Processing math: 100%

Data Definitions

This section collects and defines all the data needed to build the instance models.

Process Error in the frequency domain

Refname	DD:ddProcessError
Label	Process Error in the frequency domain
Symbol	${E_{\text{s}}}$
Units	Unitless
Equation	${E_{\text{s}}}={R_{\text{s}}}-{Y_{\text{s}}}$
Description	${E_{\text{s}}}$ is the Process Error in the frequency domain (Unitless) ${R_{\text{s}}}$ is the Set-Point in the frequency domain (Unitless) ${Y_{\text{s}}}$ is the Process Variable in the frequency domain (Unitless)
Notes	The Process Error is the difference between the Set-Point and Process Variable. The equation is converted to the frequency domain by applying the Laplace transform (from TM:laplaceTransform). The Set-Point is assumed to be constant throughout the simulation (from A:Set-Point). The initial value of the Process Variable is assumed to be zero (from A:Initial Value).
Source	johnson2008
RefBy	IM:pdEquationIM, DD:ddPropCtrl, and DD:ddDerivCtrl

Proportional control in the frequency domain

Refname	DD:ddPropCtrl
Label	Proportional control in the frequency domain
Symbol	${P_{\text{s}}}$
Units	Unitless
Equation	${P_{\text{s}}}={K_{\text{p}}}\,{E_{\text{s}}}$
Description	${P_{\text{s}}}$ is the Proportional control in the frequency domain (Unitless) ${K_{\text{p}}}$ is the Proportional Gain (Unitless) ${E_{\text{s}}}$ is the Process Error in the frequency domain (Unitless)
Notes	The Proportional Controller is the product of the Proportional Gain and the Process Error (from DD:ddProcessError). The equation is converted to the frequency domain by applying the Laplace transform (from TM:laplaceTransform).
Source	johnson2008
RefBy	DD:ddCtrlVar

Derivative control in the frequency domain

Refname	DD:ddDerivCtrl
Label	Derivative control in the frequency domain
Symbol	${D_{\text{s}}}$
Units	Unitless
Equation	${D_{\text{s}}}={K_{\text{d}}}\,{E_{\text{s}}}\,s$
Description	${D_{\text{s}}}$ is the Derivative control in the frequency domain (Unitless) ${K_{\text{d}}}$ is the Derivative Gain (Unitless) ${E_{\text{s}}}$ is the Process Error in the frequency domain (Unitless) $s$ is the Complex frequency-domain parameter (Unitless)
Notes	The Derivative Controller is the product of the Derivative Gain and the differential of the Process Error (from DD:ddProcessError). The equation is converted to the frequency domain by applying the Laplace transform (from TM:laplaceTransform). A pure form of the Derivative controller is used in this application (from A:Unfiltered Derivative).
Source	johnson2008
RefBy	DD:ddCtrlVar

Control Variable in the frequency domain

Refname	DD:ddCtrlVar
Label	Control Variable in the frequency domain
Symbol	${C_{\text{s}}}$
Units	Unitless
Equation	${C_{\text{s}}}={E_{\text{s}}}\,\left({K_{\text{p}}}+{K_{\text{d}}}\,s\right)$
Description	${C_{\text{s}}}$ is the Control Variable in the frequency domain (Unitless) ${E_{\text{s}}}$ is the Process Error in the frequency domain (Unitless) ${K_{\text{p}}}$ is the Proportional Gain (Unitless) ${K_{\text{d}}}$ is the Derivative Gain (Unitless) $s$ is the Complex frequency-domain parameter (Unitless)
Notes	The Control Variable is the output of the controller. In this case, it is the sum of the Proportional (from DD:ddPropCtrl) and Derivative (from DD:ddDerivCtrl) controllers. The parallel (from A:Parallel Equation) and de-coupled (from A:Decoupled equation) form of the PD equation is used in this document.
Source	johnson2008
RefBy	IM:pdEquationIM