分数顺序动力学通过数据驱动方法学习和控制:以软操纵器为例
概括
本研究引入了对分数顺序系统的新型数据驱动框架,提高了模型准确性和控制性能. 新方法增强了分数顺序深拉格朗日网络 (fPLCS-DeLaN) 和分数顺序控制器,用于复杂的动态.
科学领域:
- 控制工程 控制工程 控制工程
- 应用数学 应用数学 应用数学
- 机器学习 机器学习
背景情况:
- 分数式微积分能够建模复杂的动态,但在系统识别和控制方面存在挑战.
- 准确的建模和稳定的控制对于表现出内存和非局部性的系统至关重要.
研究的目的:
- 提出统一的数据驱动框架,以应对模拟和控制分数顺序系统的挑战.
- 引入新的深度学习架构和控制策略,以提高系统性能.
主要方法:
- 开发了一个分数顺序的深拉格朗日网络 (fPLCS-DeLaN),集成物理先验和自我注意力机制,用于学习系统动态.
- 提出了一种基于混合网络的干扰观察器 (T2F-CRNN),将CNN,复发和模糊推理结合起来,以进行可靠的不确定性估计.
- 设计了一个分数顺序控制器,具有有限时间收,输入和补偿和滑动模式约束.
主要成果:
- fPLCS-DeLaN实现了至少一个数量级较低的建模错误,计算时间增加最小.
- 拟议的分数顺序控制器显著减少了短暂 (23.1%) 和稳定 (87.6%) 的跟踪错误.
- 在软操纵器平台上的实验验验证了框架的卓越模型学习和跟踪性能.
结论:
- 拟议的数据驱动框架有效地解决了分数顺序系统的复杂性.
- 深度学习和控制设计的创新导致了准确性,稳定性和性能的大幅提高.
- 这种统一的方法为涉及分数顺序动态的先进控制应用提供了有希望的方向.
相关概念视频
01:07Time-Domain Interpretation of PD Control
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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
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01:26PD Controller: Design
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In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
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01:21Linear Approximation in Time Domain
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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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
387
01:26Feedback control systems
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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...
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...
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01:20Second Order systems I
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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
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01:21First Order Systems
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First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
463