diff --git a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/FirstOrderAMIGO.mo b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/FirstOrderAMIGO.mo
index 1345d4bbc09..9cf8136dc42 100644
--- a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/FirstOrderAMIGO.mo
+++ b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/FirstOrderAMIGO.mo
@@ -116,7 +116,8 @@ block FirstOrderAMIGO
     conProMod(
     final yHig=yHig - yRef,
     final yLow=yRef + yLow,
-    final deaBan=deaBan)
+    final deaBan=deaBan,
+    final reverseActing=reverseActing)
     "Calculates the parameters of a first-order time delayed model"
     annotation (Placement(transformation(extent={{40,30},{60,50}})));
   Buildings.Controls.OBC.CDL.Logical.Latch inTunPro
@@ -179,8 +180,8 @@ equation
           {30,44},{22,44}},color={0,0,127}));
   connect(resPro.tOn, conProMod.tOn) annotation (Line(points={{22,48},{32,48},{32,
           44},{38,44}},color={0,0,127}));
-  connect(rel.yErr, conProMod.u) annotation (Line(points={{-18,40},{-12,40},{-12,
-          60},{34,60},{34,48},{38,48}},color={0,0,127}));
+  connect(rel.yDiff, conProMod.u) annotation (Line(points={{-18,40},{-12,40},{-12,
+          60},{34,60},{34,48},{38,48}}, color={0,0,127}));
   connect(PIDPar.kp, conProMod.k) annotation (Line(points={{78,46},{62,46}}, color={0,0,127}));
   connect(PIDPar.T, conProMod.T) annotation (Line(points={{78,40},{62,40}}, color={0,0,127}));
   connect(PIDPar.L, conProMod.L) annotation (Line(points={{78,34},{62,34}}, color={0,0,127}));
diff --git a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Controller.mo b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Controller.mo
index b5ae105e3f5..20946ace0d4 100644
--- a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Controller.mo
+++ b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Controller.mo
@@ -32,10 +32,9 @@ block Controller
   Buildings.Controls.OBC.CDL.Interfaces.BooleanOutput yOn
     "Relay switch output, true when control output switches to the higher value"
     annotation (Placement(transformation(extent={{100,-80},{140,-40}})));
-  Buildings.Controls.OBC.CDL.Interfaces.RealOutput yErr
-    "Control error"
+  Buildings.Controls.OBC.CDL.Interfaces.RealOutput yDiff "Input difference"
     annotation (Placement(transformation(extent={{100,-10},{140,30}}),
-    iconTransformation(extent={{100,-20},{140,20}})));
+        iconTransformation(extent={{100,-20},{140,20}})));
 
 protected
   Buildings.Controls.OBC.CDL.Reals.Switch swi
@@ -49,24 +48,21 @@ protected
     final k=-yLow)
     "Lower value for the output"
     annotation (Placement(transformation(extent={{-80,20},{-60,40}})));
-  Buildings.Controls.OBC.CDL.Reals.Subtract conErr
-    "Control error (set point - measurement)"
-    annotation (Placement(transformation(extent={{40,0},{60,20}})));
   Buildings.Controls.OBC.CDL.Reals.Switch swi1
     "Switch between a higher value and a lower value"
     annotation (Placement(transformation(extent={{-10,-10},{10,10}},
     origin={-50,-60})));
   Buildings.Controls.OBC.CDL.Reals.Subtract sub
-    if reverseActing "Inputs difference"
+    if reverseActing "Inputs difference for reverse acting"
     annotation (Placement(transformation(extent={{0,-50},{20,-30}})));
   Buildings.Controls.OBC.CDL.Reals.Hysteresis hys(
-    final uLow=-deaBa,
-    final uHigh=deaBa,
+    final uLow=-deaBan,
+    final uHigh=deaBan,
     final pre_y_start=true)
-    "Check if the measured value is larger than the reference, by default the relay control is on"
+    "Check if the input difference exceeds the thresholds, by default the relay control is on"
     annotation (Placement(transformation(extent={{40,-60},{60,-40}})));
   Buildings.Controls.OBC.CDL.Reals.Subtract sub1
-    if not reverseActing "Inputs difference"
+    if not reverseActing "Inputs difference for direct acting"
     annotation (Placement(transformation(extent={{0,-80},{20,-60}})));
