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pendulum controller

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This commit is contained in:
Joppe Blondel
2026-03-10 14:36:24 +01:00
parent 75b690b19b
commit 67d40f2dcd
3 changed files with 255 additions and 108 deletions
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236
test2d.mo
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@@ -1,4 +1,107 @@
package test2d
model vis2d
import Modelica.Mechanics.MultiBody.Visualizers;
import Modelica.Mechanics.MultiBody.Frames;
parameter Real L = 1;
parameter Real w = 0.02;
parameter Real orbRadius = 0.04;
parameter Real axisLength = 0.25;
parameter Real axisWidth = 0.01;
parameter Real planeSize = 2.0;
parameter Real planeThickness = 0.002;
parameter Real planeOffset = -0.001;
Modelica.Blocks.Interfaces.RealInput phi annotation(
Placement(transformation(origin = {-98, -42}, extent = {{-20, -20}, {20, 20}}), iconTransformation(origin = {-94, 60}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Interfaces.RealInput y annotation(
Placement(transformation(origin = {-98, 0}, extent = {{-20, -20}, {20, 20}}), iconTransformation(origin = {-94, -60}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Interfaces.RealInput x annotation(
Placement(transformation(origin = {-98, 40}, extent = {{-20, -20}, {20, 20}}), iconTransformation(origin = {-94, 0}, extent = {{-10, -10}, {10, 10}})));
protected
Real Rz[3,3];
Real r[3];
Visualizers.Advanced.Shape link(
shapeType = "cylinder",
length = L/2,
width = w,
height = w,
r_shape = {L / 2, 0, 0},
lengthDirection = {-1, 0, 0},
widthDirection = {0, 1, 0},
r = r,
R = Frames.from_T(Rz, zeros(3)));
Visualizers.Advanced.Shape orb(
shapeType = "sphere",
length = 2 * orbRadius,
width = 2 * orbRadius,
height = 2 * orbRadius,
r_shape = {0, 0, 0},
lengthDirection = {1, 0, 0},
widthDirection = {0, 1, 0},
r = r,
R = Frames.from_T(Rz, zeros(3)));
Visualizers.Advanced.Shape xAxis(
shapeType = "cylinder",
length = axisLength,
width = axisWidth,
height = axisWidth,
color = {255, 0, 0},
specularCoefficient = 0.1,
r_shape = {axisLength / 2, 0, 0},
lengthDirection = {1, 0, 0},
widthDirection = {0, 1, 0},
r = zeros(3),
R = Frames.from_T([1, 0, 0;
0, 1, 0;
0, 0, 1], zeros(3)));
Visualizers.Advanced.Shape yAxis(
shapeType = "cylinder",
length = axisLength,
width = axisWidth,
height = axisWidth,
color = {0, 200, 0},
specularCoefficient = 0.1,
r_shape = {0, axisLength / 2, 0},
lengthDirection = {0, 1, 0},
widthDirection = {0, 0, 1},
r = zeros(3),
R = Frames.from_T([1, 0, 0;
0, 1, 0;
0, 0, 1], zeros(3)));
Visualizers.Advanced.Shape zAxis(
shapeType = "cylinder",
length = axisLength,
width = axisWidth,
height = axisWidth,
color = {0, 90, 255},
specularCoefficient = 0.1,
r_shape = {0, 0, axisLength / 2},
lengthDirection = {0, 0, 1},
widthDirection = {1, 0, 0},
r = zeros(3),
R = Frames.from_T([1, 0, 0;
0, 1, 0;
0, 0, 1], zeros(3)));
equation
r = {x, y, 0};
// Negate phi here since shapes use inverse frame-mapping
Rz = [cos(-phi), -sin(-phi), 0;
sin(-phi), cos(-phi), 0;
0, 0, 1];
annotation(
uses(Modelica(version = "4.1.0")),
Icon(graphics = {Rectangle(lineColor = {204, 204, 204}, fillColor = {255, 255, 255}, fillPattern = FillPattern.Sphere, extent = {{-100, 100}, {100, -100}}, radius = 10), Text(extent = {{-100, 100}, {100, -100}}, textString = "VIS")}),
