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Examples.ACADOSMPCTerminalSetExample.md

Examples.ACADOSMPCTerminalSetExample ​

Upright stabilization of the pendulum with ACADOSMPC pairing a terminal LQR cost with a terminal set: the terminal weight is the infinite-horizon LQR cost linearized at the upright operating_point   , and the terminal state is additionally confined to a small neighborhood of upright (terminal_constrained = ["theta", "omega"]), softened so the problem stays solvable while the pendulum swings up into the set from       . The reference is the upright state. Verified in test/test_acados_mpc.jl.

Usage ​

MPCComponents.Examples.ACADOSMPCTerminalSetExample()

Variables ​

NameDescriptionUnits
thetaAngle–
u1Torque–
flagacados status–

Behavior ​

Behavior of this component cannot be rendered because it includes path variables.

Source ​

dyad
"""
Upright stabilization of the pendulum with `ACADOSMPC` pairing a terminal LQR cost with a terminal
set: the terminal weight is the infinite-horizon LQR cost linearized at the upright `operating_point`
``(\\pi, 0)``, and the terminal state is additionally confined to a small neighborhood of upright
(`terminal_constrained = ["theta", "omega"]`), softened so the problem stays solvable while the
pendulum swings up into the set from ``\\theta_0 = \\pi - 0.4``. The reference is the upright state.
Verified in `test/test_acados_mpc.jl`.
"""
example component ACADOSMPCTerminalSetExample
  periodicclock = DiscreteComponents.PeriodicClock(dt = 0.05) {
    "Dyad": {"placement": {"diagram": {"x1": 300, "y1": 100, "x2": 400, "y2": 200}}}
  }
  plant = MPCComponents.Examples.ACADOSPendulumPlant(theta0 = 2.741592653589793) {
    "Dyad": {"placement": {"diagram": {"x1": 700, "y1": 300, "x2": 800, "y2": 400}}}
  }
  s1 = DiscreteComponents.Sampler() {
    "Dyad": {
      "placement": {"diagram": {"x1": 500, "y1": 500, "x2": 600, "y2": 600, "rot": 180}}
    }
  }
  s2 = DiscreteComponents.Sampler() {
    "Dyad": {
      "placement": {"diagram": {"x1": 500, "y1": 650, "x2": 600, "y2": 750, "rot": 180}}
    }
  }
  zoh = DiscreteComponents.ZeroOrderHold() {
    "Dyad": {"placement": {"diagram": {"x1": 500, "y1": 300, "x2": 600, "y2": 400}}}
  }
  rpi = BlockComponents.Sources.Constant(k = 3.141592653589793) {
    "Dyad": {"placement": {"diagram": {"x1": -100, "y1": 250, "x2": 0, "y2": 350}}}
  }
  rzero = BlockComponents.Sources.Constant(k = 0.0) {
    "Dyad": {"placement": {"diagram": {"x1": -100, "y1": 550, "x2": 0, "y2": 650}}}
  }
  mpc = MPCComponents.ACADOSMPC(dynamics = plant, inputs = ["tau"], state_variables = ["th", "om"], outputs = ["theta", "omega"], Ts = 0.05, Np = 50, Q1 = diagonal([10.0, 1.0]), Q2 = diagonal([0.5]), umin = [-6.0], umax = [6.0], terminal_lqr_cost = true, operating_point = [3.141592653589793, 0.0], terminal_constrained = ["theta", "omega"], terminal_constrained_min = [2.941592653589793, -0.8], terminal_constrained_max = [3.341592653589793, 0.8], terminal_constraints_soft = true) {
    "Dyad": {"placement": {"diagram": {"x1": 300, "y1": 300, "x2": 400, "y2": 400}}}
  }
  "Angle"
  variable theta::Real
  "Torque"
  variable u1::Real
  "acados status"
  variable flag::Real
