**1. Introduction**

Indirect rotor field-oriented control (IRFOC) is widely used in induction machine drives because of its high performance in the base speed and field-weakening region. The control scheme of IRFOC is shown in Figure 1. Currently, the flux level and torque control in IRFOC are the research highlights in the field-weakening region [1–6]. The solutions are based on the accuracy of the rotor field-oriented angle. However, the rotor field-oriented method based on the integration of the rotor angular velocity and rotor slip angular velocity in IRFOC is affected by variations in parameters such as the rotor resistance. The rotor resistance varies with temperature and can be more than twice that of the normal resistance at 25 ◦C. The well-known solution to rotor field-oriented inaccuracy is parameter identification [5–10] and observers [11–15]. In [5,6], a magnetizing curve of induction in the field-weakening region and saturated region is proposed. Off-line parameter identification methods are proposed in [7,8]. A simple calculation based on the specification of an induction machine is introduced in [9]. These methods are useful and easy to apply in industry. Online parameter identification schemes are proposed in [10,11]. Solutions to address the parameter sensitivity problem in speed sensorless control of induction machines have been proposed, such as a sliding mode observer [12–15], a low-pass filter [16], square-wave voltage injection [17], and model reference adaptive control [18]. These algorithms require considerable computational resources and mainly aim to reduce the risk of instability phenomena. However, in the IRFOC of induction machines, the inaccurate field orientation caused by variable parameters is due to not only the instability but also the load capacity and dynamic performance.

**Citation:** Liu, Y.; Zhao, J.; Yin, Q. Model-Based Predictive Rotor Field-Oriented Angle Compensation for Induction Machine Drives. *Energies* **2021**, *14*, 2049. https:// doi.org/10.3390/en14082049

Academic Editor: Ryszard Palka

Received: 14 March 2021 Accepted: 5 April 2021 Published: 7 April 2021

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**Figure 1.** Control diagram of induction machine IRFOC.

Model-based predictive control (MPC) for machine drives and power electronics is an alternative control strategy that has gained attention in recent years. This approach can be used to address multivariable system constraints and nonlinearities in a very intuitive way [19]. Therefore, MPC has been successfully used for different applications, such as power converters connected to resistor–inductor (RL) loads [20], power electronics fault tolerance [21–23], energy management of electric vehicles [24,25], autonomous vehicle control [26,27], and high-performance drives for AC machines [28–32]. In [28], an MPCbased vector control method named GTV-MPTC for induction machines is proposed to cause the instantaneous torque to reach its reference value at the end of the next control period. The weighting factors in MPC are eliminated by investigating the relationship between the torque and stator flux to avoid tedious tuning work in [29]. However, the impact of variable parameters such as stator and rotor resistors is not given. In [30–32], MPC is used to improve the dynamic performance and reduce torque ripples in permanentmagnet synchronous motors (PMSM) drives. Compared to the vector control of induction machines, the control of PMSMs does not require a calculation of the slip velocity. Therefore, the rotor flux orientation for PMSMs is easy and accurate using a speed sensor.

In this paper, a compensation approach based on a model predictive algorithm of the rotor field-oriented angle error is proposed for IRFOC of induction machines. The d-axis and q-axis currents in the rotation reference frame are predicted and compared with the currents by current sensors to correct the rotor flux oriented angle. To improve the stability and robustness, the proposed predictive algorithm is based on the current, voltage, and velocity data stored in the memory. The algorithm can be realized easily in real-time. After compensation of the rotor field-oriented angle error, the output torque and current control performance can be improved. In Section 2, the mathematical model of IRFOC is introduced. Section 3 demonstrates the proposed model-based predictive algorithm and its implementation based on the stored data. The simulated results are shown in Section 4. Finally, the experimental results are presented to verify the proposed method in Section 5.