experiment(StartTime = 0, StopTime = 1, Tolerance = 1e-06, Interval = 0.002));
end vis2d;
model pendulum
parameter Modelica.Units.SI.Mass mass;
parameter Modelica.Units.SI.Length length;
@@ -131,9 +234,10 @@ package test2d
end rTF;
model test
pendulum pendulum1(mass = 1, length = 1, momentOfInertia = 0.001, startAngle = 0) annotation(
import Modelica.Constants.pi;
pendulum pendulum1(mass = 1, length = 1, momentOfInertia = 0.001, startAngle = 1.5707963267948966) annotation(
Placement(transformation(origin = {60, 0}, extent = {{-20, -20}, {20, 20}})));
BondGraph.J0 j1(N = 2, s = {1, -1}) annotation(
BondGraph.J0 j1(N = 3, s = {1, -1, 1}) annotation(
Placement(transformation(origin = {60, 40}, extent = {{-10, -10}, {10, 10}})));
BondGraph.J1 w_hinge(N = 2, s = {-1, -1}) annotation(
Placement(transformation(origin = {20, 40}, extent = {{-10, -10}, {10, 10}})));
@@ -147,10 +251,26 @@ package test2d
Placement(transformation(origin = {30, -40}, extent = {{-10, -10}, {10, 10}})));
BondGraph.J1 j3(N = 2, s = {1, -1}) annotation(
Placement(transformation(origin = {-20, -60}, extent = {{-10, -10}, {10, 10}})));
BondGraph.J1 j4(N = 1, s = {-1}) annotation(
BondGraph.J1 j4(N = 2, s = {-1, 1}) annotation(
Placement(transformation(origin = {-20, -20}, extent = {{-10, -10}, {10, 10}})));
BondGraph.Sf sf(f0 = 0) annotation(
Placement(transformation(origin = {-58, -60}, extent = {{-10, -10}, {10, 10}})));
BondGraph.Sf sf1(f0 = 0) annotation(
Placement(transformation(origin = {-56, -20}, extent = {{-10, -10}, {10, 10}})));
BondGraph.J1 w_maxle(N = 2, s = {-1, 1}) annotation(
Placement(transformation(origin = {60, 80}, extent = {{-10, -10}, {10, 10}})));
BondGraph.mSe T_motor annotation(
Placement(transformation(origin = {20, 80}, extent = {{-10, -10}, {10, 10}})));
controller controller1(g_P = 50, g_I = 7.5, g_D = 5, sampleTime(displayUnit = "ms") = 0.01, limit = 20) annotation(
Placement(transformation(origin = {16, 110}, extent = {{10, -10}, {-10, 10}})));
Modelica.Blocks.Sources.TimeTable timeTable(table = [
0, 0; 4,0;
5, 1.5*pi; 9, 1.5*pi;
10, pi; 14, pi;
15, 0.5*pi; 19, 0.5*pi;
20, 0; 25, 0
]) annotation(
Placement(transformation(origin = {50, 130}, extent = {{-10, -10}, {10, 10}}, rotation = 180)));
equation
connect(w_hinge.P[1], j1.P[1]) annotation(
Line(points = {{20, 40}, {60, 40}}, color = {0, 0, 127}, thickness = 0.75, arrow = {Arrow.None, Arrow.Half}, arrowSize = 6));
@@ -162,17 +282,117 @@ package test2d
// Line(points = {{60, -50}, {60, -20}}, color = {0, 85, 0}, thickness = 0.75, arrow = //{Arrow.None, Arrow.Half}, arrowSize = 6));
connect(j2.P[1], pendulum1.trans_i) annotation(
Line(points = {{60, -40}, {60, -20}}, color = {0, 85, 0}));
connect(muxDemux.p, j2.P[2]) annotation(
connect(muxDemux.p, j2.P[2]) annotation(
Line(points = {{40, -40}, {60, -40}}, color = {0, 85, 0}));
connect(j3.P[2], muxDemux.p2) annotation(
connect(j3.P[2], muxDemux.p2) annotation(
Line(points = {{-20, -60}, {8, -60}, {8, -44}, {20, -44}}, color = {0, 0, 127}));
connect(j4.P[1], muxDemux.p1) annotation(
connect(j4.P[1], muxDemux.p1) annotation(
Line(points = {{-20, -20}, {8, -20}, {8, -36}, {20, -36}}, color = {0, 0, 127}));
connect(sf.p, j3.P[1]) annotation(
