The Rigid-Body Dynamic Analysis of the Control and Containment Requirements for the Swash-Plate of an Axial-Piston Pump

随着对机器、结构、车辆和其他机械系统的要求越来越高，分析和设计所必须面对的数学模型的顺序和复杂性也越来越高。物理洞察力和分析方法变得不那么有效。然而，随着系统维度的增加，多个时间尺度的可能性也在增加。两个或两个以上广泛分离的时间尺度的存在提供了系统分解和随之而来的简化分析和设计的机会。对于线性时不变系统，时域和频域方法都可以利用这个机会。对于非线性系统，可以采用解析奇异摄动法。但是这种方法只适用于奇异摄动形式的数学模型，而这种形式在没有多时间尺度结构的先验知识的情况下是不可能得到的，因此本文的研究目标是发展一种用于有限维非线性动力系统的时间尺度辨识和降阶模型开发的方法。在以前的NSF资助下，已经开发了基于有限时间李雅普诺夫指数和向量的方法的基础。在目前的项目中，该方法被用来研究的时间尺度结构的非线性动力系统，模拟机械系统。已经屈服于分析奇异摄动方法的示例性系统，因此已知具有两个或更多个时间尺度，首先进行研究以进一步完善该方法。接下来，研究已知或怀疑具有多时间尺度行为的系统。然后，一种方法被开发用于使用的时间尺度信息来构造一个状态转换，将系统模型的形式服从降阶分析和控制设计。 该研究将为非线性系统的分析和设计建立一个重要的新能力。降阶，更好的条件，和物理的理解-以前只能获得低阶系统的聪明的分析师应用分析奇异摄动方法-将获得一般的非线性动力系统。

As the requirements for machines, structures, vehicles, and other mechanical systems become more ambitious and more demanding, the order and complexity of the mathematical models that must be confronted for analysis and design increases. Physical insight and analytical methods become less effective. Yet as the system dimension increases, so does the likelihood of multiple time-scales. The presence of two or more widely separated time-scales offers the opportunity for system decomposition and consequent simplified analysis and design. For a linear time-invariant system, both time and frequency domain methods are available to exploit this opportunity. For a nonlinear system, the analytical singular perturbation method is available. But this method is only applicable to a mathematical model in singularly perturbed form, and this form is not generally obtainable without a priori knowledge of the multiple time-scale structure.The research objective is thus to develop a methodology for time-scale identification and reduced-order model development for application to finite dimensional nonlinear dynamical systems. Under previous NSF funding, the foundations of the methodology, which is based on finite-time Lyapunov exponents and vectors, have been developed. In the current project the methodology is used to investigate the time-scale structure in nonlinear dynamical systems that model mechanical systems. Exemplary systems that have yielded to the analytical singular perturbation method, and thus are known to have two or more time-scales, are investigated first to further refine the methodology. Next systems either known or suspected to have multiple time-scale behavior are investigated. An approach is then developed for using the time-scale information to construct a state transformation that will bring the system model into a form amenable to reduced-order analysis and control design. The research will establish a significant new capability for nonlinear system analysis and design. The order reduction, better conditioning, and physical understanding -- previously obtainable only for low-order systems by clever analysts applying the analytical singular perturbation method -- will be obtainable for general nonlinear dynamical systems.