Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis

IF 1.8 4区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS
Andrea Mattioni, Christophe Prieur, Sophie Tarbouriech
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引用次数: 0

Abstract

This paper deals with the modelling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing configuration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptotically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the origin’s global asymptotic stability of the nonlinear closed-loop system.

Abstract Image

利用自感应压电致动器稳定横梁的控制设计:管理迟滞的存在和不存在
本文论述了在自感应配置中使用压电致动器控制的柔性夹紧梁的建模和稳定问题。我们从一般原理出发,利用压电的一般规律推导出模型。得到的模型由一个描述柔性变形动力学的 PDE 和一个描述电荷动力学的 ODE 组成。首先,我们证明了推导出的线性模型具有良好的求解能力,并且在应用包含自感配置中估算项的电压控制法时,原点具有全局渐近稳定性。其次,我们提出了一个更为现实的假设,即电气领域存在滞后现象。在应用无源控制法时,我们证明了非线性闭环系统的良好假设性和原点的全局渐近稳定性。
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来源期刊
Mathematics of Control Signals and Systems
Mathematics of Control Signals and Systems 工程技术-工程:电子与电气
CiteScore
2.90
自引率
0.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Mathematics of Control, Signals, and Systems (MCSS) is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing. Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential equations, differential algebraic equations or difference equations. Potential topics include, but are not limited to controllability, observability, and realization theory, stability theory of nonlinear systems, system identification, mathematical aspects of switched, hybrid, networked, and stochastic systems, and system theoretic aspects of optimal control and other controller design techniques. Application oriented papers are welcome if they contain a significant theoretical contribution.
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