relations
  theta = plant.theta
  u1 = mpc.u[1]
  flag = mpc.exitflag
  connect(zoh.y, plant.tau)
  connect(plant.theta, s1.u)
  connect(plant.omega, s2.u)
  connect(rpi.y, mpc.r[1])
  connect(rzero.y, mpc.r[2])
  connect(s1.y, mpc.x[1], periodicclock.y)
  connect(s2.y, mpc.x[2])
  connect(mpc.u[1], zoh.u)
metadata {"Dyad": {"doc": {"behavior": false}}}
end
Flattened Source
dyad
"""
Upright stabilization of the pendulum with `ACADOSMPC` pairing a terminal LQR cost with a terminal
set: the terminal weight is the infinite-horizon LQR cost linearized at the upright `operating_point`
``(\\pi, 0)``, and the terminal state is additionally confined to a small neighborhood of upright
(`terminal_constrained = ["theta", "omega"]`), softened so the problem stays solvable while the
pendulum swings up into the set from ``\\theta_0 = \\pi - 0.4``. The reference is the upright state.
Verified in `test/test_acados_mpc.jl`.
"""
example component ACADOSMPCTerminalSetExample
  periodicclock = DiscreteComponents.PeriodicClock(dt = 0.05) {
    "Dyad": {"placement": {"diagram": {"x1": 300, "y1": 100, "x2": 400, "y2": 200}}}
  }
  plant = MPCComponents.Examples.ACADOSPendulumPlant(theta0 = 2.741592653589793) {
    "Dyad": {"placement": {"diagram": {"x1": 700, "y1": 300, "x2": 800, "y2": 400}}}
  }
  s1 = DiscreteComponents.Sampler() {
    "Dyad": {
      "placement": {"diagram": {"x1": 500, "y1": 500, "x2": 600, "y2": 600, "rot": 180}}
    }
  }
  s2 = DiscreteComponents.Sampler() {
    "Dyad": {
      "placement": {"diagram": {"x1": 500, "y1": 650, "x2": 600, "y2": 750, "rot": 180}}
    }
  }
  zoh = DiscreteComponents.ZeroOrderHold() {
    "Dyad": {"placement": {"diagram": {"x1": 500, "y1": 300, "x2": 600, "y2": 400}}}
  }
  rpi = BlockComponents.Sources.Constant(k = 3.141592653589793) {
    "Dyad": {"placement": {"diagram": {"x1": -100, "y1": 250, "x2": 0, "y2": 350}}}
  }
  rzero = BlockComponents.Sources.Constant(k = 0.0) {
    "Dyad": {"placement": {"diagram": {"x1": -100, "y1": 550, "x2": 0, "y2": 650}}}
  }
  mpc = MPCComponents.ACADOSMPC(dynamics = plant, inputs = ["tau"], state_variables = ["th", "om"], outputs = ["theta", "omega"], Ts = 0.05, Np = 50, Q1 = diagonal([10.0, 1.0]), Q2 = diagonal([0.5]), umin = [-6.0], umax = [6.0], terminal_lqr_cost = true, operating_point = [3.141592653589793, 0.0], terminal_constrained = ["theta", "omega"], terminal_constrained_min = [2.941592653589793, -0.8], terminal_constrained_max = [3.341592653589793, 0.8], terminal_constraints_soft = true) {
    "Dyad": {"placement": {"diagram": {"x1": 300, "y1": 300, "x2": 400, "y2": 400}}}
  }
  "Angle"
  variable theta::Real
  "Torque"
  variable u1::Real
  "acados status"
  variable flag::Real
relations
  theta = plant.theta
  u1 = mpc.u[1]
  flag = mpc.exitflag
  connect(zoh.y, plant.tau)
  connect(plant.theta, s1.u)
  connect(plant.omega, s2.u)
  connect(rpi.y, mpc.r[1])
  connect(rzero.y, mpc.r[2])
  connect(s1.y, mpc.x[1], periodicclock.y)
  connect(s2.y, mpc.x[2])
  connect(mpc.u[1], zoh.u)
metadata {"Dyad": {"doc": {"behavior": false}}}
end


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No test cases defined.

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