网络综合及其在悬挂系统中的应用

The main purpose of the proposed research is to investigate the theory of passive network synthesis and its application in vehicle suspension systems. The network synthesis problem considered plays a fundamental role in circuit theory and systems theory, which is also directly related to the passive mechanical control such as the vehicle suspension control. Although the correspondence is perfect between the spring/damper and the inductor/resistor in the standard "force-current" analogy between mechanical and electrical networks, the capacitor does not have a corresponding two-terminal mechanical element. A new mechanical element called "inerter" was therefore introduced several years ago. It has been successfully applied to a series of passive mechanical control systems, in which the performance advantages have been well demonstrated. More importantly, the invention of this kind of element completes the analogy between passive mechanical systems and electrical ones. Therefore, the theory of electrical networks can be directly mapped onto mechanical networks, making it possible to design passive mechanical systems based on the theory of passive network synthesis. This makes the design process more systematic instead of using the trial-and-error approach. Although many important results have been achieved in passive network synthesis, many issues remain unsolved. The invention and application of the inerter has renewed the interest in this field. This proposed research mainly addresses the simplified realization problem of passive network synthesis. The key focuses of the research include (1) minimal one-port realization problems of several positive-real functions of low degrees; (2) establishment of one-port realization algorithms suitable for arbitrary positive-real functions. In addition, applications of the inerter in vehicle suspension systems (a quarter-car model) will be investigated. Here, the potential for low-complexity network synthesis will be considered in the suspension design. Finally, the software and hardware simulation platforms will be established.

本项目的主要目的是研究无源网络综合问题及其在汽车悬挂系统中的应用。 本世纪初，工程界提出了一种称为"惯容"的机械元件，并将其成功运用于多类机械系统的控制之中。惯容的提出在理论上完善了无源机械系统与无源电路系统之间的类比关系，使得无源机械系统的设计能借助于无源网络综合来推进。尽管无源网络综合理论已有较长的研究历史，但仍有许多问题尚未解决。本项目将主要围绕不含变压器无源网络的简化实现问题展开以下讨论：1.低阶正实函数的一端口无变压器最简实现问题；2.任意正实函数的一端口无变压器综合算法的构造问题。 此外，本项目还将研究惯容在悬挂系统（1/4车模型）中的应用，特别是将低复杂度网络综合理论应用到车辆悬挂系统设计中，将惯容与悬挂系统的优点结合的同时保持低成本。同时考虑易被工业界接受的控制算法，建立契合实际的软件和硬件平台，实现科技成果的有效转化。

无源网络综合理论虽然已有很长的研究历史，但随着工程界一类称为惯容的元件的提出，又赋予了无源网络综合理论新的研究意义。此外，以惯容和网络综合理论为基础的机械控制系统设计也具有重要的工程意义。.本项目研究内容从基于惯容的网络综合理论与机械控制系统设计两方面展开。在无源网络综合方面，主要包括：1. 含1个惯容1个阻尼器及最多3个弹簧的无源机械网络实现；2. 双二次函数的五元件桥式网络实现；3. 一类双二次函数的七元件串并联实现；4. 适用于双二次最小函数的广义Reichert定理证明；5. 三端口纯电阻网络的最简实现问题；6. 给定增益参数的RC梯形二端口网络的一类传递函数实现。在机械控制系统设计方面，主要包括：1. 基于惯容的无源和半主动悬挂系统设计问题；2. 半主动惯容及其在悬挂系统和动力吸振系统中的应用问题；3. 基于惯容的振动系统分析、隔振系统和动力吸振系统设计问题；4. 风机系统振动控制及惯容应用问题。.本项目已在低复杂度无源网络综合最简实现、双二次最小函数的广义Reichert定理证明、无源和半主动悬挂系统设计、振动系统分析与综合、半主动惯容的实现、风机系统振动控制等方面取得了一定的研究成果。这些理论和应用成果，一方面推动了无源网络综合理论和振动理论的发展，另一方面为基于惯容的机械系统设计以及有效的成果转化奠定了基础。