   Buildings.Controls.OBC.CDL.Reals.Greater gre
     "Check if the higher value is greater than the lower value"
@@ -85,39 +81,25 @@ equation
   connect(higVal.y, swi.u1)
     annotation (Line(points={{-58,80},{-20,80},{-20,58},{58,58}},color={0,0,127}));
   connect(lowVal.y, swi.u3) annotation (Line(points={{-58,30},{-20,30},{-20,42},
-          {58,42}},
-                color={0,0,127}));
-  connect(conErr.y, yErr) annotation (Line(points={{62,10},{120,10}},
-         color={0,0,127}));
+          {58,42}},color={0,0,127}));
   connect(swi1.u3, u_s) annotation (Line(points={{-62,-68},{-90,-68},{-90,0},{
-          -120,0}},
-               color={0,0,127}));
+          -120,0}},color={0,0,127}));
   connect(trigger, swi1.u2) annotation (Line(points={{-80,-120},{-80,-60},{-62,
-          -60}},
-        color={255,0,255}));
+          -60}},color={255,0,255}));
   connect(u_m, swi1.u1) annotation (Line(points={{0,-120},{0,-90},{-70,-90},{
-          -70,-52},{-62,-52}},
-                           color={0,0,127}));
-   connect(swi1.y, conErr.u1) annotation (Line(points={{-38,-60},{-20,-60},{-20,
-          16},{38,16}}, color={0,0,127}));
-   connect(conErr.u2, u_s) annotation (Line(points={{38,4},{-42,4},{-42,0},{
-          -120,0}},
-               color={0,0,127}));
+          -70,-52},{-62,-52}},color={0,0,127}));
   connect(sub1.y, hys.u) annotation (Line(points={{22,-70},{30,-70},{30,-50},{
-          38,-50}},
-                 color={0,0,127}));
+          38,-50}},color={0,0,127}));
   connect(sub.y, hys.u) annotation (Line(points={{22,-40},{30,-40},{30,-50},{38,
           -50}}, color={0,0,127}));
   connect(u_s, sub.u1) annotation (Line(points={{-120,0},{-90,0},{-90,-34},{-2,
-          -34}},
-        color={0,0,127}));
+          -34}},color={0,0,127}));
   connect(u_s, sub1.u2) annotation (Line(points={{-120,0},{-90,0},{-90,-76},{-2,
           -76}}, color={0,0,127}));
   connect(swi1.y, sub.u2) annotation (Line(points={{-38,-60},{-20,-60},{-20,-46},
           {-2,-46}}, color={0,0,127}));
   connect(swi1.y, sub1.u1) annotation (Line(points={{-38,-60},{-20,-60},{-20,
-          -64},{-2,-64}},
-                      color={0,0,127}));
+          -64},{-2,-64}},color={0,0,127}));
   connect(hys.y, swi.u2) annotation (Line(points={{62,-50},{80,-50},{80,30},{50,
           30},{50,50},{58,50}}, color={255,0,255}));
   connect(gre.y, assMes.u)
@@ -129,9 +111,12 @@ equation
   connect(higVal.y, gre.u1)
     annotation (Line(points={{-58,80},{-2,80}}, color={0,0,127}));
   connect(hys.y, yOn) annotation (Line(points={{62,-50},{80,-50},{80,-60},{120,
-          -60}},
-        color={255,0,255}));
-  annotation (defaultComponentName = "relCon",
+          -60}},color={255,0,255}));
+  connect(yDiff, sub.y) annotation (Line(points={{120,10},{36,10},{36,-40},{22,
+          -40}}, color={0,0,127}));
+  connect(sub1.y, yDiff) annotation (Line(points={{22,-70},{36,-70},{36,10},{
+          120,10}}, color={0,0,127}));
+    annotation (defaultComponentName = "relCon",
         Icon(coordinateSystem(preserveAspectRatio=false), graphics={
         Rectangle(
           extent={{-100,-100},{100,100}},
@@ -164,21 +149,22 @@ equation
           fillPattern=FillPattern.Solid,
           fillColor={175,175,175},
           textString="Relay"),
-        Line(points={{-70,24},{-34,24},{-34,58},{38,58},{38,24},{66,24}}, color
-            ={28,108,200})}), Diagram(
+        Line(points={{-70,24},{-34,24},{-34,58},{38,58},{38,24},{66,24}}, color=
+             {28,108,200})}), Diagram(
         coordinateSystem(preserveAspectRatio=false)),
 Documentation(info="<html>
 <p>
 This block generates a real control output <code>y</code>, a
-boolean relay switch output <code>yOn</code>, and the control error
-<code>yErr</code>. They are calculated as below:
+boolean relay switch output <code>yOn</code>, 
+and an input difference <code>yDiff</code>. 
