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The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.
Visibility graphs may be used to find Euclidean shortest paths among a set of polygonal obstacles in the plane: the shortest path between two obstacles follows straight line segments except at the vertices of the obstacles, where it may turn, so the Euclidean shortest path is the shortest path in a visibility graph that has as its nodes the start and destination points and the vertices of the ...
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
A Nyquist plot is a parametric plot of a frequency response used in automatic control and signal processing. The most common use of Nyquist plots is for assessing the stability of a system with feedback. In Cartesian coordinates, the real part of the transfer function is plotted on the X-axis while the imaginary part is plotted on the Y-axis ...
normalization of dimensional quantities (dividing both the RMS difference and the standard deviation of the "test" field by the standard deviation of the observations) so that the "observed" point is plotted at unit distance from the origin along the x-axis, and statistics for different fields (with different units) can be shown in a single plot;
The fact that the no-three-in-line problem has a solution with linearly many points can be translated into graph drawing terms as meaning that every graph, even a complete graph, can be drawn without unwanted vertex-edge incidences using a grid whose area is quadratic in the number of vertices, and that for complete graphs no such drawing with ...
There are three equivalent methods that can be used to determine the values of a point on the plot: Parallel line or grid method. The first method is to use a diagram grid consisting of lines parallel to the triangle edges. A parallel to a side of the triangle is the locus of points constant in the component situated in the vertex opposed to ...
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an invariant set.