An Adaptive Super Twisting Nonlinear Fractional Order PID Sliding Mode Control of Permanent Magnet Synchronous Motor Speed Regulation System Based on Extended State Observer

Abstract

In this article, a novel adaptive super-twisting nonlinear Fractional-order PID sliding mode control (ASTNLFOPIDSMC) strategy using extended state observer (ESO) for the speed operation of permanent magnet synchronous motor (PMSM) is proposed. Firstly, this paper proposes a novel nonlinear Fractional-order PID (NLFOPID) sliding surface with nonlinear proportion term, nonlinear integral term and nonlinear differential term. Secondly, the novel NLFOPID switching manifold and an adaptive supertwisting reaching law (ASTRL) are applied to obtain excellent control performance in the sliding mode phase and the reaching phase, respectively. The novel ASTNLFOPIDSMC strategy is constructed by the ASTRL and the NLFOPID sliding surface. Due to the utilization of NLFOPID switching manifold, the characteristics of fast convergence, good robustness and small steady state error can be ensured in the sliding mode phase. Due to the utilization of ASTRL, the chattering phenomenon can be weakened, and the characteristics of high accuracy and strong robustness can be obtained in the reaching phase. Further, an ESO is designed to achieve dynamic feedback compensation for external disturbance. Furthermore, Lyapunov stability theorem and Fractional calculus are used to prove the stability of the system. Finally, comparison results under different controllers demonstrate that the proposed control strategy not only achieves good stability and dynamic properties, but also is robust to external disturbance. INDEX TERMS Adaptive super-twisting nonlinear Fractional-order PID sliding mode control (ASTNL-FOPIDSMC) strategy, extended state observer (ESO), permanent magnet synchronous motor (PMSM), nonlinear Fractional-order PID (NLFOPID) sliding surface, adaptive super-twisting reaching law (ASTRL).

Adaptive Super Twisting Sliding Mode Control With Fractional Order Sliding Surface for Trajectory Tracking of a Mobile Robot

“…Researchers have defined a variety of forms of fractional calculus, and two kinds of fractional calculus which are widely used in control field are Riemann Liouville (RL) and Caputo definitions [22,27].The RL fractional calculus of function ) (t f is defined as:…”

“…At the same time, it is difficult to determine the uncertainty domain, which makes it difficult to select the appropriate parameters 1 k and 2 k . In order to improve the control performance, the following adaptive super-twisting reaching law (ASTRL) is selected [22]: The improved adaptive fractional order super twisting sliding mode control (AFOSTSMC) scheme is shown in the Fig. 2.…”

Model-Free Control Using Improved Smoothing Extended State Observer and Super-Twisting Nonlinear Sliding Mode Control for PMSM Drives

“…The sliding mode controller (SMC) strategy has become an important research branch in the field of automatic control. During the past few decades, various SMC strategies have been widely used in the PMSM speed control system such as fractional order SMC [11,12], integral SMC [13], fuzzy SMC [14,15], high-order SMC [16] and non-singular terminal SMC [17]. As a high-order SMC algorithm, the super-twisting (ST) structure has been widely studied by many scholars.…”

Speed Regulation Based on Adaptive Control and RBFNN for PMSM Considering Parametric Uncertainty and Load Fluctuation

“…Fast convergence and good tracking precision are achieved through this method. In [18], a SMC method combining a nonlinear fractional-order PID switching manifold, an extended state observer, and a super twisting reaching law is investigated to achieve small steadystate error, fast convergence, and strong anti-fluctuation performance. In [19], a speed control scheme with respect to a backstepping controller (BSPC) and a disturbance observer (DOB) is introduced to obtain strong anti-fluctuation performance.…”