A Nonlinear Extended State Observer Design for Torsional Vibrations Estimation in PMSM Drive

In every drivetrain, torque harmonics coming from electrical and mechanical sources lead to torsional vibrations. In this paper, a Nonlinear Extended State Observer (NESO) is designed to estimate the shaft torque in a Two Degree-of-Freedom (DOF) system, comprising a Permanent Magnet Synchronous Machine (PMSM), an elastic shaft, a rotating load. The system is modeled as a Multi-Input Multi-Output (MIMO) nonlinear system. Being the NESO commonly defined for single-output systems, a procedure to implement it for the MIMO nonlinear system under consideration is presented. Moreover, a general method to transform a generic MIMO system into an integral-chain form is provided, enabling NESO application. The observer performance is evaluated through computer simulations.