Abstract
This paper studies global nonsingular fixed-time terminal sliding mode control (GNFTSMC) for a second-order uncertain permanent magnet synchronous motor (PMSM) system to further improve its speed tracking performance. The newly proposed GNFTSMC consists of a time-dependent terminal sliding surface and a piecewise continuous sliding mode control law. By a time-dependent function constructed from the initial conditions of the system and a predefined time, the sliding surface is always reached at the initial instant and forced to a traditional fast terminal sliding surface after the predefined time. Based on Filippov's stability principles, the globally fixed-time stability of the GNFTSMC is proved. Furthermore, a priori time independent of the initial conditions is derived to estimate the boundary of the settling time of the closed control loop. Then, the control law is analyzed to be always nonsingular. Thus, the GNFTSMC-based speed controller for the PMSM speed tracking system is developed. Finally, simulations are conducted for the proposed controller and other terminal sliding mode controllers. The results show that compared to the other controllers, the PMSM system based on GNFTSMC displays improved performance characteristics of faster speed response, smaller chattering and higher current efficiency.
Highlights
The permanent magnet synchronous motor (PMSM) is known to be a highly efficient drive for various modern electromechanical systems
To overcome the weaknesses of the existing NFTSMCs [30], [31] and achieve the fixed-time speed tracking control for the PMSM system, we proposed time-dependent global nonsingular fixed-time terminal sliding mode control (GNFTSMC) in this paper
Overall, compared to [30], [31], the proposed GNFTSMC makes four distinctive contributions: 1) Fixed-time stability can be accomplished with a simpler and more nonconservative a priori time; 2) The sliding surface of GNFTSMC is stabilized to zero from the initial instant, leading to the global robustness and the elimination of the reaching phase; 3) The singularity phenomenon is avoided during the whole control process without modifying the control law; 4) The number of the control parameters is strongly decreased
Summary
The permanent magnet synchronous motor (PMSM) is known to be a highly efficient drive for various modern electromechanical systems. The control law is complicated and there are more limitations on the parameters in the sliding surface to avoid singularity compared to those of the traditional NTSMCs. To overcome the weaknesses of the existing NFTSMCs [30], [31] and achieve the fixed-time speed tracking control for the PMSM system, we proposed time-dependent global nonsingular fixed-time terminal sliding mode control (GNFTSMC) in this paper. Overall, compared to [30], [31], the proposed GNFTSMC makes four distinctive contributions: 1) Fixed-time stability can be accomplished with a simpler and more nonconservative a priori time; 2) The sliding surface of GNFTSMC is stabilized to zero from the initial instant, leading to the global robustness and the elimination of the reaching phase; 3) The singularity phenomenon is avoided during the whole control process without modifying the control law; 4) The number of the control parameters is strongly decreased. The switching gain k can be set as close to D as possible to reduce control chattering
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