Purpose

The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types.

Design/methodology/approach

An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function.

Findings

The related analysis can be carried out easily depending on the values of classical elements.

Originality/value

Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.

中文翻译：

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利用离散形式的拉格朗日函数、哈密顿函数和耗散函数对离散时间工程动态系统进行可观性、可控性和稳定性分析

目的

本文的目的是分析离散时间工程/物理动态系统的动态状态。分析基于可观测性、可控性和稳定性首先使用通过离散拉格朗日耗散模型[{L,D}-模型]推导的耗散广义运动的离散时间方程获得的广义运动的差分方程进行短观测离散时间动态系统。作为下一步，还对与可观测性、可控性和稳定性概念相关的同一系统进行了分析，但这次使用从离散哈密顿系统导出的离散耗散正则方程以及离散广义速度比例瑞利耗散函数。这些方法已应用于不同配方类型的耦合（机电）示例。

设计/方法/方法

使用通过离散 {L,D} 模型获得的广义运动离散方程和通过离散哈密顿量获得的离散耗散正则方程以及离散广义速度比例瑞利耗散函数，对离散时间观测动态系统的可观测性、可控性和稳定性进行分析。

发现

根据经典元素的值，可以很容易地进行相关分析。

原创性/价值

利用离散拉格朗日函数和离散哈密顿函数分别得到的广义运动离散方程和离散耗散正则方程，结合速度比例离散耗散函数，利用状态变量理论，对离散时间观测工程系统进行可观测性、可控性和稳定性分析。在所提出的方法中，物理量不需要相互转换。