有约束复杂随动被控对象理论分析与模型建立

Theory Analysis and model development on a constraint servo control system

本文研究缘于医疗康复领域的需求,帮助一些运动机能受损的患者部分恢复生活自理能力。针对这一问题,本文提出建立一种以神经康复为背景并符合日常场景的被控任务。分别从基于达朗伯原理的动静法和动态临界能量两个角度进行理论分析,针对日常生活中常见的移动水杯并无液体溢出这一实际过程提出了概念化的"碗-球"动态复杂系统,并依据平衡方程和动力学普遍方程(欧拉-拉格朗日方程)建立了该被控对象的数学模型,得到动态微分表达式、传递函数和状态空间方程,揭示了系统内部的运动状态,为此被控任务的实现提供理论基础。并进一步对该被控对象的能控性及能观性进行分析,结果证明了本系统的外界输入量对系统状态具有很高的控制能力以及输出量对状态具有很好的反映能力,为神经康复研究提供了一个新的研究对象。

This research comes from the field of medical rehabilitation, it helps disabled person repair human sensory-motor functions. On this background, a task by emulating everyday scenario is modeled. The system analyses are processed from different aspects of D’Alembet principle and energy safety margin. A conceptual ‘cup and ball’ model is proposed to emulate the everyday activity of transporting a cup of water without water spilling. Based on equilibrium equations and Euler-Lagrange equation, an appropriate mathematical model of the system is developed, which can reveal motion states in this system and provide the theoretic foundation for realizing this task. The controllability and observability analyses are given after the mathematical model obtained, and experiment results show that this system is both completely state controllable and observable. This study provides a new dynamic object for control research in the field of medical rehabilitation.