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 of the spring (\({\text{s}}\)) 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