+They are calculated as below:
 </p>
 <ul>
 <li>
-if the parameter <code>reverseActing = false</code>
+if the parameter <code>reverseActing = true</code>
 <ul>
 <li>
-<code>yErr = u_m - u_s</code>,
+<code>yDiff = u_s - u_m</code>,
 </li>
 </ul>
 </li>
@@ -186,16 +172,16 @@ if the parameter <code>reverseActing = false</code>
 else
 <ul>
 <li>
-<code>yErr = u_s - u_m </code>,
+<code>yDiff = u_m - u_s</code>,
 </li>
 </ul>
 </li>
 <li>
-if <code>yErr &lt; -deaBan</code> and <code>trigger</code> is <code>true</code>,
+if <code>yDiff &gt; deaBan</code> and <code>trigger</code> is <code>true</code>,
 then <code>y = yHig</code>, <code>yOn = true</code>,
 </li>
 <li>
-else if <code>yErr &gt; deaBan</code> and <code>trigger</code> is <code>true</code>,
+else if <code>yDiff &lt; -deaBan</code> and <code>trigger</code> is <code>true</code>,
 then <code>y = -yLow</code>, 
 <code>yOn = false</code>,
 </li>
diff --git a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Gain.mo b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Gain.mo
index 909059a5713..26fe105beba 100644
--- a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Gain.mo
+++ b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Gain.mo
@@ -4,6 +4,8 @@ block Gain "Identify the gain of a first order time delayed model"
     "Higher value for the output (assuming the reference output is 0)";
   parameter Real yLow(min=1E-6) = 0.5
     "Lower value for the output (assuming the reference output is 0)";
+  parameter Boolean reverseActing=true
+    "Set to true for reverse acting, or false for direct acting control action";
   Buildings.Controls.OBC.CDL.Interfaces.RealInput u
     "Relay controller output"
     annotation (Placement(transformation(extent={{-140,20},{-100,60}}),
@@ -39,7 +41,7 @@ protected
     annotation (Placement(transformation(extent={{-10,30},{10,50}})));
   Buildings.Controls.OBC.CDL.Reals.Sources.Constant refRelOut(
     final k=0) "Reference value of the relay control output"
-    annotation (Placement(transformation(extent={{-60,10},{-40,30}})));
+    annotation (Placement(transformation(extent={{-60,-10},{-40,10}})));
   Buildings.Controls.OBC.CDL.Reals.Divide divIyIu "Calculate the gain"
     annotation (Placement(transformation(extent={{40,-10},{60,10}})));
   Buildings.Controls.OBC.CDL.Reals.AddParameter addPar(final p=1E-3)
@@ -53,12 +55,17 @@ protected
     final k=-yLow)
     "Product of tOff and yLow"
     annotation (Placement(transformation(extent={{-80,-90},{-60,-70}})));
-
+  Buildings.Controls.OBC.CDL.Reals.MultiplyByParameter gai1(final k=-1)
+    if reverseActing
+    "Negative sign for reverse acting"
+    annotation (Placement(transformation(extent={{-60,70},{-40,90}})));
+  Buildings.Controls.OBC.CDL.Reals.MultiplyByParameter gai2(final k=1)
+    if not reverseActing
+    "Positive sign for direct acting"
+    annotation (Placement(transformation(extent={{-60,30},{-40,50}})));
 equation
-  connect(Iy.u, u) annotation (Line(points={{-12,40},{-120,40}},
-        color={0,0,127}));
-  connect(refRelOut.y, Iy.y_reset_in) annotation (Line(points={{-38,20},{-20,20},
-          {-20,32},{-12,32}}, color={0,0,127}));
+  connect(refRelOut.y, Iy.y_reset_in) annotation (Line(points={{-38,0},{-20,0},{
+          -20,32},{-12,32}},  color={0,0,127}));
   connect(Iy.trigger, triSta) annotation (Line(points={{0,28},{0,-120}},
           color={255,0,255}));
   connect(divIyIu.u1, Iy.y) annotation (Line(points={{38,6},{18,6},{18,40},{12,
