Predefined-Time Control of Full-Scale 4D Model of Permanent-Magnet Synchronous Motor with Deterministic Disturbances and Stochastic Noises

Abstract

This paper presents a predefined-time convergent robust control algorithm that allows the control designer to set the convergence time in advance, independently of initial conditions, deterministic disturbances, and stochastic noises. The control law is consequently designed and verified by simulations for a full-scale 4-degrees-of-freedom (4D) permanent-magnet synchronous motor (PMSM) system in cases of a disturbance-free system with completely measurable states, a disturbance-free system with incompletely measurable states, a system with incompletely measurable states in the presence of deterministic disturbances, and a system with incompletely measurable states in the presence of both deterministic disturbances and stochastic noises. Numerical simulations are provided for the full-scale 4D PMSM system in order to validate the obtained theoretical results in each of the considered cases. To the best of our knowledge, this is the first attempt to design a predefined-time convergent control law for multi-dimensional systems with incompletely measurable states in the presence of both deterministic disturbances and stochastic noises.

Predefined-Time Backstepping Stabilization of Autonomous Nonlinear Systems

“…This problem was originally investigated in [15]. Here, we present an alternative solution to this problem and demonstrate its advantages with respect to some performance indices, such as a control input magnitude.…”

“…The predefined-time convergent linear time-varying control law, stabilizing the system state at the origin in presence of unknown nonlinearities, is designed based on the conventional backstepping technique, which makes it straightforwardly obtainable and intuitively consistent. The conducted numerical simulations show that the designed control input provides a lesser magnitude and, in some cases, faster real convergence times and is easier computable than some existing control laws, such as those proposed in [15].…”

“…This letter considers a class of autonomous nonlinear systems, where nonlinear terms are unknown but satisfy a linear growth condition, similarly to [15]. As known, the linear growth condition essentially means that the system state cannot diverge to infinity in finite time.…”

“…, where is the true convergence time. Problem statement: Consider the following autonomous nonlinear system [15]:…”

“…Here, we present an alternative solution to this problem and demonstrate its advantages with respect to some performance indices, such as a control input magnitude. Note that the linear growth condition (3) does not have to be in a triangular form, as it was assumed in [15]. In contrast to [11], the system (2) contains unmatched nonlinear disturbances appearing in each system equation.…”