lqr.mdl

model of a LQR controller for the inverted pendulum in simulink

	  Orientation		  "left"
	  ShowName		  off
	}
	Block {
	  BlockType		  Abs
	  Name			  " 2"
	  Position		  [235, 285, 265, 315]
	  ShowName		  off
	}
	Block {
	  BlockType		  Constant
	  Name			  "Constant"
	  Position		  [235, 125, 265, 155]
	  Value			  "0"
	}
	Block {
	  BlockType		  Constant
	  Name			  "Constant1"
	  Position		  [235, 235, 265, 265]
	  Value			  "10"
	}
	Block {
	  BlockType		  Constant
	  Name			  "Constant2"
	  Position		  [530, 180, 560, 210]
	  Value			  "pi"
	}
	Block {
	  BlockType		  Gain
	  Name			  "Gain"
	  Position		  [240, 175, 270, 205]
	  Gain			  "1.5"
	}
	Block {
	  BlockType		  SubSystem
	  Name			  "Pendulum"
	  Ports			  [2, 2]
	  Position		  [425, 165, 475, 245]
	  DropShadow		  on
	  TreatAsAtomicUnit	  off
	  System {
	    Name		    "Pendulum"
	    Location		    [218, 249, 782, 475]
	    Open		    off
	    ModelBrowserVisibility  off
	    ModelBrowserWidth	    200
	    ScreenColor		    "white"
	    PaperOrientation	    "landscape"
	    PaperPositionMode	    "auto"
	    PaperType		    "A4"
	    PaperUnits		    "centimeters"
	    ZoomFactor		    "100"
	    Block {
	      BlockType		      Inport
	      Name		      "Vel"
	      Position		      [65, 88, 95, 102]
	    }
	    Block {
	      BlockType		      Inport
	      Name		      "Acc"
	      Position		      [65, 148, 95, 162]
	      Port		      "2"
	    }
	    Block {
	      BlockType		      Gain
	      Name		      "AccCof"
	      Position		      [135, 140, 165, 170]
	      Gain		      "0.0002 * 0.0002/ (0.46 / 37500.0)"
	    }
	    Block {
	      BlockType		      Gain
	      Name		      "Angle Encoder"
	      Position		      [460, 150, 490, 180]
	      Gain		      "-(pi * 2.0 / 2400)"
	    }
	    Block {
	      BlockType		      Reference
	      Name		      "Get Cart's Position"
	      Ports		      [0, 1]
	      Position		      [330, 54, 420, 86]
	      Priority		      "1"
	      SourceBlock	      "googolbox/GT-400-SV Block Library/Get C"
"urrent Axis' Position"
	      SourceType	      "GetPos"
	      axis		      "1"
	    }
	    Block {
	      BlockType		      Reference
	      Name		      "Get Pend's Angle"
	      Ports		      [0, 1]
	      Position		      [335, 149, 425, 181]
	      Priority		      "1"
	      SourceBlock	      "googolbox/GT-400-SV Block Library/Get C"
"urrent Axis' Position"
	      SourceType	      "GetPos"
	      axis		      "2"
	    }
	    Block {
	      BlockType		      Gain
	      Name		      "Pos Encoder"
	      Position		      [460, 55, 490, 85]
	      Gain		      "0.46 / 37500.0"
	    }
	    Block {
	      BlockType		      Reference
	      Name		      "Set Cart's Acc And Vel"
	      Ports		      [2]
	      Position		      [200, 103, 290, 147]
	      Priority		      "1"
	      SourceBlock	      "googolbox/GT-400-SV Block Library/Set C"
"urrent Axis' Acc and Vel"
	      SourceType	      "SetAccVel"
	      axis		      "1"
	      vel		      "2"
	      pos		      "25000"
	    }
	    Block {
	      BlockType		      Gain
	      Name		      "VelCof"
	      Position		      [135, 80, 165, 110]
	      Gain		      "0.0002 / (0.46 / 37500.0)"
	    }
	    Block {
	      BlockType		      Outport
	      Name		      "Pos"
	      Position		      [530, 63, 560, 77]
	    }
	    Block {
	      BlockType		      Outport
	      Name		      "Angle"
	      Position		      [530, 158, 560, 172]
	      Port		      "2"
	    }
	    Line {
	      SrcBlock		      "AccCof"
	      SrcPort		      1
	      Points		      [0, -20]
	      DstBlock		      "Set Cart's Acc And Vel"
	      DstPort		      2
	    }
	    Line {
	      SrcBlock		      "VelCof"
	      SrcPort		      1
	      Points		      [0, 20]
	      DstBlock		      "Set Cart's Acc And Vel"