@@ -76,6 +83,14 @@ equation
           -46},{-42,-46}}, color={0,0,127}));
   connect(divIyIu.y, k)
     annotation (Line(points={{62,0},{120,0}}, color={0,0,127}));
+  connect(gai2.u, u)
+    annotation (Line(points={{-62,40},{-120,40}}, color={0,0,127}));
+  connect(gai2.y, Iy.u)
+    annotation (Line(points={{-38,40},{-12,40}}, color={0,0,127}));
+  connect(gai1.y, Iy.u) annotation (Line(points={{-38,80},{-20,80},{-20,40},{
+          -12,40}}, color={0,0,127}));
+  connect(gai1.u, u) annotation (Line(points={{-62,80},{-80,80},{-80,40},{-120,
+          40}}, color={0,0,127}));
   annotation (
         defaultComponentName = "gai",
         Icon(coordinateSystem(preserveAspectRatio=false), graphics={
@@ -106,8 +121,10 @@ where <i>I<sub>y</sub></i> and <i>I<sub>u</sub></i> are the integral of the proc
 output and the integral of the relay output, respectively.
 </p>
 <p><i>I<sub>y</sub></i> is calculated by </p>
-<p>I<sub>y</sub> = &int; u(t) dt;</p>
-<p>where <i>u</i> is the process output.</p>
+<p>I<sub>y</sub> = &int; -u(t) dt;</p>
+<p>where <i>u</i> is the input difference of a relay controller, see details in <a href=\"modelica://Buildings.Controls.OBC.Utilities.PIDWithAutotuning.Relay.Controller\">
+Buildings.Controls.OBC.Utilities.PIDWithAutotuning.Relay.Controller</a>
+</p>
 <p><i>I<sub>u</sub></i> is calculated by </p>
 <p align=\"center\" style=\"font-style:italic;\">
 I<sub>u</sub> = t<sub>on</sub> (y<sub>hig</sub> - y<sub>ref</sub>)+ t<sub>off</sub>(-y<sub>low</sub> - y<sub>ref</sub>),
diff --git a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Validation/Gain.mo b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Validation/Gain.mo
index d4251ecb888..fff0e1f3aed 100644
--- a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Validation/Gain.mo
+++ b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/BaseClasses/Validation/Gain.mo
@@ -1,7 +1,7 @@
 within Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.FirstOrderTimedelayed.BaseClasses.Validation;
 model Gain "Test model for identifying the gain of the control process"
   Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.FirstOrderTimedelayed.BaseClasses.Gain
-    gai
+    gai(reverseActing=false)
     "Block that calculates the gain of a first-order model"
     annotation (Placement(transformation(extent={{-10,-10},{10,10}})));
   Buildings.Controls.OBC.CDL.Reals.Sources.Pulse u(
diff --git a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/ControlProcessModel.mo b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/ControlProcessModel.mo
index b4c1497b8ae..89667f4c95a 100644
--- a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/ControlProcessModel.mo
+++ b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/ControlProcessModel.mo
@@ -7,6 +7,8 @@ block ControlProcessModel
     "Lower value for the output";
   parameter Real deaBan(min=0) = 0.5
     "Deadband for holding the output value";
+  parameter Boolean reverseActing=true
+    "Set to true for reverse acting, or false for direct acting control action";
   Buildings.Controls.OBC.CDL.Interfaces.RealInput tOn(
     final quantity="Time",
     final unit="s",
@@ -74,7 +76,8 @@ protected
     annotation (Placement(transformation(extent={{12,-30},{32,-10}})));
   Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.FirstOrderTimedelayed.BaseClasses.Gain gain(
     final yHig=yHig,
-    final yLow=yLow)
