Fixed‐Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

Abstract

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

“…According to the sliding mode control theory, the sliding mode manifold and its derivative must satisfy ( ) = 0 and( ) = 0 (29) By substituting (26) without combination harmonic excitation into (28), one can havė ( ) = ( ) + ( )…”

“…Compared with the finite-time stability, fixed-time stability possesses a faster convergence rate, higher precision estimation, and stronger disturbance rejection. The fixed-time stability of nonlinear systems with uncertain parameters, unmodeled dynamics, and unknown disturbances has been a well-established area [26][27][28]. Ma et al [29] proposed an adaptive fixed-time fast terminal sliding mode control method for the second-order chaotic oscillation power system.…”

Predefined-time smooth stability analysis of nonlinear chaotic systems with applications in the PMSM system and Hindmarsh-Rose neuron model

“…After that, the adaptive and finite-time control strategies have been also proposed to stabilize and synchronize the PMSMs [33,34]. For overcoming the heavy dependence on the initial states, the fixed-time stabilization and synchronization of PMSMs have been investigated successively [35,36]. Recently, the predefined-time stability of PMSM with perturbations has been studied [37,38], but the discontinuous absolute value and signum functions are used inevitably, which may incur the unfavorable chattering phenomenon.…”

Finite-Time Stochastic Stability Analysis of Permanent Magnet Synchronous Motors with Noise Perturbation

“…The oscillation or irregular movement caused by chaotic behaviors can, in extreme circumstances, lead to the collapse of the systems [ 23 ]. Therefore, chaos control, aiming at eliminating the undesired chaotic behavior, has become an important nonlinear control problem [ 24 , 25 , 26 , 27 , 28 , 29 ]. A common method such as feedback sliding mode control is usually used for systems with parameter uncertainty and disturbance, which requires that the bounds of the uncertainty and disturbance must be known in advance.…”