I. Introduction
Permanent magnet synchronous machines (PMSMs) have been widely used in domestic and industrial applications due to their having both high torque density and efficiency [1]. Precise torque control of PMSM is required in many applications, such as robotics, elevators, and electric vehicles [2]. Accurate torque feedback of the machine is essential for both control and monitoring purposes. Hardware transducers such as strain gauges [3] and torsional displacement [4] can be used to measure the machine torque. However, they are usually very expensive and require extra installation space and cables. Therefore, torque estimation without a sensor is a preferable solution.