stability criterion

简明释义

稳性准则

英英释义

例句

1.The engineer applied the stability criterion to ensure the bridge could withstand high winds.

工程师应用了稳定性标准以确保桥梁能够承受强风。

2.The stability criterion for the chemical reaction indicates whether it will proceed safely.

该化学反应的稳定性标准表明它是否会安全进行。

3.In control theory, the stability criterion helps determine if a system will return to equilibrium after a disturbance.

在控制理论中，稳定性标准帮助确定一个系统在受到干扰后是否会恢复到平衡状态。

4.Before launching the satellite, engineers checked the stability criterion to prevent any orbital issues.

在发射卫星之前，工程师检查了稳定性标准以防止任何轨道问题。

5.The software was tested against the stability criterion to guarantee it would perform reliably under load.

该软件经过测试，以符合稳定性标准，以保证在负载下可靠运行。

作文

In the field of engineering and control systems, the concept of a stability criterion is crucial for ensuring that systems behave predictably over time. A stability criterion refers to the specific conditions or requirements that must be met for a system to remain stable under various operating conditions. Stability is a fundamental aspect of any dynamic system, whether it be a mechanical structure, an electronic circuit, or even an economic model. Without a proper understanding of these criteria, engineers and scientists risk creating systems that could fail or behave erratically.One of the most common stability criteria used in control theory is the Routh-Hurwitz criterion. This criterion provides a method to determine the stability of a linear time-invariant system by analyzing its characteristic polynomial. If all the roots of the polynomial have negative real parts, the system is deemed stable. This mathematical approach allows engineers to assess stability without directly solving for the roots, which can be complex and time-consuming.Another important stability criterion is the Nyquist stability criterion. This graphical method involves plotting the frequency response of a system and determining how many times the plot encircles the critical point in the complex plane. By understanding the relationship between the gain and phase of the system, engineers can design controllers that ensure stability across a range of operating conditions.In addition to these specific methods, the concept of stability criteria can also be applied to more abstract systems, such as economic models. For example, in economics, a model may be considered stable if small deviations from equilibrium do not lead to large fluctuations. In this context, the stability criterion could involve examining the responsiveness of supply and demand to changes in price or other external factors. A stable economic model is essential for effective policy-making and long-term planning.The importance of stability criteria extends beyond theoretical applications; it is vital in practical scenarios as well. For instance, in aerospace engineering, the stability of an aircraft during flight is influenced by numerous factors, including aerodynamic forces and control inputs. Engineers must apply stability criteria to ensure that the aircraft can withstand disturbances, such as turbulence or sudden maneuvers, without losing control. Failure to adhere to these criteria could result in catastrophic outcomes.Moreover, the concept of stability criteria is not limited to engineering and economics; it also finds relevance in fields like ecology and biology. For example, in ecological models, stability can refer to the resilience of an ecosystem in response to environmental changes. A stable ecosystem can recover from disturbances, while an unstable one may collapse under pressure. Understanding the stability criteria for these systems can help in conservation efforts and in predicting the impacts of climate change.In conclusion, the stability criterion is a fundamental concept that spans multiple disciplines, providing a framework for understanding and ensuring stability in various systems. Whether through mathematical analysis in engineering or conceptual models in economics and ecology, recognizing and applying these criteria is essential for the successful design and management of systems. As technology advances and systems become increasingly complex, the importance of stability criteria will only continue to grow, highlighting the need for ongoing research and education in this vital area.

在工程和控制系统领域，稳定性标准的概念对于确保系统随时间的可预测行为至关重要。稳定性标准是指必须满足的特定条件或要求，以使系统在各种操作条件下保持稳定。稳定性是任何动态系统的基本方面，无论是机械结构、电子电路还是经济模型。如果没有对这些标准的正确理解，工程师和科学家就有可能创建出可能发生故障或表现不稳定的系统。在控制理论中，最常用的稳定性标准之一是Routh-Hurwitz标准。该标准提供了一种通过分析特征多项式来确定线性时不变系统稳定性的方法。如果多项式的所有根都具有负实部，则系统被认为是稳定的。这种数学方法使工程师能够在不直接求解根的情况下评估稳定性，因为求解根可能是复杂且耗时的。另一个重要的稳定性标准是Nyquist稳定性标准。该图形方法涉及绘制系统的频率响应，并确定绘图在复平面上围绕临界点的圈数。通过理解系统增益和相位之间的关系，工程师可以设计控制器，以确保在一系列操作条件下的稳定性。除了这些特定方法外，稳定性标准的概念还可以应用于更抽象的系统，例如经济模型。例如，在经济学中，如果小的偏离均衡不会导致大的波动，则模型可以被视为稳定。在这种情况下，稳定性标准可能涉及检查供需对价格或其他外部因素变化的响应。稳定的经济模型对于有效的政策制定和长期规划至关重要。稳定性标准的重要性不仅限于理论应用；在实际场景中也至关重要。例如，在航空航天工程中，飞机在飞行期间的稳定性受到多种因素的影响，包括气动力和控制输入。工程师必须应用稳定性标准，以确保飞机能够承受干扰，如湍流或突然机动，而不会失去控制。不遵循这些标准可能导致灾难性的后果。此外，稳定性标准的概念不仅限于工程和经济学；在生态学和生物学等领域也有相关性。例如，在生态模型中，稳定性可以指生态系统对环境变化的韧性。稳定的生态系统能够从干扰中恢复，而不稳定的生态系统可能在压力下崩溃。了解这些系统的稳定性标准可以帮助保护工作和预测气候变化的影响。总之，稳定性标准是一个跨多个学科的基本概念，为理解和确保各种系统的稳定性提供了框架。无论是在工程中的数学分析，还是在经济学和生态学中的概念模型，认识和应用这些标准对于系统的成功设计和管理至关重要。随着技术的进步和系统变得越来越复杂，稳定性标准的重要性只会继续增长，突显了在这一重要领域进行持续研究和教育的必要性。