connect(sf.p, j3.P[1]) annotation(
Line(points = {{-50, -60}, {-20, -60}}, color = {0, 0, 127}));
connect(sf1.p, j4.P[2]) annotation(
Line(points = {{-48, -20}, {-20, -20}}, color = {0, 0, 127}));
connect(w_maxle.P[1], j1.P[3]) annotation(
Line(points = {{60, 80}, {60, 40}}, color = {0, 0, 127}, thickness = 0.5));
connect(T_motor.p, w_maxle.P[2]) annotation(
Line(points = {{28, 80}, {60, 80}}, color = {0, 0, 127}));
connect(pendulum1.phi, controller1.angle) annotation(
Line(points = {{80, 8}, {92, 8}, {92, 110}, {26, 110}}, color = {0, 0, 127}));
connect(controller1.motor, T_motor.e0) annotation(
Line(points = {{6, 110}, {6, 109}, {0, 109}, {0, 80}, {20, 80}, {20, 72}}, color = {0, 0, 127}));
connect(timeTable.y, controller1.setpoint) annotation(
Line(points = {{39, 130}, {39, 117}, {26, 117}}, color = {0, 0, 127}));
annotation(
experiment(StartTime = 0, StopTime = 10, Tolerance = 1e-06, Interval = 0.02));
experiment(StartTime = 0, StopTime = 25, Tolerance = 1e-06, Interval = 0.02),
Diagram(coordinateSystem(extent = {{-80, 140}, {100, -80}})));
end test;
model controller
import Modelica.Blocks.Interfaces.RealInput;
import Modelica.Blocks.Interfaces.RealOutput;
parameter Real g_P = 1;
parameter Real g_I = 1;
parameter Real g_D = 1;
parameter Modelica.Units.SI.Time sampleTime = 0.0025;
parameter Real limit = 100;
RealInput setpoint(quantity="Angle") "Setpoint" annotation(
Placement(transformation(origin = {-158, 20}, extent = {{-10, -10}, {10, 10}}), iconTransformation(origin = {-96, 70}, extent = {{-10, -10}, {10, 10}})));
RealInput angle(quantity="Angle") "Angle of the pendulum" annotation(
Placement(transformation(origin = {-158, -6}, extent = {{-10, -10}, {10, 10}}), iconTransformation(origin = {-96, 0}, extent = {{-10, -10}, {10, 10}})));
RealOutput motor(quantity="Torque") "Motor drive" annotation(
Placement(transformation(origin = {226, 0}, extent = {{-10, -10}, {10, 10}}), iconTransformation(origin = {104, 0}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Discrete.Sampler sampler(samplePeriod = sampleTime) annotation(
Placement(transformation(origin = {-126, -6}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Math.Add add(k1 = 1, k2 = -1) annotation(
Placement(transformation(origin = {-86, 0}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Math.Gain gain(k = g_P) annotation(
Placement(transformation(origin = {-30, 0}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Discrete.UnitDelay unitDelay(samplePeriod = sampleTime) annotation(
Placement(transformation(origin = {-36, 32}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Math.MultiSum multiSum(nu = 3) annotation(
Placement(transformation(origin = {122, 0}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Math.Gain gain1(k = g_D / sampleTime) annotation(
Placement(transformation(origin = {56, 38}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Math.Add add1(k1 = +1, k2 = -1) annotation(
Placement(transformation(origin = {8, 38}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Discrete.Sampler sampler1(samplePeriod = sampleTime) annotation(
Placement(transformation(origin = {-126, 20}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Discrete.ZeroOrderHold zeroOrderHold(samplePeriod = sampleTime) annotation(
