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- W2894621159 abstract "In the analysis of feedback control systems in the state-space, the understanding of the mechanisms of their operation is lost. To regain the understanding of a physical background, a phase space notion is introduced. A linear transformation, suitably chosen, brings the mathematical model of the system in the state-space into a set of two differential equations, defining the phase space, spanned by generalized position and velocity hypercoordinates, in a close analogy to well known coordinates in the phase plane. A new mathematical model generates a parametric bilinear representation for the trajectories. The phase space becomes a vector field where energetic levels of reference are specified and trajectories are seen as the energy projections on the phase space. Using the principles of the Hamilton-Lagrangian mechanics and the principle of the least effort, it is shown that the parametric bilinear form also provides the energetic balance equation. This allows the definition of kinetic, potential, dissipative or absorptive and control components of energy. At the same time, the structural coefficients of the system are classified into the conservative and dissipative. The first are responsible for natural frequencies and the latter - for damping characteristics. Thus, the operation of the system is seen through the energetic mechanisms of storage, dissipation and exchange. Furthermore, it is shown that the dissipation of energy is related to the existence of negative feedback, and inversely, the negative feedback introduces the dissipation of energy, while the positive feedback is synonymous with the absorption of energy. Thus, the physical foundations of feedback controls and the mechanisms of stability and instability are established, and the understanding of automatic control systems functioning gained." @default.
- W2894621159 created "2018-10-12" @default.
- W2894621159 creator A5078613853 @default.
- W2894621159 date "1993-01-01" @default.
- W2894621159 modified "2023-09-30" @default.
- W2894621159 title "PHYSICAL FOUNDATIONS OF FEEDBACK CONTROLS11This research has been supported by the Natural Sciences and Engineering Research Council of Canada under the grant OGP0016480." @default.
- W2894621159 cites W1487702225 @default.
- W2894621159 doi "https://doi.org/10.1016/b978-0-08-041897-1.50073-0" @default.
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