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Bifurcation diagram for the Rössler attractor for varying Here, a {\displaystyle a} is fixed at 0.2, c {\displaystyle c} is fixed at 5.7 and b {\displaystyle b} changes. As shown in the accompanying diagram, as b {\displaystyle b} approaches 0 the attractor approaches infinity (note the upswing for very small values of b {\displaystyle b} ).
The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor. A fixed point of a function or transformation is a point that is mapped to itself by the function or ...
The Lorenz attractor is difficult to analyze, but the action of the differential equation on the attractor is described by a fairly simple geometric model. [24] Proving that this is indeed the case is the fourteenth problem on the list of Smale's problems. This problem was the first one to be resolved, by Warwick Tucker in 2002. [25]
In vector control, an AC induction or synchronous motor is controlled under all operating conditions like a separately excited DC motor. [21] That is, the AC motor behaves like a DC motor in which the field flux linkage and armature flux linkage created by the respective field and armature (or torque component) currents are orthogonally aligned such that, when torque is controlled, the field ...
An attractor is a stable point which is also called a "sink". The repeller is considered as an unstable point, which is also known as a "source". A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a phase space.
The frequency response of this oscillator describes the amplitude of steady state response of the equation (i.e. ()) at a given frequency of excitation . For a linear oscillator with β = 0 , {\displaystyle \beta =0,} the frequency response is also linear.
A Nichols plot. The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. [1] [2] [3] It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response.
TSM is robust non-linear control approach. The main idea of terminal sliding mode control evolved out of seminal work on terminal attractors done by Zak in the JPL, and is evoked by the concept of terminal attractors which guarantee finite time convergence of the states.