LIBRARY

Examples.CartPoleIncrementMPCExample

The cart-pole example of the DyadControlSystems generic-MPC documentation ("Getting started"): all four state variables start at 1 and are regulated to the origin with Q1 = I, Q2 = 0.1, a penalty Q3 = 0.1 on the force increments, the force bounded to ±3 and the pendulum angular velocity to ±4 (soft here, where the tutorial's stage constraint is hard). The tutorial's LQR-based terminal cost is replaced by the default Qf = Q1. Verified in test/test_acados_tutorials.jl.

Usage

MPCComponents.Examples.CartPoleIncrementMPCExample()

Variables

Name	Description	Units
pos	Cart position	–
theta	Pendulum angle	–
omega	Pendulum angular velocity	–
u1	Force	–
flag	acados status	–

Behavior

Source

"""
The cart-pole example of the DyadControlSystems generic-MPC documentation ("Getting started"): all four
state variables start at 1 and are regulated to the origin with `Q1 = I`, `Q2 = 0.1`, a penalty
`Q3 = 0.1` on the force increments, the force bounded to ±3 and the pendulum angular velocity to ±4
(soft here, where the tutorial's stage constraint is hard). The tutorial's LQR-based terminal cost is
replaced by the default `Qf = Q1`. Verified in `test/test_acados_tutorials.jl`.
"""
example component CartPoleIncrementMPCExample
  periodicclock = DiscreteComponents.PeriodicClock(dt = 0.1) {}
  plant = MPCComponents.Examples.CartPolePlant(p0 = 1.0, th0 = 1.0, v0 = 1.0, w0 = 1.0) {}
  "Samplers of the four state variables"
  s = [DiscreteComponents.Sampler() for i in 1:4] {}
  zoh = DiscreteComponents.ZeroOrderHold() {}
  mpc = MPCComponents.ACADOSMPC(dynamics = plant, inputs = ["F"], state_variables = ["p", "th", "v", "w"], outputs = ["p", "th", "v", "w"], Ts = 0.1, Np = 10, Q1 = diagonal([1.0, 1.0, 1.0, 1.0]), Q2 = diagonal([0.1]), penalize_increments = true, Q3 = diagonal([0.1]), umin = [-3.0], umax = [3.0], constrained = ["w"], constrained_min = [-4.0], constrained_max = [4.0], reference_tracking = false, integrator = ACADOSIntegrator.IRK(), integrator_stages = 3) {}
  "Cart position"
  variable pos::Real
  "Pendulum angle"
  variable theta::Real
  "Pendulum angular velocity"
  variable omega::Real
  "Force"
  variable u1::Real
  "acados status"
  variable flag::Real
relations
  pos = plant.pos
  theta = plant.theta
  omega = plant.omega
  u1 = mpc.u[1]
  flag = mpc.exitflag
  connect(plant.pos, s[1].u)
  connect(plant.theta, s[2].u)
  connect(plant.vel, s[3].u)
  connect(plant.omega, s[4].u)
  connect(s[1].y, mpc.x[1], periodicclock.y)
  for i in 2:4
    connect(s[i].y, mpc.x[i])
  end
  connect(mpc.u[1], zoh.u) {}
  connect(zoh.y, plant.F) {}
end

Flattened Source

"""
The cart-pole example of the DyadControlSystems generic-MPC documentation ("Getting started"): all four
state variables start at 1 and are regulated to the origin with `Q1 = I`, `Q2 = 0.1`, a penalty
`Q3 = 0.1` on the force increments, the force bounded to ±3 and the pendulum angular velocity to ±4
(soft here, where the tutorial's stage constraint is hard). The tutorial's LQR-based terminal cost is
replaced by the default `Qf = Q1`. Verified in `test/test_acados_tutorials.jl`.
"""
example component CartPoleIncrementMPCExample
  periodicclock = DiscreteComponents.PeriodicClock(dt = 0.1) {}
  plant = MPCComponents.Examples.CartPolePlant(p0 = 1.0, th0 = 1.0, v0 = 1.0, w0 = 1.0) {}
  "Samplers of the four state variables"
  s = [DiscreteComponents.Sampler() for i in 1:4] {}
  zoh = DiscreteComponents.ZeroOrderHold() {}
  mpc = MPCComponents.ACADOSMPC(dynamics = plant, inputs = ["F"], state_variables = ["p", "th", "v", "w"], outputs = ["p", "th", "v", "w"], Ts = 0.1, Np = 10, Q1 = diagonal([1.0, 1.0, 1.0, 1.0]), Q2 = diagonal([0.1]), penalize_increments = true, Q3 = diagonal([0.1]), umin = [-3.0], umax = [3.0], constrained = ["w"], constrained_min = [-4.0], constrained_max = [4.0], reference_tracking = false, integrator = ACADOSIntegrator.IRK(), integrator_stages = 3) {}
  "Cart position"
  variable pos::Real
  "Pendulum angle"
  variable theta::Real
  "Pendulum angular velocity"
  variable omega::Real
  "Force"
  variable u1::Real
  "acados status"
  variable flag::Real
relations
  pos = plant.pos
  theta = plant.theta
  omega = plant.omega
  u1 = mpc.u[1]
  flag = mpc.exitflag
  connect(plant.pos, s[1].u)
  connect(plant.theta, s[2].u)
  connect(plant.vel, s[3].u)
  connect(plant.omega, s[4].u)
  connect(s[1].y, mpc.x[1], periodicclock.y)
  for i in 2:4
    connect(s[i].y, mpc.x[i])
  end
  connect(mpc.u[1], zoh.u) {}
  connect(zoh.y, plant.F) {}
metadata {}
end

Test Cases

No test cases defined.

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