An Extension of Adaptive State Observers Using Dynamic Regressor Extension and Mixing With Relaxed Excitation Conditions

Abstract

The recently proposed DREM-based adaptive state observer (DREMBAO) design approach assumes that there exists transformation of the system model into a cascade form, linearly dependent on parameters vector and depends only on measured input and output. This paper proposes an extension to relax that assumption and extend the approach to state affine systems. Like the original version of DREMBAO, the proposed approach ensures global convergence of an estimation error to zero under a relatively weak condition. The advantages of the extension are demonstrated in the example with a permanent magnet synchronous motor. In contrast to the original approach, the proposed extension allows taking into account viscous friction in the motor and obtaining a simplified load torque estimation algorithm. Moreover, finite-time convergence to zero is ensured for the load torque and speed estimation error under a weak interval excitation.