Placement(transformation(origin = {192, 0}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Nonlinear.Limiter limiter(uMax = limit) annotation(
Placement(transformation(origin = {158, 0}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Discrete.UnitDelay unitDelay1(samplePeriod = sampleTime) annotation(
Placement(transformation(origin = {50, -50}, extent = {{-10, -10}, {10, 10}})));
Modelica.Blocks.Math.Gain gain11(k = g_I*sampleTime) annotation(
Placement(transformation(origin = {-30, -44}, extent = {{10, -10}, {-10, 10}}, rotation = 180)));
Modelica.Blocks.Math.Add add11(k1 = +1, k2 = +1) annotation(
Placement(transformation(origin = {14, -50}, extent = {{-10, -10}, {10, 10}}, rotation = -0)));
equation
connect(angle, sampler.u) annotation(
Line(points = {{-158, -6}, {-138, -6}}, color = {0, 0, 127}));
connect(sampler.y, add.u2) annotation(
Line(points = {{-115, -6}, {-99, -6}}, color = {0, 0, 127}));
connect(add.y, gain.u) annotation(
Line(points = {{-75, 0}, {-42, 0}}, color = {0, 0, 127}));
connect(gain.y, multiSum.u[1]) annotation(
Line(points = {{-19, 0}, {112, 0}}, color = {0, 0, 127}));
connect(gain1.y, multiSum.u[2]) annotation(
Line(points = {{67, 38}, {95, 38}, {95, 0}, {111, 0}}, color = {0, 0, 127}));
connect(unitDelay.y, add1.u2) annotation(
Line(points = {{-25, 32}, {-4, 32}}, color = {0, 0, 127}));
connect(add.y, add1.u1) annotation(
Line(points = {{-74, 0}, {-62, 0}, {-62, 54}, {-12, 54}, {-12, 44}, {-4, 44}}, color = {0, 0, 127}));
connect(add.y, unitDelay.u) annotation(
Line(points = {{-74, 0}, {-62, 0}, {-62, 32}, {-48, 32}}, color = {0, 0, 127}));
connect(add1.y, gain1.u) annotation(
Line(points = {{20, 38}, {44, 38}}, color = {0, 0, 127}));
connect(setpoint, sampler1.u) annotation(
Line(points = {{-158, 20}, {-138, 20}}, color = {0, 0, 127}));
connect(sampler1.y, add.u1) annotation(
Line(points = {{-114, 20}, {-110, 20}, {-110, 6}, {-98, 6}}, color = {0, 0, 127}));
connect(multiSum.y, limiter.u) annotation(
Line(points = {{134, 0}, {146, 0}}, color = {0, 0, 127}));
connect(limiter.y, zeroOrderHold.u) annotation(
Line(points = {{170, 0}, {180, 0}}, color = {0, 0, 127}));
connect(zeroOrderHold.y, motor) annotation(
Line(points = {{204, 0}, {226, 0}}, color = {0, 0, 127}));
connect(unitDelay1.y, multiSum.u[3]) annotation(
Line(points = {{61, -50}, {94, -50}, {94, 0}, {112, 0}}, color = {0, 0, 127}));
connect(unitDelay1.y, add11.u2) annotation(
Line(points = {{62, -50}, {80, -50}, {80, -74}, {-10, -74}, {-10, -56}, {2, -56}}, color = {0, 0, 127}));
connect(gain11.y, add11.u1) annotation(
Line(points = {{-19, -44}, {2, -44}}, color = {0, 0, 127}));
connect(add.y, gain11.u) annotation(
Line(points = {{-74, 0}, {-62, 0}, {-62, -44}, {-42, -44}}, color = {0, 0, 127}));
connect(add11.y, unitDelay1.u) annotation(
Line(points = {{26, -50}, {38, -50}}, color = {0, 0, 127}));
annotation(
Icon(graphics = {Rectangle(lineColor = {211, 211, 211}, fillColor = {255, 255, 255}, fillPattern = FillPattern.Sphere, lineThickness = 2, extent = {{-100, 100}, {100, -100}}, radius = 25)}),
experiment(StartTime = 0, StopTime = 1, Tolerance = 1e-06, Interval = 0.002),
Diagram(coordinateSystem(extent = {{-180, 60}, {240, -20}})));
end controller;
annotation(
uses(Modelica(version = "4.1.0")));
end test2d;