This section focuses on the general equations and laws that PD Controller is based on.
Refname TM:laplaceTransform
Label Laplace Transform Equation \[{F_{\text{s}}}=\int_{\mathit{-∞}}^{∞}{{f_{\text{t}}}\,e^{-s\,t}}\,dt\] Description
\({F_{\text{s}}}\) is the Laplace Transform of a function (Unitless)
\({f_{\text{t}}}\) is the Function in the time domain (Unitless)
\(s\) is the Complex frequency-domain parameter (Unitless)
\(t\) is the time (\({\text{s}}\))
Notes
Bilateral Laplace Transform. The Laplace transforms are typically inferred from a pre-computed table of Laplace Transforms (laplaceWiki ).
Source laplaceWiki RefBy GD:gdPowerPlant , DD:ddPropCtrl , DD:ddProcessError , and DD:ddDerivCtrl
Refname TM:invLaplaceTransform
Label Inverse Laplace Transform Equation \[{f_{\text{t}}}=\mathit{L⁻¹[F(s)]}\] Description
\({f_{\text{t}}}\) is the Function in the time domain (Unitless)
\(\mathit{L⁻¹[F(s)]}\) is the Inverse Laplace Transform of a function (Unitless)
Notes
Inverse Laplace Transform of F(S). The Inverse Laplace transforms are typically inferred from a pre-computed table of Laplace Transforms (laplaceWiki ).
Source laplaceWiki RefBy IM:pdEquationIM
Refname TM:tmSOSystem
Label Second Order Mass-Spring-Damper System Equation \[\frac{1}{m\,s^{2}+c\,s+k}\] Description
\(m\) is the mass (\({\text{kg}}\))
\(s\) is the Complex frequency-domain parameter (Unitless)
\(c\) is the Damping coefficient of the spring (Unitless)
\(k\) is the Stiffness coefficient (\({\text{s}}\))
Notes
The Transfer Function (from A:Transfer Function ) of a Second Order System (mass-spring-damper) is characterized by this equation.
Source abbasi2015 RefBy GD:gdPowerPlant