Design and Discretization of Adaptive Sliding-Mode Controllers

自适应滑模控制器的设计与离散化

• 批准号: 416911519
• 负责人: Professor Dr.-Ing. Johann Reger
• 金额: --
• 依托单位: Fachgebiet Regelungstechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/416911519?language=en
• 关键词: Design; Discretization; Adaptive; Sliding; Mode

Sliding-mode control (SMC) is an established approach with outstanding robustness properties. A stronghold of SMC is its capacity to attenuate unstructured uncertainties, requiring no information other than an upper bound. On the downside, many SMC approaches cannot handle uncertainties that show explicit state-dependencies. Complementary, modern adaptive controllers are capable of dealing with structured uncertainties guaranteeing Lyapunov-stability, given that parameter variations are slow. Yet, obtaining good performance and transient behavior may be difficult.We propose to combine both methods and exploit their individual strengths to the benefit of the overall robustness and performance of the control system while keeping actuator action moderately low. This is achieved by using indirect adaptive controllers that yield an “estimate” for the structured uncertainty by exploiting the maximum available information. For best possible robustness we use SMC approaches on the remaining unstructured uncertainty. This way, large portions of the control signal are given to the adaptive part leaving less control action to the SMC-part of the controller. Based on the certainty equivalence principle, we explore new combinations of adaptive SMC approaches and examine their benefits and requirements. Lyapunov functions for higher-order SMC approaches will yield entirely novel adaptive control laws that render the closed-loop system robustly stable against a large class of uncertainties.For implementing these control-schemes we will transform them into discrete-time versions. Digital realization of SMC, however, may lead to undesirable oscillations in the system variables. Such oscillations, often termed discretization chattering, may cause excessive wear of mechanical components and low control accuracy. The amplitude and frequency characteristics of these chattering effects strongly depend on the properties of the control algorithm and the applied discretization scheme. The proposed separation of uncertainty in structured and unstructured parts offers a high potential to reduce the discontinuous control gains. Thus, also discretization chattering may be reduced. Since continuity properties of the nominal SMC are partly inherited to the adaptation law, additional sources of discretization chattering may be the consequence. Therefore, we will thoroughly analyze the discretization process and the digital realization of sliding-mode based adaptive controllers. The goal of the analysis is to find out which properties of these controllers will prevail after discretization. In this regard, special attention is kept on the stability properties of the closed-loop system and the achieved control accuracy.Our methods will be applied to a state-of-the-art nano-positioning stage. The model structure of this system shows specific uncertainties which are appropriate for the assessment of the proposed concepts and comparison with existing methods.

滑模控制(SMC)是一种成熟的方法，具有良好的鲁棒性。SMC的一个优点是它能够减弱非结构化不确定性，除了上限之外不需要任何信息。不利的一面是，许多SMC方法无法处理显式状态依赖关系的不确定性。作为补充，现代自适应控制器能够处理保证Lyapunov稳定性的结构不确定性，假设参数变化很慢。然而，获得良好的性能和暂态行为可能很困难。我们建议将这两种方法结合起来，并发挥各自的优势，在保持执行器动作适度较低的同时，有利于控制系统的整体鲁棒性和性能。这是通过使用间接自适应控制器来实现的，该控制器通过利用最大可用信息来产生对结构化不确定性的“估计”。为了获得最好的稳健性，我们对剩余的非结构化不确定性使用了SMC方法。这样，大部分控制信号被提供给自适应部分，而将较少的控制动作留给控制器的SMC部分。基于确定性等价原则，我们探索了自适应SMC方法的新组合，并分析了它们的优点和要求。高阶SMC方法的Lyapunov函数将产生全新的自适应控制律，使闭环系统对一大类不确定性保持鲁棒稳定。为了实现这些控制方案，我们将它们转化为离散时间形式。然而，SMC的数字化实现可能会导致系统变量出现不希望看到的振荡。这种通常称为离散化抖动的振荡可能会导致机械部件过度磨损和控制精度降低。这些抖振效应的幅值和频率特性强烈地依赖于控制算法和所采用的离散化方案的特性。建议的结构和非结构部分的不确定性分离提供了很高的潜力来减少不连续的控制增益。因此，也可以减少离散化抖动。由于标称SMC的连续性属性部分继承自适应律，因此可能会产生额外的离散化抖振来源。因此，我们将深入分析基于滑模的自适应控制器的离散化过程和数字实现。分析的目的是找出离散化后这些控制器的哪些性质将占优势。在这方面，我们特别关注闭环系统的稳定性和所获得的控制精度。我们的方法将被应用于最先进的纳米定位工作台。这一系统的模型结构显示了特定的不确定性，这些不确定性适合于评估拟议的概念并与现有方法进行比较。