## 1 Introduction
Various other issues, such as parametric variation, low back EMF, saturation problem, flux distortion, current ripples, and input constraint handling, create hindrance in the accurate estimation of position and speed. Therefore, by keeping in view all the aforementioned attributes, a novel MPC-UKF control scheme is proposed for the sensorless control of PMSM. In UKF, the unscented transformation technique has many advantages over the other observers, namely, finding the initial value and hassle-free tuning. The UKF is a derivative-free approach and does not require any linearization steps, so no Jacobean is needed. As the error of the motor parameters is considered at the beginning, the UKF-based speed and flux observation have strong robustness to motor parameters. The UKF acts as an observer because of its simplicity of two-step procedures: prediction and correction. Moreover, it estimates the parameters even at a relatively low speed that cannot be estimated with other controllers. According to the operation frequency, there are two main types of sensorless motor control: one is the model-based method that detects the fundamental component of back EMF. The other injects an additional excitation signal to utilize the asymmetrical effect of the inductance in PMSM. The first method works well in the high-speed range but fails at low speed when the signal-to-noise ratio (SNR) of the EMF is too small for observation. On the contrary, the second method can derive position at low and even zero speed but performs poorly at high speed due to the limitation of observer bandwidth. To achieve a whole-speed-range of sensorless operation, a hybrid position estimation strategy combining both methods at middle speed is adopted. Two variables describe the UKF states: an estimate of the current state's derivative is based on the knowledge of observation and error covariance matrix, that is, the uncertainty of the observation in the estimation process. The benefit of using MPC can be justified since in UKF, there are small errors during dynamical working caused by inaccurate modeling of the inverter, which is nonlinear, and MPC also handles the gates switching very efficiently within defined constraints. The main contributions of the paper are:  
* A hybrid approach, MPC-UKF, is tuned to a challenging PMSM control and estimation problem in order to efficiently deal with the issues of fastly varying dynamics, severe nonlinearities, random uncertainties, and unavailability of measurements [22]. * The MPC and the UKF are efficient control and estimation algorithms, respectively, and extension of these as a combination creates a novel solution to the challenges. Parametric invariance, disturbance rejection, and improved accuracy and estimates are the advantages of our proposed novel hybrid technique [23]. * In an effort to closely replicate the practical PMSM dynamics and to have more realistic findings with respect to the actual experimental setup, the practical factors, such as disturbances and uncertainties, process and measurement noise, have been taken into account. Such efforts certainly allow the observer, the UKF, to provide more accurate estimates that are otherwise sacrificed due to inappropriate, inaccurate, or incomplete system information. The UKF is successfully tuned to estimate speed and position of PMSM based on the direct available states, currents, and voltages. * The MPC-UKF approach is compared with the combination of the MPC with state-of-the-art observer technique, the Sliding Mode Observer (SMO), and also with the more traditional approach, the EKF, in terms of robustness and reliability. The remainder of the paper is organized as follows: Section 2 describes the mathematical modeling of the PMSM and discrete version of the model. Description of the control structure in the proposed scheme is presented in Section 3. Simulation results and discussions are presented in Section 4. The paper is concluded in Section 5 along with future directions.