Controllability and Observability of Parallel Magnetic Suspension Systems

Mizuno, Takeshi; Takasaki, Masaya; Ishino, Yuji

doi:10.1002/asjc.1263

Cited by 6 publications

(5 citation statements)

References 21 publications

(29 reference statements)

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“…In the (13), the first derivative of flux linkage is obtained in the control program using a discretization method within a fixed sampling time.…”

Section: Design Of Controllermentioning

confidence: 99%

“…Due to the characteristics of noncontact and high energy efficiency, magnetic levitation technologies have been applied to many fields, such as maglev train [1,2], magnetic bearing [3], thin steel plate processing [4], vibration isolation system [5,6], biomedicine [7], and aerospace microgravity devices [8,9]. For maglev systems, most of the established models are second-order current models [10][11][12][13] and third-order voltage models [14][15][16][17]. Among them, the second-order current models are easy to implement but not close to reality, while the third-order voltage models are close to reality but relatively complex.…”

Section: Introductionmentioning

confidence: 99%

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Global fast terminal integral sliding mode control based on magnetic field measurement for magnetic levitation system

Ren

et al. 2021

Asian Journal of Control

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Magnetic levitation systems are widely applied in many fields. In this paper, a global fast terminal integral sliding mode controller (GFTISMC) based on the second‐order flux linkage model is proposed to improve the response speed and steady‐state error of the maglev system. Firstly, the dynamic model of the maglev system is deduced, and the second‐order flux state model is established. Secondly, to improve the global response speed of the system and reduce the steady‐state error, a GFTISMC is constructed. A position model based on magnetic field measurement is determined to achieve closed‐loop control. Finally, compared with the traditional sliding mode control, the simulation and experimental results show that the proposed controller has better global response speed, stronger robustness, and smaller steady‐state error.

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“…In the (13), the first derivative of flux linkage is obtained in the control program using a discretization method within a fixed sampling time.…”

Section: Design Of Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global fast terminal integral sliding mode control based on magnetic field measurement for magnetic levitation system

Ren

et al. 2021

Asian Journal of Control

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“…Definition 3.5. The operator K * defined by (7) is called an observer of MF-BSDE (4). Equation ( 4) together with its observer K * is called the dual system to the original system (1).…”

Section: Observation Inequalitymentioning

confidence: 99%

“…There are a plenty of literatures on this issue. For the deterministic systems, one can refer to Lee and Markus [2] for the ordinary differential equation (ODE, for short) systems, Russell [3], Lions [4,5], and Zuazua [6] for the partial differential equation (PDE, for short) systems, and Mizuno et al [7], Li et al [8], and so on for some applications in engineering.…”

Section: Introductionmentioning

confidence: 99%

Exact controllability of linear mean‐field stochastic systems and observability inequality for mean‐field backward stochastic differential equations

2020

Asian Journal of Control

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This paper is concerned with the exact controllability of linear mean-field stochastic systems with time-variant random coefficients. We prove that the exact controllability, the validity of the observability inequality for the dual equation, the unique solvability of a family of optimal control problems, the unique solvability of a family of mean-field forward-backward stochastic differential equations (MF-FBSDEs), and the unique solvability of a family of norm optimal control problems are all equivalent. Therefore, some approaches are provided to investigate the issue of exact controllability.

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“…Generally, magnetic suspension stage (MSS) 9,10 refers to the systems that use attractive force, and magnetic levitation stage (MLS) 11–13 refers to the systems that use repulsive force. 14 MSS/MLS is a kind of stage that directly suspends/levitates and drives an unconstrained floater with magnetic force.…”

Section: Introductionmentioning

confidence: 99%

Analysis of coupled motion constraints and coupling errors for a six-axis magnetic levitation stage

Sheng

Menq

Tao

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents the coupled motion constraints and coupling errors analysis of a magnetic levitation stage, which are two aspects of the coupling characteristics of magnetic levitation stage caused by force coupling. Aiming at the motion constraint coupling problem, this paper proposes a motion constrain method based on the force distribution matrix of the magnetic levitation stage. By this method, the motion constraint intervals without input saturation for single-degree-of-freedom motion, in-plane motion, and out-of-plane motion of magnetic levitation stage are established. When used for motion control, these constraints can provide the motion constraint specifications for the magnetic levitation stage, avoid the input saturation problem caused by the actuation force coupling, and provide a theoretical basis for magnetic levitation stage trajectory planning. Aiming at reducing the coupling error, this paper proposes a strategy to evaluate the coupling degree of the magnetic levitation stage actuation force by the condition number of the actuation force transfer matrix and the singular value of the force and torque error matrix. On this basis, the force and torque coupling errors caused by the translational and rotational movements of the magnetic levitation stage are studied, and the mechanism and characteristics of the coupling error between the interaction of translational and rotational movements are revealed. Based on the obtained results, the decoupling algorithm of the magnetic levitation stage is designed. Experimental results of the normalized step response demonstrate that the linearity of the magnetic levitation stage will be destroyed by the current saturation, and coupling error can also be introduced. Therefore, it is necessary to study the motion constrain strategy to provide comprehensive criteria for the trajectory planning and controller design. Experimental results of six-axis coupling error analysis show that the coupling error of x- and y-axes translational movement is reduced by 69.34% and 69.60%, respectively. This method provides a theoretical basis for the decoupling of the magnetic levitation stage and reducing the coupling error.

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Controllability and Observability of Parallel Magnetic Suspension Systems

Cited by 6 publications

References 21 publications

Global fast terminal integral sliding mode control based on magnetic field measurement for magnetic levitation system

Global fast terminal integral sliding mode control based on magnetic field measurement for magnetic levitation system

Exact controllability of linear mean‐field stochastic systems and observability inequality for mean‐field backward stochastic differential equations

Analysis of coupled motion constraints and coupling errors for a six-axis magnetic levitation stage

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