	      DstPort		      1
	    }
	    Line {
	      SrcBlock		      "Angle Encoder"
	      SrcPort		      1
	      DstBlock		      "Angle"
	      DstPort		      1
	    }
	    Line {
	      SrcBlock		      "Pos Encoder"
	      SrcPort		      1
	      DstBlock		      "Pos"
	      DstPort		      1
	    }
	    Line {
	      SrcBlock		      "Get Pend's Angle"
	      SrcPort		      1
	      DstBlock		      "Angle Encoder"
	      DstPort		      1
	    }
	    Line {
	      SrcBlock		      "Acc"
	      SrcPort		      1
	      DstBlock		      "AccCof"
	      DstPort		      1
	    }
	    Line {
	      SrcBlock		      "Vel"
	      SrcPort		      1
	      DstBlock		      "VelCof"
	      DstPort		      1
	    }
	    Line {
	      SrcBlock		      "Get Cart's Position"
	      SrcPort		      1
	      DstBlock		      "Pos Encoder"
	      DstPort		      1
	    }
	  }
	}
	Block {
	  BlockType		  Saturate
	  Name			  "Saturation"
	  Position		  [170, 285, 200, 315]
	  UpperLimit		  "15"
	  LowerLimit		  "-15"
	}
	Block {
	  BlockType		  Signum
	  Name			  "Sign"
	  Position		  [180, 175, 210, 205]
	}
	Block {
	  BlockType		  Sum
	  Name			  "Sum"
	  Ports			  [2, 1]
	  Position		  [600, 196, 615, 234]
	  ShowName		  off
	  Inputs		  "+-"
	  InputSameDT		  off
	  OutDataTypeMode	  "Inherit via internal rule"
	}
	Block {
	  BlockType		  Switch
	  Name			  "Switch1"
	  Position		  [325, 124, 340, 206]
	  Threshold		  "20*pi/180"
	  InputSameDT		  off
	}
	Block {
	  BlockType		  Switch
	  Name			  "Switch2"
	  Position		  [325, 234, 340, 316]
	  Threshold		  "20*pi/180"
	  InputSameDT		  off
	}
	Block {
	  BlockType		  Outport
	  Name			  "Pos"
	  Position		  [525, 148, 555, 162]
	}
	Block {
	  BlockType		  Outport
	  Name			  "Angle"
	  Position		  [575, 248, 605, 262]
	  Port			  "2"
	}
	Line {
	  SrcBlock		  "Constant1"
	  SrcPort		  1
	  DstBlock		  "Switch2"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  " 2"
	  SrcPort		  1
	  DstBlock		  "Switch2"
	  DstPort		  3
	}
	Line {
	  SrcBlock		  "Constant"
	  SrcPort		  1
	  DstBlock		  "Switch1"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Gain"
	  SrcPort		  1
	  DstBlock		  "Switch1"
	  DstPort		  3
	}
	Line {
	  SrcBlock		  "Sum"
	  SrcPort		  1
	  Points		  [10, 0; 0, -110]
	  DstBlock		  " -pi~pi"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Constant2"
	  SrcPort		  1
	  Points		  [20, 0]
	  DstBlock		  "Sum"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Switch1"
	  SrcPort		  1
	  Points		  [20, 0; 0, 20]
	  DstBlock		  "Pendulum"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Switch2"
	  SrcPort		  1
	  Points		  [30, 0; 0, -50]
	  DstBlock		  "Pendulum"
	  DstPort		  2
	}
	Line {
	  SrcBlock		  " -pi~pi"
	  SrcPort		  1
	  DstBlock		  " 1"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  " 1"
	  SrcPort		  1
	  Points		  [-75, 0; 0, 60]
	  Branch {
	    DstBlock		    "Switch1"
	    DstPort		    2
	  }
	  Branch {
	    Points		    [0, 110]
	    DstBlock		    "Switch2"
	    DstPort		    2
	  }
	}
	Line {
	  SrcBlock		  "Saturation"
	  SrcPort		  1
	  DstBlock		  " 2"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Pendulum"
	  SrcPort		  1
	  Points		  [30, 0]
	  DstBlock		  "Pos"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Pendulum"
	  SrcPort		  2
	  Points		  [65, 0]
	  Branch {
	    DstBlock		    "Sum"
	    DstPort		    2
	  }
	  Branch {
	    Points		    [0, 30]
	    DstBlock		    "Angle"
	    DstPort		    1
	  }
	}
	Line {
	  SrcBlock		  "Sign"
	  SrcPort		  1
	  DstBlock		  "Gain"
	  DstPort		  1
	}
	Line {
	  SrcBlock		  "Acc"
	  SrcPort		  1
	  Points		  [0, 0; 25, 0]
	  Branch {
	    Points		    [0, -35]
	    DstBlock		    "Sign"
	    DstPort		    1
	  }
	  Branch {
	    Points		    [0, 75]
