On controllability and observability of chains formed by point masses connected with springs and dashpots

TL;DR

This paper analyzes a chain of point masses connected by springs and dashpots, demonstrating that proportional elastic and damping constants ensure complete controllability and observability regardless of chain length.

Contribution

It establishes conditions under which such mechanical chains are fully controllable and observable, extending control theory to complex physical systems with proportional parameters.

Findings

System is controllable and observable when elastic and dashpot constants are proportional.

Controllability and observability are independent of the number of masses.

The system is also completely reachable and reconstructible under the same conditions.

Abstract

We consider a physical system constituted by a finite chain of point masses consecutively linked by linear springs and dashpots. At one of the end points acts an external control force aligned with the chain and the system is observable by the position of the other end point. We show that, whatever is the number of the point masses, if the sequence of the elastic constants is proportional to the sequence of the dashpot constants, then the mechanical system is completely controllable, completely observable, completely reachable and completely re-construictible, in the sense of control theory.