无记忆的双观察者基于输出反稳定线性系统的输入和输出延迟
IEEE transactions on cybernetics
|June 17, 2024
概括
本研究介绍了一种新的无内存双观察器控制器,用于稳定具有输入和输出延迟的线性系统. 该方法简化了控制器设计,并确保了连续和离散时间系统的稳定性.
科学领域:
- 控制系统工程 控制系统工程
- 系统理论 系统理论
- 应用数学 应用数学 应用数学
背景情况:
- 输入和输出延迟的线性系统带来了重大的控制挑战.
- 现有的基于双观察者的控制器可以是无限维或基于内存的,使实际实施复杂化.
- 模型减少技术提供了一种简化延迟系统的途径,但可能导致复杂的控制器结构.
研究的目的:
- 为具有输入和输出延迟的线性系统开发无内存的基于双观察员的稳定控制器.
- 在特定条件下证明拟议的控制器的闭环稳定性.
- 为了比较控制器的维度与减少顺序的基于观察者的控制器.
主要方法:
- 使用模型减速方法将延迟系统转换为相当的无延迟系统.
- 一个经过修改的无内存的基于双观察员的稳定控制器是为减少系统设计的.
- 使用Lyapunov-Krasovskii函数来证明闭环稳定性.
- 该方法适用于连续时间和离散时间系统.
主要成果:
- 一个没有内存的双观察者控制器成功设计,其稳定性得到了证明.
- 拟议的控制器提供了一个较小的维度相比,减少顺序的基于观察者的控制器,当系统有更多的输入比输出.
- 设计和稳定性分析需要更复杂的数学工具,例如先进的利亚普诺夫-克拉索夫斯基函数.
- 数字模拟证实了拟议的稳定方法的有效性.
结论:
- 开发的基于双观察者的无内存控制器为稳定具有输入和输出延迟的线性系统提供了有效的解决方案.
- 这种方法是多功能性的,适用于连续时间和离散时间系统.
- 该方法在控制器维度方面提供了潜在的优势,特别是在输入超过输出的系统中.
相关概念视频
01:18Second Order systems II
96
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
96
01:26Feedback control systems
304
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...
304
01:24Effects of feedback
548
Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
548
01:21Linear Approximation in Time Domain
81
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,...
81
01:23Linear time-invariant Systems
248
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...
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...
248
01:26Classification of Systems-I
179
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
179