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• Partial Differential Equations/The Laplacian and Laplace's Equation
  ==The Laplacian and Laplace's Equation== ... he sake of variety let's introduce a fresh new equation and, even though it's not strictly a separation of variables concept, a really cool quantity cal ...
  36 KB (5817 words) - 21:58, 3 November 2008
• Electrodynamics/Laplace's Equation
  == Laplace's Equation == ... electric potential function, we get a special equation called '''Laplace's Equation'''.
  505 B (63 words) - 02:26, 30 July 2007
• Circuit Theory/Laplace Transform
  == Laplace Transform == ... ed|[[Wikipedia:Pierre Simon Laplace|Pierre Simon Laplace]], after whom the Laplace Transform is named, lived from 1749 till 1827.]]
  11 KB (1830 words) - 21:11, 9 November 2008
• Control Systems/Transforms
  ... maybe cannot remember the topic perfectly. If you do not know what the '''Laplace Transform''' or the '''Fourier Transform''' are yet, it is highly recommen ... ... main variable, and all instances of that variable will be removed from the equation. An integral transform that converts from a domain variable ''a'' to a ran ...
  18 KB (3131 words) - 12:16, 2 July 2008
• Differential Equations/Non Homogenous 1
  From [[Differential_Equations|Differential Equations]] :::[[Differential_Equations:Higher_Order|Higher Order Differential Equations]]
  20 KB (3629 words) - 17:54, 31 July 2008
• Control Systems/Sampled Data Systems
  In this chapter, we are going to introduce the ideal sampler and the '''Star Transform'''. First, we need to introduce (or review) the '''Geometric ... ... of this infinite sequence will yield us with a special result called the '''Star Transform'''. The Star Transform is also occasionally called the "Starr ...
  21 KB (3651 words) - 01:12, 9 October 2008
• Control Systems/Transforms Appendix
  == Laplace Transform == {{wikipedia|Laplace Transform}}
  7 KB (1102 words) - 00:24, 20 July 2008
• Control Systems/State-Space Equations
  ... transform domain. When we want to control the system in general we use the Laplace transform (Z-Transform for digital systems) to represent the system, and w ... Let's look at a basic second-order Laplace Transform transfer function:
  24 KB (3992 words) - 13:38, 6 October 2008
• Control Systems/Transfer Functions
  ... '' is the ratio of the output of a system to the input of a system, in the Laplace domain considering its initial conditions to be zero. If we have an input ... ... recognize the transfer function as being the Laplace transform of a circuit's impulse response.
  10 KB (1606 words) - 12:27, 28 November 2007
• Control Systems/Introduction
  ... onents, to increase functionality, or to meet a set of design criteria. Let's start off with an immediate example: ... ''Fourier Transform''', can be employed to change an Ordinary Differential Equation (ODE) in the time domain into a regular algebraic polynomial in the transf ...
  24 KB (3898 words) - 14:27, 19 November 2008
• Control Systems/Glossary
  ... e system is finite, then the output must also be finite. A condition for '''stability'''. ;Eigenvalues:Solutions to the characteristic equation of a matrix. If the matrix is itself a function of time, the eigenvalues m ...
  19 KB (2930 words) - 05:53, 16 February 2008
• Control Systems/MIMO Systems
  ... ystems that are lumped and linear can be described easily with state-space equations. To represent multiple inputs we expand the input ''u(t)'' into a vector ... ... ese are related in our system through the following system of differential equations:
  8 KB (1434 words) - 17:37, 22 June 2008
• Control Systems/Linear System Solutions
  {{Control Systems/Page|State-Space Equations|Time Variant System Solutions}} == State Equation Solutions ==
  12 KB (1940 words) - 14:35, 13 July 2007
• Control Systems/Digital State Space
  Digital systems, expressed previously as difference equations or Z-Transform transfer functions can also be used with the state-space r ... For digital systems, we can write similar equations, using discrete data sets:
  10 KB (1683 words) - 04:39, 16 October 2008
• Control Systems/System Modeling
  ... or all linear systems, and every linear system can be described by such an equation. ... stem is time-invariant (and causal), we can rewrite the system description equation as follows:
  8 KB (1283 words) - 15:18, 19 November 2008
• Partial Differential Equations/Introduction and Classifications
  An equation of the form ... of this letter is common in this context. Examples of partial differential equations (referring to the definition above):
  14 KB (2248 words) - 22:31, 22 January 2008
• Control Systems/Z Transform Mappings
  ... f different mappings that can be used to convert a system from the complex Laplace domain into the Z-Domain. None of these mappings are perfect, and every ma ... ... here are some similarities. Here are some of the similiarities between the Laplace domain and the W domain:
  3 KB (563 words) - 00:21, 19 May 2007
• Materials in Electronics/Schrödinger's Equation
  ... ribes the evolution of ''Ψ(x)'' over time. By solving the differential equation for a particular situation, the wave function can be found. It is a statem ... ==Schrödinger's Equation in 1-Dimension==
  7 KB (1176 words) - 20:24, 3 August 2007
• Control Systems/Controllers and Compensators
  ... K''. A P controller can only force the system poles to a spot on the system's root locus. A P controller cannot be used for arbitrary pole placement. In the Laplace domain, we can show the derivative of a signal using the following notatio ...
  9 KB (1488 words) - 06:38, 23 June 2008
• Circuit Theory/Fourier Transform
  The '''Fourier Transform''' is a specific case of the Laplace transform. If we separate s into its real and imaginary parts: Where s is the complex laplace variable, <math>\sigma</math> is the real part of s, and <math>\omega</mat ...
  7 KB (1075 words) - 21:29, 20 October 2008

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