\({E_{\text{s}}}\) 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).
\({P_{\text{s}}}\) 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).
\({D_{\text{s}}}\) 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).
\({C_{\text{s}}}\) 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.