Physical system analysis related to observability, controllability and stability using its equations of generalized motion and canonical equations both in dissipative forms

Abstract

Using tensorial variables in contravariant, covariant forms and different formulation types, the reader is informed about a coupled physical nonlinear system with f degree of freedom. f second-order differential equations of dissipative generalized motion obtained by the extended Euler-Lagrange differential equations can be transformed to a system of 2f differential equations of order one using the theory of state variables or Hamiltonian approaches. Besides analyzing the system, these equations can also be used to analyze such a system in terms of observability, controllability and stability. In this article, another property of Lagrange-Dissipative system modeling ({L, D}-modeling briefly) is presented. And thus, this sort of modeling approach of physical/engineering systems are enriched by means of observability, controllability applying Lie algebra, which has the classical observability and controllability matrices of the linear case. Stability analysis is also performed. Using Lagrangian and Hamiltonian approaches together with dissipation, one can obtain the state equations for a system in an easy way. Moreover, different forms in different formulation types of state equations can be presented. How these forms are achieved is also explained. The approach is convenient specially when using coupled systems, where different physical quantities are available together. The only restriction compared to the classical state space analysis is that the generalized coordinate (and momentum) depending on formulation must be selected as the state variable. A coupled electromechanical example in different forms and formulations is given.