By Fritz Colonius
This e-book incorporates a collection of the papers awarded on the third NCN Workshop which was once serious about "Dynamics, Bifurcations and Control". The peer-reviewed papers describe a couple of methods how dynamical platforms innovations should be utilized for research and layout difficulties up to speed with issues starting from bifurcation keep an eye on through balance and stabilizaton to the worldwide dynamical behaviour of keep watch over platforms. The ebook supplies an outline of the present prestige of the sphere.
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Additional resources for Dynamics, Bifurcations and Control
The complexity of this nonlinearity make the problem very involved but, it has been shown that with the describing function method interesting and intuitive conclusions can be drawn. In fact, this intuition has been very useful in the election of the three examples, which correspond to a saddle-node bifurcation of limit cycles, a subcritical Hopf bifurcation at in nity and a supercritical Hopf-like bifurcation. In practical applications, we can make use of the gained intuition in order to design compensators that avoid pathological behaviour.
1. 5 Combined Stability Monitoring and Control Early occurrence of subcritical Hopf bifurcation in a periodically forced model of an actual physical system can be used as a warning signal for loss of stability and the associated bifurcation. Here we assume that a good system model is available. The idea considered next is to run a monitoring model of the system in parallel with the operation of the (physical) plant. The monitoring system is steered with identical control inputs as the plant.
A m Table 1. a . Mode (a) Mode (b) 1 Remark 1. The analysis of systems with a rate limiter is very di cult. Notice that, at least, the nonlinearity is not C 1 since it contains a saturation. Furthermore, during some periods of time it is static (its output is equal to the input) while, during some others it is dynamical with one state _ = m. am ) Angle corresponds to the intersection of the line with slope m with the sinusoidal input y(t). a ): (4) This expression is an implicit de nition of which can be obtained numerically.