	    DstBlock		    "Saturation"
	    DstPort		    1
	  }
	}
      }
    }
    Block {
      BlockType		      Scope
      Name		      "Scope1"
      Ports		      [2]
      Position		      [950, 31, 980, 64]
      Location		      [6, 54, 806, 576]
      Open		      off
      NumInputPorts	      "2"
      TickLabels	      "on"
      ZoomMode		      "yonly"
      List {
	ListType		AxesTitles
	axes1			"%<SignalLabel>"
	axes2			"%<SignalLabel>"
      }
      TimeRange		      "10"
      YMin		      "0.013~3.146"
      YMax		      "0.024~3.16"
      DataFormat	      "StructureWithTime"
    }
    Block {
      BlockType		      Sum
      Name		      "Sum"
      Ports		      [2, 1]
      Position		      [325, 316, 340, 434]
      ShowName		      off
      Inputs		      "+-"
      InputSameDT	      off
      OutDataTypeMode	      "Inherit via internal rule"
    }
    Block {
      BlockType		      Sum
      Name		      "Sum1"
      Ports		      [2, 1]
      Position		      [325, 175, 340, 290]
      ShowName		      off
      Inputs		      "+-"
      InputSameDT	      off
      OutDataTypeMode	      "Inherit via internal rule"
    }
    Block {
      BlockType		      Constant
      Name		      "Teta=pi"
      Position		      [135, 334, 170, 356]
      Value		      "pi"
    }
    Line {
      SrcBlock		      "Mux"
      SrcPort		      1
      DstBlock		      "LQR Controller"
      DstPort		      1
    }
    Line {
      Labels		      [2, 0]
      SrcBlock		      "Mux1"
      SrcPort		      1
      Points		      [0, 160; -795, 0]
      DstBlock		      "Demux"
      DstPort		      1
    }
    Line {
      SrcBlock		      "Sum"
      SrcPort		      1
      Points		      [15, 0]
      Branch {
	Points			[0, -20]
	DstBlock		" -pi~pi"
	DstPort			1
      }
      Branch {
	Points			[0, 50]
	DstBlock		"Derivative"
	DstPort			1
      }
    }
    Line {
      SrcBlock		      "Derivative1"
      SrcPort		      1
      DstBlock		      "Mux"
      DstPort		      2
    }
    Line {
      Labels		      [1, 0]
      SrcBlock		      "Demux"
      SrcPort		      2
      DstBlock		      "Sum"
      DstPort		      2
    }
    Line {
      SrcBlock		      "Derivative"
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      DstBlock		      "Mux"
      DstPort		      4
    }
    Line {
      SrcBlock		      "Demux"
      SrcPort		      1
      DstBlock		      "Sum1"
      DstPort		      2
    }
    Line {
      SrcBlock		      "Sum1"
      SrcPort		      1
      Points		      [15, 0]
      Branch {
	Points			[0, -20]
	DstBlock		"Mux"
	DstPort			1
      }
      Branch {
	Points			[0, 50]
	DstBlock		"Derivative1"
	DstPort			1
      }
    }
    Line {
      SrcBlock		      "Position"
      SrcPort		      1
      DstBlock		      "Sum1"
      DstPort		      1
    }
    Line {
      SrcBlock		      "LQR Controller"
      SrcPort		      1
      Points		      [0, 5]
      DstBlock		      "Real Control"
      DstPort		      1
    }
    Line {
      Name		      "Angle"
      Labels		      [0, 0]
      SrcBlock		      "Real Control"
      SrcPort		      2
      Points		      [0, 20; 75, 0]
      Branch {
	Points			[0, -320]
	DstBlock		"Scope1"
	DstPort			2
      }
      Branch {
	DstBlock		"Mux1"
	DstPort			2
      }
    }
    Line {
      SrcBlock		      "Teta=pi"
      SrcPort		      1
      DstBlock		      "Sum"
      DstPort		      1
    }
    Line {
      SrcBlock		      " -pi~pi"
      SrcPort		      1
      DstBlock		      "Mux"
      DstPort		      3
    }
    Line {
      Name		      "Pos"
      Labels		      [2, 1]
      SrcBlock		      "Real Control"
      SrcPort		      1
      Points		      [0, 10; 40, 0]
      Branch {
	Points			[0, -260]
	DstBlock		"Scope1"
	DstPort			1
      }
      Branch {
	DstBlock		"Mux1"
	DstPort			1
      }
    }
  }
}