposed. The proposed method is easy to apply: only the desired closed-loop bandwidth and the three motor parameters (R s , L d , L q ) are required. The robustness of the proposed current control design against parameter errors is analyzed. The controller is experimentally verified using a 6.7-kW SyRM drive. Index Terms-Current control, delay, discrete-time model, interior permanent-magnet synchronous motor (IPM), saliency, synchronous reluctance motor (SyRM), zero-order hold (ZOH). I. INTRODUCTIONS YNCHRONOUS motors with a magnetically salient rotor-such as interior permanent-magnet synchronous motors (IPMs), synchronous reluctance motors (SyRMs), and permanent-magnet (PM)-assisted SyRMs-are more and more applied in hybrid (or electric) vehicles, heavy-duty working machines, and industrial applications. In these applications, the maximum speeds and, consequently, the maximum operating frequencies can be very high (e.g., 12 000 r/min corresponding to the frequency of 1000 Hz for a ten-pole machine). Since the switching frequency of the converter feeding the motor Manuscript

Abstract-Two back-electromotive-force (EMF)-based position observers are compared for motion-sensorless synchronous motor drives: the reduced-order observer and the adaptive full-order observer. A stabilizing gain is proposed for the adaptive fullorder observer, which guarantees the local stability of the closedloop system, if the motor parameters are known. Equations for the steady-state position error and for the linearized estimationerror dynamics under erroneous parameters are derived, and the robustness of the two observers against parameter errors is analyzed and compared. The observers are experimentally evaluated using a 6.7-kW synchronous reluctance motor drive in low-speed operation and under parameter errors. The gain selection of the reduced-order observer is easier, but the adaptive full-order observer can be made more robust against parameter variations and noise.

All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Abstract-This paper deals with the modeling of the magnetic saturation in synchronous reluctance motors (SyRMs). The saturation is modeled by means of analytical expressions, which can be easily embedded in dynamic equivalent-circuit models. A modified power function-proposed in this paper-can take into account the cross saturation between the orthogonal windings, it is physically consistent, and the number of its parameters is small. The function can be used in real-time control applications and in computer simulations. The model fits well to the experimentally measured inductances of a 6.7-kW SyRM. As an application example, the proposed saturation model was implemented in a full-order observer of a motion-sensorless drive, and experimental results are shown.

Abstract-Saturation due to the main flux and rotor leakage flux interaction appears in induction machines, especially if the rotor slots are skewed or closed. Conventional saturation models used in connection with dynamic equivalent-circuit models do not take this phenomenon into account. In this paper, explicit functions for modeling this mutual saturation are proposed. These functions are physically reasonable, they are easy to fit, and the number of their parameters is small. The proposed functions can be used in real-time applications and in computer simulations if high accuracy and physical consistency are preferable. The model fits well to the data obtained from finite element analysis or experimental data of a 2.2-kW motor. The model predicts the stator current with good accuracy both in steady state and in transients.

Abstract-A reduced-order position observer with statorresistance adaptation is proposed for motion-sensorless permanent-magnet synchronous motor drives. A general analytical solution for the stabilizing observer gain and stability conditions for the stator-resistance adaptation are derived. Under these conditions, the local stability of the position and stator-resistance estimation is guaranteed at every operating point except the zero frequency, if other motor parameters are known. Furthermore, the effect of inaccurate model parameters on the local stability of the position estimation is studied, and an observer gain design that makes the observer robust is proposed. The proposed observer is experimentally tested using a 2.2-kW motor drive; stable operation at very low speeds under different loading conditions is demonstrated.

Abstract-A back-EMF-based position observer for motionsensorless synchronous reluctance motor drives is augmented with high-frequency signal-injection method for improved lowspeed operation. Previously proposed observer structure is further improved to account for the cross saturation in the motor. The combined observer is experimentally evaluated using a 6.7-kW synchronous reluctance motor drive in low-speed operation and under various load conditions. The resulting position error at low speeds and standstill is small.

Abstract-This paper deals with the speed and position estimation of interior permanent-magnet synchronous motor (IPMSM) and synchronous reluctance motor (SyRM) drives. A speedadaptive full-order observer is designed and analyzed in the discrete-time domain. The observer design is based on the exact discrete-time motor model, which inherently takes the delays in the control system into account. The proposed observer is experimentally evaluated using a 6.7-kW SyRM drive. The analysis and experimental results indicate that drastic performance improvements can be obtained with the direct discrete-time design, especially if the sampling frequency is relatively low compared to the fundamental frequency.

Tuovinen, T. (2018)Abstract-This paper deals with the speed and position estimation for synchronous reluctance motors (SyRMs) and interior permanent-magnet synchronous motors (IPMs). A unified design and analysis framework for a class of back-electromotive-force (back-EMF)-based observers is developed and the links between apparently different estimation methods are brought out. State observers equipped with a speed-adaptation law are shown to be mathematically equivalent to voltage-model-based flux observers equipped with a position-tracking loop. The error signal driving the adaptation law or the tracking loop is presented in a generalized form. Using the framework, a stabilizing gain design is reviewed and detailed design guidelines are given. Selected observer designs are experimentally evaluated using a 6.7-kW SyRM drive and a 2.2-kW IPM drive.