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Here the state variables for each finite element are determined by linearized differential equations, and a coordination step is used to update the control variables and integration length.
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It starts by deriving a mathematical model of UPFC, with which its linearized differential equations are integrated to design an overall control strategy for enhancing small signal stability of the so connected power systems.
The MTL-based linearized differential equations thus become explicitly integrable.
Furthermore, a transistor level view of the system employs component models based on linearized differential equations and works in the continuous time domain.
A system response matrix method, which directly solves the linearized differential equations in the matrix form without Laplace transformation, is introduced for the supercritical fluids flow instability analysis.
(2) The fourth order system of linearized differential equations of the DS buckling in a curvilinear channel is deduced with the use of differential geometry methods, theory of channel surfaces, and classical mechanics of systems with nonlinear constraints.
Its rotatory dynamics are described by linear differential equations.
If so, the differential equation can be solved in a method analogous to that used for solving second order linear differential equations, as follows: Many differential equations simply cannot be solved by the above methods.
Using this technique, the non-linear problem is reduced to the solution of a set of linearized partial differential equations.
Physical modeling of this process results in coupled linearized partial differential equations which are then reduced into low-order nominal process models using an orthogonal collocation approximation method.
Many real-life processes can be modeled by non-linear Ordinary Differential Equations (ODEs) or Partial Differential Equations (PDEs).
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