Structural Theory of Vibration Protection Systems

Abstract

Modern theory of automatic control of dynamical systems contains in its arsenal an extremely valuable tool. We are talking about the structural representation of an arbitrary dynamical system. Such representation allows us to divert attention from the physical nature of a process (thermal, vibrational, diffusion, etc) to the physical nature of the elements (mechanical, pneumatic, etc). In the context of structural representation of a mechanical system, we can explore diverse aspects of dynamic processes (controllability, invariance, stability, etc.) [1–3]. The theory of vibration protection is a very attractive application area of structural theory for several reasons. First, many fundamental aspects and concepts of control theory in general and the theory of vibration protection coincide; these include input–output concepts, transfer function, etc. Second, a vibration protection system consists of pronounced blocks and can be represented in symbolic form by a functional block diagram. Successful attempts that consider the problems of vibration protection in terms of the structural theory have been performed by Kolovsky [4, 5], Eliseev [6], and Bozhko et al. [7]. Systematic exposition of the structural theory to systems with distributed parameters was presented by Butkovsky [8]. Structural representation of the system in conjunction with the vibration protection device is a common way of describing complex dynamical systems with lumped and distributed parameters. Structural theory allows us to easily introduce changes into a vibration protection system of the object and find a relationship between any coordinates of a system, while the differential equation of the system assumes a fixed input–output. The Simulink (MATLAB) package has a full set of blocks that allows us to implement just about any structural model.