+    final yLow=yLow,
+    final reverseActing = reverseActing)
     "Block that calculates the gain"
     annotation (Placement(transformation(extent={{-84,10},{-64,30}})));
   Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.FirstOrderTimedelayed.BaseClasses.TimeConstantDelay
diff --git a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/Validation/ControlProcessModel.mo b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/Validation/ControlProcessModel.mo
index 08a1f4072b8..420c309fca4 100644
--- a/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/Validation/ControlProcessModel.mo
+++ b/Buildings/Controls/OBC/Utilities/PIDWithAutotuning/SystemIdentification/FirstOrderTimedelayed/Validation/ControlProcessModel.mo
@@ -2,7 +2,8 @@ within Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.F
 model ControlProcessModel
   "Test model for identifying the reduced-order model of the control process"
   Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.FirstOrderTimedelayed.ControlProcessModel
-    conProMod(yLow=0.1, deaBan=0.05)
+    conProMod(yLow=0.1, deaBan=0.05,
+    reverseActing=false)
     "Calculate the parameters of a first-order model"
     annotation (Placement(transformation(extent={{-10,-10},{10,10}})));
   Buildings.Controls.OBC.CDL.Reals.Sources.Pulse u(
diff --git a/Buildings/Resources/Scripts/Dymola/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Validation/Controller.mos b/Buildings/Resources/Scripts/Dymola/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Validation/Controller.mos
index ec5423133e8..b40e52e278a 100644
--- a/Buildings/Resources/Scripts/Dymola/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Validation/Controller.mos
+++ b/Buildings/Resources/Scripts/Dymola/Controls/OBC/Utilities/PIDWithAutotuning/Relay/Validation/Controller.mos
@@ -4,4 +4,4 @@ plotExpression(apply(Controller[end].relCon.u_s-0.4), false, "controller[end].re
 plotExpression(apply(Controller[end].relCon.u_s+0.4), false, "controller[end].relCon.u_s+deaBan", 1);
 createPlot(id=1, position={15, 15, 1148, 620}, y={"enaSig.y"}, range={0.0, 1.0, -1.0, 2.0}, grid=true, subPlot=102, colors={{28,108,200}});
 createPlot(id=1, position={15, 15, 1148, 620}, y={"relCon.y"}, range={0.0, 1.0, -2.0, 2.0}, grid=true, subPlot=103, colors={{28,108,200}});
-createPlot(id=1, position={15, 15, 1148, 620}, y={"relCon.yErr", "relCon.yOn"}, range={0.0, 1.0, -2.0, 2.0}, grid=true, subPlot=104, colors={{28,108,200}, {238,46,47}});
\ No newline at end of file
+createPlot(id=1, position={15, 15, 1148, 620}, y={"relCon.yDiff", "relCon.yOn"}, range={0.0, 1.0, -2.0, 2.0}, grid=true, subPlot=104, colors={{28,108,200}, {238,46,47}});
\ No newline at end of file
diff --git a/Buildings/Resources/Scripts/OpenModelica/compareVars/Buildings.Controls.OBC.Utilities.PIDWithAutotuning.Relay.Validation.Controller.mos b/Buildings/Resources/Scripts/OpenModelica/compareVars/Buildings.Controls.OBC.Utilities.PIDWithAutotuning.Relay.Validation.Controller.mos
index 39f12c5b1e3..bf63a686995 100644
--- a/Buildings/Resources/Scripts/OpenModelica/compareVars/Buildings.Controls.OBC.Utilities.PIDWithAutotuning.Relay.Validation.Controller.mos
+++ b/Buildings/Resources/Scripts/OpenModelica/compareVars/Buildings.Controls.OBC.Utilities.PIDWithAutotuning.Relay.Validation.Controller.mos
@@ -3,6 +3,6 @@ compareVars :=
     "relCon.u_m",
     "enaSig.y",
     "relCon.y",
-    "relCon.yErr",
+    "relCon.yDiff",
     "relCon.yOn"
   };