对于使用非二进制的利亚普诺夫函数的 Takagi-Sugeno 系统具有不可测量的前提变量的观察者设计
Wail Hamdi1, Mohamed Yacine Hammoudi1, Madina Hamiane2
1Mohamed KHIDER University of Biskra, Algeria.
ISA transactions
|August 29, 2024
概括
这项研究减少了 Takagi-Sugeno 模糊系统的非线性观察者的保守主义,使用非正方形的 Lyapunov 函数. 这种方法为诸如感应电机之类的复杂系统提供了计算效率和改进的稳定性分析.
科学领域:
- 控制系统工程 控制系统工程
- 模糊逻辑系统 模糊逻辑系统
- 非线性系统分析 非线性系统分析
背景情况:
- 塔卡吉-苏杰诺模糊系统的非线性观察者经常表现出保守主义,因为他们依赖于二次的利亚普诺夫函数.
- 模糊系统中不可测量的前提变量对观察者设计和稳定性分析构成挑战.
研究的目的:
- 为了减少 Takagi-Sugeno 模糊系统与不可测量的前提变量的非线性观察者中的保守主义.
- 开发一种使用非二次式莱普诺夫函数的更有效的稳定性分析方法.
- 提出一种有效的计算方法来解决衍生的双线矩阵不等式.
主要方法:
- 应用平均值定理来解决不可测量的前提变量.
- 利用非二次的利亚普诺夫函数 (NQLF) 来降低观察者的保守主义.
- 稳定性条件的表述为双线矩阵不等式 (BMI).
- 采用高效的线性解决方法来解决BMI问题.
主要成果:
- 与之前的基于方位Lyapunov函数的方法相比,观察者保守主义的减少.
- 用双线矩阵不等式成功制定和解决稳定性条件.
- 通过数值示例和实时感应电机观察员实现验证了有效性和计算效率.
结论:
- 提出的方法有效地减少了Takagi-Sugeno模糊系统的非线性观察者的保守主义.
- 使用NQLF和高效的BMI解决器提供了一个实用和计算可行的方法.
- 感应电机的实时实现验证了观察者在复杂,高度不平等的场景中的性能.
更多相关视频
相关概念视频
01:26Linear Approximation in Frequency Domain
88
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....
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....
88
01:22Multi-input and Multi-variable systems
105
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...
In the absence...
105
01:23Linear time-invariant Systems
229
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...
229
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
56
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
56
01:21Linear Approximation in Time Domain
72
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,...
72
01:20Second Order systems I
139
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...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
139