Finite-time controller design of multiple integrator nonlinear systems with input saturation

Mei, Keqi; Ma, Li; He, Rong; Ding, Shihong

doi:10.1016/j.amc.2019.124986

Cited by 32 publications

(19 citation statements)

References 40 publications

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“…If the matrix A ∈ R n×n is Hurwitz, then there is a scalar c > 0 such that ‖e At ‖ ≤ ce (λ max (A)/2)t , where λ max (A) � max Re(λ i (A)) . Taking the time derivative of the designed sliding manifold s along (13) and substituting the extended state observer (12) and the output-feedback controller (14), we have…”

Section: Stability Analysismentioning

confidence: 99%

“…is Hurwitz and the controller parameter β in (13) and (14) is chosen such that − ((B/J) + ((3n p ψ f β)/2J)) < 0, then the estimation errors and the output tracking error of the PMSM system (2) will converge to a bounded neighbourhood of the origin, and the ultimate bound can be made arbitrarily small. Furthermore, if _ π u q tends to zero as t ⟶ ∞, then the closedloop system (20) is globally asymptotically stable.…”

Section: Theoremmentioning

confidence: 99%

“…However, it should be noted that the servo control performance is significantly affected by nonlinearities, uncertainties, and disturbances in PMSM systems, and the traditional linear control strategies including the proportional-integral (PI) controller [5] are unable to provide satisfactory control performance [6]. In order to obtain better performance, many advanced nonlinear control methods have been developed for PMSM servo systems in recent years, such as adaptive control [2,7], robust control [8,9], linearization control [10], disturbance observer-based control [2,11], fuzzy-logic based control [6,12], finite time control [13,14], fractional order control [15], sliding mode control [16,17], and neuro-network based control [5,12]. ese control strategies improve control performance for PMSM servo systems from different aspects.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Output-Feedback Sliding Mode Control for Permanent Magnet Synchronous Motor Servo System Subject to Unmatched Disturbances

Jiang

Zhang

2021

Mathematical Problems in Engineering

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This paper aims to investigate the speed regulation problem for permanent magnet synchronous motor (PMSM) servo systems subject to unknown load torque disturbances. The proposed method utilizes sliding mode control (SMC), invariant manifold theory, and disturbance observation technique. In the PMSM servo systems, the unknown load torques will affect the control performance to a large extent, which is unmatched. In addition, compared with full-state measurement, the output-feedback framework is easy to implement and reduces the sensor costs. However, it is difficult to handle unmatched disturbance and unmeasured states simultaneously. To this end, this paper specifically combines the sliding mode control theory with the invariant manifold theory and puts forward an output-feedback disturbance rejection control method. The key idea is that the unmatched disturbance in the PMSM servo systems is transformed into matched one by taking advantage of the invariant manifold, which is different from existing results. The transformation maintains most of dynamics of the PMSM system for control design, which improves the accuracy. In addition, an extended state observer is designed to estimate the current and lumped disturbance simultaneously; then, the output-feedback SMC method is proposed by introducing the estimations. Besides, the switching gain in the proposed sliding mode controller can change with estimation errors adaptively, and the chattering reduces. Simulation results on a PMSM system validate the effectiveness of the proposed control strategy.

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Section: Stability Analysismentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Output-Feedback Sliding Mode Control for Permanent Magnet Synchronous Motor Servo System Subject to Unmatched Disturbances

Jiang

Zhang

2021

Mathematical Problems in Engineering

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“…If the powers of positive odd rational numbers are 1 and the nonlinear terms are not considered in References 26-29, then a corresponding conventional model is in the form of the multiple integrator nonlinear systems. 30 For cases in which the powers of positive odd rational numbers are larger than 0, Fu et al 31 solved the global finite-time stabilization problem for switched nonlinear systems, and Fu et al 32 studied the global adaptive finite-time stabilization problem for uncertain nonlinear systems with an unknown control coefficient by using logic-based switching control. For the case where the powers are positive odd integers, Qian and Li 33 studied the finite-time stabilization problem for second-order nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

“…Accordingly, Sun et al, 26 Cai et al, 27 Li et al, 28 and Sun et al 29 studied the finite‐time stabilization problem for this type of high‐order nonlinear system, in which the powers are equal to or larger than 1. If the powers of positive odd rational numbers are 1 and the nonlinear terms are not considered in References 26‐29, then a corresponding conventional model is in the form of the multiple integrator nonlinear systems 30 . For cases in which the powers of positive odd rational numbers are larger than 0, Fu et al 31 solved the global finite‐time stabilization problem for switched nonlinear systems, and Fu et al 32 studied the global adaptive finite‐time stabilization problem for uncertain nonlinear systems with an unknown control coefficient by using logic‐based switching control.…”

Section: Introductionmentioning

confidence: 99%

Distributed finite‐time output consensus tracking for a class of high‐order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints

Liu

Wang

Ding

2020

Intl J Robust & Nonlinear

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This article considers the distributed finite-time output consensus tracking problem for a class of high-order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints. First, since the finite-time tracking design method for a single system with the powers of positive odd rational numbers cannot be extended to the finite-time consensus tracking for multiagent systems, an especial configuration method of the powers is constructed. Second, a new exponential brake function (EBF) that purely depends on the outputs is proposed to address the asymmetric output constraints directly. By adjusting a related parameter, the large converted value can be avoided when the output approaches the constrained boundaries, which may reduce the control input over a large output scale. Third, given some reasonable assumptions, a distributed finite-time output consensus tracking controller is proposed to guarantee that the tracking error converges to an adjustable small region around the origin in a finite time and that the output constraints of all subsystems are not violated. The result with output constraints can also be extended to the case without output constraints. Finally, simulation verifications also confirm the benefits and effectiveness of the proposed control methods.

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Observer‐based fixed‐time SOSM hybrid control with a nonvanishing mismatched disturbance

Yuan

Mei

2021

Math Methods in App Sciences

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In this paper, the control problem for a class of second‐order sliding mode (SOSM) systems with a nonvanishing mismatched disturbance is investigated via a composite SOSM hybrid control manner. The composite SOSM hybrid control is proposed by utilizing a fixed‐time disturbance observer (DOB) and a fixed‐time composite SOSM controller. The fixed‐time DOB is firstly developed to estimate mismatched disturbances. Secondly, by using adding a power integrator technique, the fixed‐time composite SOSM controller can be designed step by step. Based on the hybrid strategy, the proposed controller can switch from a finite‐time SOSM controller to a fixed‐time SOSM controller. The former finite‐time controller is proposed to avoid finite‐time escape problem for the controlled system within the setting time of the proposed fixed‐time DOB. The latter fixed‐time controller can drive system states to zero within a fixed time whose setting time is free of initial values. The novelty of the developed control methodology is that it cannot only avoid the finite‐time escape problem but also provide fixed‐time stability for the controlled system. Moreover, strict Lyapunov analysis is provided to show that the controlled system under the fixed‐time DOB and the fixed‐time composite SOSM controller is fixed‐time stable. Finally, the validity of the proposed control methodology is verified by an academic example.

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Finite-time controller design of multiple integrator nonlinear systems with input saturation

Cited by 32 publications

References 40 publications

Output-Feedback Sliding Mode Control for Permanent Magnet Synchronous Motor Servo System Subject to Unmatched Disturbances

Output-Feedback Sliding Mode Control for Permanent Magnet Synchronous Motor Servo System Subject to Unmatched Disturbances

Distributed finite‐time output consensus tracking for a class of high‐order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints

Observer‐based fixed‐time SOSM hybrid control with a nonvanishing mismatched disturbance

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