model

Control.Mpc.Test.DoubleIntegratorTrackingMpc

Receding-horizon tracking of a position step on a sampled double integrator

Fully discrete clocked composition: the MPC measures the plant state of the previous tick, takes one warm-started Gauss-Newton step on a 10-interval horizon linearized through the port equations, and its first control drives the plant over the same tick. The step reference is the constant target seen from the zero initial state. Unconstrained Gauss-Newton tracking; constrained variants arrive with the M-B QP solver.

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
parameter	`samplePeriod`	`Real`	`(unit="s") = 0.05`
parameter	`positionReference_m`	`Real`	`= 1.0`	Position step target in meters
parameter	`jacobianStep`	`Real`	`= 1.0e-6`

Members

Name	Kind	Description
Transcription	block

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

model DoubleIntegratorTrackingMpc
  "Receding-horizon tracking of a position step on a sampled double integrator"
  parameter Real samplePeriod(unit="s") = 0.05;
  parameter Real positionReference_m = 1.0
    "Position step target in meters";
  parameter Real jacobianStep = 1.0e-6;
  replaceable block Transcription = Control.Mpc.MultipleShooting
    constrainedby Control.Mpc.PartialTranscription
    "Selected OCP transcription";
  Transcription mpc(
    ocp=Control.Mpc.OcpSpec(
      stateCount=2,
      inputCount=1,
      horizonLength=10,
      samplePeriod=samplePeriod,
      regularization=1.0e-9),
    stateWeight={100.0, 10.0},
    inputWeight={1.0},
    terminalWeight={500.0, 50.0},
    redeclare function NlpSolver = Control.Mpc.gaussNewtonSqpStep);
  discrete Real plantState[2](each start=0.0)
    "Plant position and velocity, advanced by the same ZOH step";
  Real position_m "Plant position in meters";
  Real velocity_m_s "Plant velocity in meters per second";
  Real command_m_s2 "Applied acceleration command in meters per second squared";
equation
  mpc.currentState = {pre(plantState[1]), pre(plantState[2])};
  mpc.reference = {positionReference_m, 0.0};
  (mpc.stateJacobians, mpc.inputJacobians, mpc.nominalNodes) =
    Control.Mpc.Test.doubleIntegratorLinearization(
      mpc.linearizationStates,
      mpc.linearizationControls,
      samplePeriod,
      jacobianStep);
  position_m = plantState[1];
  velocity_m_s = plantState[2];
  command_m_s2 = mpc.command[1];
algorithm
  when sample(0.0, samplePeriod) then
    plantState := Control.Mpc.Test.doubleIntegratorStep(
      pre(plantState), mpc.command, samplePeriod);
  end when;
  annotation(experiment(StartTime=0.0, StopTime=5.0,
    Tolerance=1.0e-8, Interval=0.05),
    Documentation(info="<html>
    <p>Fully discrete clocked composition: the MPC measures the plant state
    of the previous tick, takes one warm-started Gauss-Newton step on a
    10-interval horizon linearized through the port equations, and its
    first control drives the plant over the same tick. The step reference
    is the constant target seen from the zero initial state. Unconstrained
    Gauss-Newton tracking; constrained variants arrive with the M-B QP
    solver.</p>
  </html>"));
end DoubleIntegratorTrackingMpc;