distributed parameter system

简明释义

分布参数系统

英英释义

例句

1.Fluid dynamics is a field that frequently deals with distributed parameter systems in the analysis of flow.

流体动力学是一个经常处理分布参数系统的领域，分析流动情况。

2.The modeling of electrical circuits can sometimes involve distributed parameter systems when considering transmission lines.

在考虑输电线时，电路的建模有时会涉及到分布参数系统。

3.In engineering, a distributed parameter system refers to a system where parameters vary over space and time.

在工程学中，分布参数系统是指参数在空间和时间上变化的系统。

4.The heat transfer in a rod can be modeled as a distributed parameter system due to temperature gradients along its length.

由于沿着杆的温度梯度，杆中的热传递可以建模为一个分布参数系统。

5.Control strategies for distributed parameter systems often require advanced mathematical tools.

对分布参数系统的控制策略通常需要先进的数学工具。

作文

In the field of engineering and applied mathematics, the term distributed parameter system refers to a system where the state variables depend on both time and spatial variables. This contrasts with lumped parameter systems, where the state variables are only functions of time. Understanding distributed parameter systems is crucial for modeling and controlling various physical systems that are distributed over a certain domain, such as heat conduction in a rod or fluid flow in a pipe. One of the primary characteristics of distributed parameter systems is that they can be described by partial differential equations (PDEs). These equations account for the spatial distribution of the system's properties, making them more complex than ordinary differential equations (ODEs) used in lumped systems. For instance, in thermal analysis, the temperature distribution along a material can be described using the heat equation, a type of PDE. The challenge lies in solving these equations, especially when boundary conditions and initial conditions must also be considered. The applications of distributed parameter systems are vast and varied. In civil engineering, for example, the behavior of beams under load can be analyzed using the Euler-Bernoulli beam theory, which is a distributed parameter system. Similarly, in control theory, the dynamics of a flexible structure can be modeled as a distributed parameter system, leading to more accurate predictions of its behavior under various conditions. Moreover, the control of distributed parameter systems poses unique challenges. Traditional control methods designed for lumped systems may not be directly applicable. Instead, advanced techniques such as feedback control strategies and observer design are often employed. For example, in the case of a heated rod, one must consider how temperature changes at one point affect the temperature at other points along the rod. This interdependence requires a comprehensive understanding of the system's dynamics. In recent years, the advent of modern computational tools has greatly facilitated the analysis and control of distributed parameter systems. Numerical methods, such as finite element analysis (FEA) and finite difference methods (FDM), allow engineers to simulate and solve complex PDEs that describe these systems. With the help of software tools, it is now possible to visualize the behavior of distributed parameter systems in real-time, providing valuable insights for design and optimization. In conclusion, the concept of distributed parameter systems is fundamental to many fields of science and engineering. By recognizing the spatial dependencies of system behaviors, engineers can develop more sophisticated models that lead to better designs and controls. As technology continues to advance, the importance of distributed parameter systems will only grow, paving the way for innovations in various industries, from aerospace to biomedical engineering. Understanding this concept is essential for anyone looking to make significant contributions to the field of engineering and applied sciences.

在工程和应用数学领域，术语分布参数系统指的是系统的状态变量依赖于时间和空间变量。这与只依赖于时间的集中参数系统形成对比。理解分布参数系统对于建模和控制各种在特定领域内分布的物理系统至关重要，例如杆中的热传导或管道中的流体流动。分布参数系统的一个主要特征是它们可以通过偏微分方程（PDE）来描述。这些方程考虑了系统属性的空间分布，使其比用于集中系统的常微分方程（ODE）更为复杂。例如，在热分析中，材料沿线的温度分布可以使用热方程（一种PDE）来描述。解决这些方程的挑战在于，必须同时考虑边界条件和初始条件。分布参数系统的应用广泛而多样。在土木工程中，例如，可以使用欧拉-伯努利梁理论分析梁在载荷下的行为，这是一种分布参数系统。同样，在控制理论中，柔性结构的动态行为可以建模为分布参数系统，从而更准确地预测其在各种条件下的行为。此外，控制分布参数系统面临独特的挑战。为集中系统设计的传统控制方法可能不适用。相反，通常采用先进的技术，如反馈控制策略和观测器设计。例如，在加热杆的情况下，必须考虑一个点的温度变化如何影响杆上其他点的温度。这种相互依赖性需要全面理解系统的动态行为。近年来，现代计算工具的出现大大促进了分布参数系统的分析和控制。数值方法，如有限元分析（FEA）和有限差分法（FDM），使工程师能够模拟和解决描述这些系统的复杂PDE。借助软件工具，现在可以实时可视化分布参数系统的行为，为设计和优化提供宝贵的见解。总之，分布参数系统的概念是科学和工程许多领域的基础。通过认识到系统行为的空间依赖性，工程师可以开发出更复杂的模型，从而实现更好的设计和控制。随着技术的不断进步，分布参数系统的重要性只会增加，为航空航天、生命医学工程等各个行业的创新铺平道路。理解这一概念对于任何希望在工程和应用科学领域做出重大贡献的人来说都是至关重要的。