Changeset 378

Timestamp:

02/27/2006 12:22:04 PM (3 years ago)

Author:

Martin

Message:

Changed initialization for PID and LimPID block such that SteadyState means also that the derivative
of the integrator state is zero. Changed documentations of these blocks and the example
Blocks.Examples.PID_Controller correspondingly

Location:

Modelica/trunk/Blocks

Files:

• Continuous.mo (modified) (9 diffs)
• package.mo (modified) (6 diffs)

Modelica/trunk/Blocks/Continuous.mo

@@ -823 +823 @@
  
   <tr><td><b>SteadyState</b></td>
-      <td>NoInit</td>
+      <td>SteadyState</td>
       <td>SteadyState</td></tr>
  
@@ -840 +840 @@
 </table>
  
- 
 <p>
 In many cases, the most useful initial condition is
 <b>SteadyState</b> because initial transients are then no longer
-present. If initType = InitPID.SteadyState, then the
-integrator is initialized with NoInit. The reason is the 
+present. If initType = InitPID.SteadyState, then in some
+cases difficulties might occur. The reason is the 
 equation of the integrator:
 </p>
@@ -854 +853 @@
  
 <p>
-The steady state equation \"der(x)=0\" would lead to the condition that the input u to the
+The steady state equation \"der(x)=0\" leads to the condition that the input u to the
 integrator is zero. If the input u is already (directly or indirectly) defined
 by another initial condition, then the initialization problem is <b>singular</b>
 (has none or infinitely many solutions). This situation occurs often
 for mechanical systems, where, e.g., u = desiredSpeed - measuredSpeed and
-since speed is both a state and a derivative, it is always defined by
-InitialState or SteadyState initializtion.
-</p>
- 
-<p>
-Since <b>NoInit</b> is used for the integrator in SteadyState,
-an additional initial equation has to be added to the system
-to which the integrator is connected. E.g., useful initial conditions
-for a 1-dim. rotational inertia controlled by a PI controller are:
-<b>angle</b>, <b>speed</b>, and <b>acceleration</b> of the inertia are zero.
-</p>
+since speed is both a state and a derivative, it is natural to
+initialize it with zero. As sketched this is, however, not possible.
+The solution is to not initialize u or the variable that is used
+to compute u by an algebraic equation.
+</p>
+
  
 </HTML>
@@ -876 +870 @@
       annotation (extent=[-60,60; -20,100]);
     Blocks.Continuous.Integrator I(k=1/Ti, y_start=xi_start,
-      initType=if initType==InitPID.InitialState or 
+      initType=if initType==InitPID.SteadyState then 
+                  InitPID.SteadyState else 
+               if initType==InitPID.InitialState or 
                   initType==InitPID.DoNotUse_InitialIntegratorState then 
                   InitPID.InitialState else InitPID.NoInit) 
@@ -895 +891 @@
        y = y_start;
     end if;
+    
   equation 
     connect(u, P.u) annotation (points=[-120,0; -80,0; -80,80; -64,80], style(
@@ -1096 +1093 @@
  
   <tr><td><b>SteadyState</b></td>
-      <td>NoInit</td>
+      <td>SteadyState</td>
       <td>SteadyState</td></tr>
  
@@ -1113 +1110 @@
 </table>
  
- 
 <p>
 In many cases, the most useful initial condition is
 <b>SteadyState</b> because initial transients are then no longer
-present. If initType = InitPID.SteadyState, then the
-integrator is initialized with NoInit. The reason is the 
+present. If initType = InitPID.SteadyState, then in some
+cases difficulties might occur. The reason is the 
 equation of the integrator:
 </p>
@@ -1127 +1123 @@
  
 <p>
-The steady state equation \"der(x)=0\" would lead to the condition that the input u to the
+The steady state equation \"der(x)=0\" leads to the condition that the input u to the
 integrator is zero. If the input u is already (directly or indirectly) defined
 by another initial condition, then the initialization problem is <b>singular</b>
 (has none or infinitely many solutions). This situation occurs often
 for mechanical systems, where, e.g., u = desiredSpeed - measuredSpeed and
-since speed is both a state and a derivative, it is always defined by
-InitialState or SteadyState initializtion.
-</p>
- 
-<p>
-Since <b>NoInit</b> is used for the integrator in SteadyState,
-an additional initial equation has to be added to the system
-to which the integrator is connected. E.g., useful initial conditions
-for a 1-dim. rotational inertia controlled by a PI controller are:
-<b>angle</b>, <b>speed</b>, and <b>acceleration</b> of the inertia are zero.
+since speed is both a state and a derivative, it is natural to
+initialize it with zero. As sketched this is, however, not possible.
+The solution is to not initialize u_m or the variable that is used
+to compute u_m by an algebraic equation.
 </p>
 
@@ -1161 +1151 @@
     Blocks.Math.Gain P annotation (extent=[-40, 40; -20, 60]);
     Blocks.Continuous.Integrator I(k=1/Ti, y_start=xi_start,
-      initType=if initType==InitPID.InitialState or 
+      initType=if initType==InitPID.SteadyState then 
+                  InitPID.SteadyState else 
+               if initType==InitPID.InitialState or 
                   initType==InitPID.DoNotUse_InitialIntegratorState then 
                   InitPID.InitialState else InitPID.NoInit) if with_I 

