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相关概念视频

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

58
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
58
Feedback control systems01:26

Feedback control systems

256
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
256
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

79
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
79
Linear time-invariant Systems01:23

Linear time-invariant Systems

190
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
190
Open and closed-loop control systems01:17

Open and closed-loop control systems

577
Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...
577
PI Controller: Design01:24

PI Controller: Design

155
Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...
155

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Updated: May 15, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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对于非线性无限维系统的稳定线性化模型预测控制.

Hamza El-Kebir1, Richard Berlin2, Joseph Bentsman3

  • 1Dept. of Aerospace Engr., Urbana, IL 61801, USA.

IFAC-PapersOnLine
|May 12, 2025
PubMed
概括
此摘要是机器生成的。

本研究为复杂系统引入了强大的线性化模型预测控制,确保尽管近似误差,输出约束得到满足. 这种计算效率高的方法增强了对非线性分布式参数系统的控制.

关键词:
分布式参数系统的模型预测控制.有限制的控制控制.不确定系统的不确定性

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科学领域:

  • 控制理论 控制理论
  • 应用数学 应用数学 应用数学
  • 系统工程 系统工程

背景情况:

  • 模型预测控制 (MPC) 被广泛使用,但与非线性系统和近似误差作斗争.
  • 由于线性化和离散化不准确,现有的MPC框架往往无法保证真实系统的输出约束.
  • 非线性分布式参数系统 (DPS) 由于其无限维的状态空间,存在重大控制挑战.

研究的目的:

  • 为无限维系统中的非线性进化方程开发一种计算效率高,稳健的模型预测控制 (MPC) 方法.
  • 在MPC法中明确考虑线性化和离散化错误,确保在实际系统上满足输出约束.
  • 通过输出约束将这些近似误差纳入非线性DPS的可处理的MPC.

主要方法:

  • 为非线性亲属控制进化方程提出了强大的线性化方法.
  • 紧密的积分不等式是根据对非线性系统动态的轻微假设来推导的,以制定输出约束.
  • 这些约束被设计成可以轻松实时评估,平衡计算效率和约束严格性.

主要成果:

  • 开发的方法产生了一个模型预测控制规律,该规律首次对近似误差具有稳定性.
  • 线性化和离散化错误被明确处理,保证对真实系统的约束满足.
  • 该方法允许在计算效率和输出约束的严格性之间进行权衡.

结论:

  • 这项工作使得非线性分布式参数系统的稳健和计算效率高的模型预测控制成为可能.
  • 这种新的方法通过严格考虑近似误差来确保输出约束的满足.
  • 该方法在诸如基于能源的自主手术等领域有潜在的应用,在1D热方程示例上证明了这一点.