Stabilization of gondola lift 1
Introduction 1
Mathematical model of gondola 2
How to stabilize gondola 4
Application of control theory 6
How to stabilize several gondola simultaneously 7
Design of a control stabilizing gondola 9
Conclusion. 10
Bibliography 11
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In this part of exploration I use some results of the mathematical control theory. This theory was intensively developed during the last sixty years, due to various engineering and technical problems, in which it was a need for control of different objects. An example of such problems is cosmology research: landing on the Moon, stabilization of telecommunication satellites orbits; airplane technologies, industry automatics, robotics and other. Fundamentals of the control theory, stability and stabilizability of systems described by differential equations, were stated in the mid of XX century by L. Pontriagin, R. Bellman, R. Kalman and other mathematicians.
The analysis of the Bulgarian research system has shown that it has stagnated in recent years following a prolonged period of downsizing, facing a lot of restructuring challenges, as well as very low investment in R&D in the 1990s. Bulgaria faces most of the challenges described in the Green Paper «The European Research Area: New Perspectives». The country’s EU accession has promoted the process of setting up modern governance institutions though often their existence remains mostly «on paper» with little effect on R&D policy implementation. A particularly persistent weakness of the Bulgarian R&D system re-mains the very low participation of the private sector in R&D expenditures. Bulgaria faces challenges in all four domains presented in this report, including in the coordination and coherence between them, but low R&D expenditures coupled with the increasing deficit of qualified R&D personnel are probably the biggest and hardest of them.
Pendulum
1. https://en.wikipedia.org/wiki/Pendulum_%28mathematics%29
Controllability and Stabilization
1. https://en.wikipedia.org/wiki/Controllability
2. E.D. Sontag. Mathematical Control Theory, volume 6 of Texts in Applied Mathematics. Springer-Verlag, New York, second edition, 1998. Deterministic finitedimensional systems.
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