Modelica/trunk/Blocks/package.mo

@@ -104 +104 @@
     parameter Modelica.SIunits.Angle driveAngle=1.57;
     Modelica.Blocks.Continuous.LimPID PI(
-      controllerType=Modelica.Blocks.Types.SimpleController.PI, 
-      k=100, 
-      Ti=0.1, 
-      yMax=12, 
-      Ni=0.1, 
-      initType=Modelica.Blocks.Types.Init.SteadyState, 
+      controllerType=Modelica.Blocks.Types.SimpleController.PI,
+      k=100,
+      Ti=0.1,
+      yMax=12,
+      Ni=0.1,
+      initType=Modelica.Blocks.Types.Init.SteadyState,
       limitsAtInit=false) 
       annotation (extent=[-56,-20; -36,0]);
     Modelica.Mechanics.Rotational.Inertia inertia1(initType=Modelica.Mechanics.
-          Rotational.Types.Init.InitialAngleSpeedAcceleration) 
+          Rotational.Types.Init.InitialAngleAcceleration) 
                                               annotation (extent=[2,-20; 22,0]);
     annotation (
       Diagram(
-        Rectangle(extent=[-99,48; -32,8], style(color=1, rgbcolor={255,0,0})), 
+        Rectangle(extent=[-99,48; -32,8], style(color=1, rgbcolor={255,0,0})),
         Text(
-          extent=[-98,59; -31,51], 
-          style(color=1, rgbcolor={255,0,0}), 
-          string="reference speed generation"), 
+          extent=[-98,59; -31,51],
+          style(color=1, rgbcolor={255,0,0}),
+          string="reference speed generation"),
         Text(
-          extent=[-98,-46; -60,-52], 
-          style(color=1, rgbcolor={255,0,0}), 
-          string="PI controller"), 
+          extent=[-98,-46; -60,-52],
+          style(color=1, rgbcolor={255,0,0}),
+          string="PI controller"),
         Line(points=[-76,-44; -57,-23], style(
-            color=1, 
-            rgbcolor={255,0,0}, 
-            arrow=1)), 
-        Rectangle(extent=[-25,6; 99,-50], style(color=1, rgbcolor={255,0,0})), 
+            color=1,
+            rgbcolor={255,0,0},
+            arrow=1)),
+        Rectangle(extent=[-25,6; 99,-50], style(color=1, rgbcolor={255,0,0})),
         Text(
-          extent=[4,14; 71,7], 
-          style(color=1, rgbcolor={255,0,0}), 
+          extent=[4,14; 71,7],
+          style(color=1, rgbcolor={255,0,0}),
           string="plant (simple drive train)")),
       Coordsys(
@@ -140 +140 @@
         scale=0),
       experiment(StopTime=4),
-      experimentSetupOutput, 
+      experimentSetupOutput,
       Documentation(info="<html>
 
 <p>
-This is a simple drive train controller by a PID controller:
+This is a simple drive train controlled by a PID controller:
 </p>
 
@@ -159 +159 @@
      is used as PI controller.</li>
 
-<li> The output of the controller is a torque that drive a motor inertia
+<li> The output of the controller is a torque that drives a motor inertia
      \"inertia1\". Via a complöiant spring/damper component, the load
      inertia \"inertia2\" is attached. A constant external torque of 10 Nm
@@ -165 +165 @@
 </ul>
 
-</p>
+<p>
 The PI controller settings included \"limitAtInit=false\", in order that
 the controller output limits of 12 Nm are removed from the initialization
-problem. The PI controller is initialized in steady state (initType=SteadyState).
-This means that the integrator part is <b>not</b> initialized (see discussion
-in the info layer of block 
-<a href=\"Modelica://Modelica.Blocks.Continuous.LimPID\">LimPID</a>).
-Therefore, <b>one extra initial equation</b> has to be added to the plant.
-For this reason, angle, speed and acceleration are initialized for \"inertia1\"
-(i.e., 3 instead of 2 conditions) and component \"spring\" is also
-initialized in SteadyState.
+problem. 
+</p>
+
+<p>
+The PI controller is initialized in steady state (initType=SteadyState)
+and the drive shall also be initialized in steady state.
+However, it is not possible to initialize \"inertia1\" in SteadyState, because
+\"der(inertia1.phi)=inertia1.w=0\" is an input to the PI controller that
+defines that the derivative of the integrator state is zero (= the same
+condition that was already defined by option SteadyState of the PI controller).
+Furthermore, one initial condition is missing, because the absolute position
+of inertia1 or inertia2 is not defined. The solution shown in this examples is
+to initialize the angle and the angular acceleration of \"inertia1\".
 </p>
 
@@ -203 +208 @@
       annotation (extent=[-25,-20; -5,0]);
     Modelica.Mechanics.Rotational.SpringDamper spring(c=1e4, d=100,
-      initType=Modelica.Mechanics.Rotational.Types.Init.SteadyState, 
+      initType=Modelica.Mechanics.Rotational.Types.Init.SteadyState,
       stateSelection=Modelica.Blocks.Types.StateSelection.Prefer) 
       annotation (extent=[32,-20; 52,0]);
@@ -233 +238 @@
     connect(speedSensor.w, PI.u_m)  annotation (points=[1,-40; -46,-40; -46,-22],
         style(color=74, rgbcolor={0,0,127}));
-    connect(integrator.y, PI.u_s)  annotation (points=[-42,30; -37,30; -37,11; 
+    connect(integrator.y, PI.u_s)  annotation (points=[-42,30; -37,30; -37,11;
           -67,11; -67,-10; -58,-10], style(color=74, rgbcolor={0,0,127}));
   end PID_Controller;
-
+  
      model ShowLogicalSources 
        extends Modelica.Icons.Example;