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Examples.LinearMPCEconomicExample.md

Examples.LinearMPCEconomicExample ​

Economic MPC of a first-order plant with LinearMPCController: a time-varying price enters the linear control cost (Eu p + eu)' u through the generalized-parameter input p, so the controller trades tracking against the cost of actuation when the price is high. The prediction model is the plant itself (dynamics = plant), which the controller discretizes exactly with the sample time 0.1.

Usage ​

MPCComponents.Examples.LinearMPCEconomicExample()

Variables ​

NameDescriptionUnits
y1Plant output–
u1Control signal–

Behavior ​

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

Source ​

dyad
"""
Economic MPC of a first-order plant with `LinearMPCController`: a time-varying price enters
the linear control cost `(Eu p + eu)' u` through the generalized-parameter input `p`, so the
controller trades tracking against the cost of actuation when the price is high. The prediction
model is the plant itself (`dynamics = plant`), which the controller discretizes exactly with the
sample time 0.1.
"""
example component LinearMPCEconomicExample
  periodicclock = DiscreteComponents.PeriodicClock(dt = 0.1) {}
  plant = BlockComponents.Continuous.FirstOrder(k = 1.0, T = 0.5, x(initial = 0)) {}
  s1 = DiscreteComponents.Sampler() {}
  sr = DiscreteComponents.Sampler() {}
  sp = DiscreteComponents.Sampler() {}
  zoh = DiscreteComponents.ZeroOrderHold() {}
  ref = BlockComponents.Sources.Constant(k = 1.0) {}
  price = BlockComponents.Sources.Sine(amplitude = 0.5, frequency = 0.2, offset = 0.5) {}
  mpc = MPCComponents.LinearMPCController(dynamics = plant, inputs = ["u"], outputs = ["y"], state_variables = ["x"], Ts = 0.1, Q1 = [1.0], Q2 = [0.01], Eu = [[1.0]], umin = [0.0], umax = [2.0], Np = 8, R1 = [0.01], R2 = [0.01]) {}
  "Plant output"
  variable y1::Real
  "Control signal"
  variable u1::Real
relations
  y1 = plant.y
  u1 = mpc.u[1]
  connect(zoh.y, plant.u)
  connect(plant.y, s1.u)
  connect(s1.y, mpc.y[1], periodicclock.y)
  connect(ref.y, sr.u)
  connect(sr.y, mpc.r[1])
  connect(price.y, sp.u)
  connect(sp.y, mpc.p[1])
  connect(mpc.u[1], zoh.u)
metadata {"Dyad": {"tests": {"case1": {"stop": 10}}, "doc": {"behavior": false}}}
end
Flattened Source
dyad
"""
Economic MPC of a first-order plant with `LinearMPCController`: a time-varying price enters
the linear control cost `(Eu p + eu)' u` through the generalized-parameter input `p`, so the
controller trades tracking against the cost of actuation when the price is high. The prediction
model is the plant itself (`dynamics = plant`), which the controller discretizes exactly with the
sample time 0.1.
"""
example component LinearMPCEconomicExample
  periodicclock = DiscreteComponents.PeriodicClock(dt = 0.1) {}
  plant = BlockComponents.Continuous.FirstOrder(k = 1.0, T = 0.5, x(initial = 0)) {}
  s1 = DiscreteComponents.Sampler() {}
  sr = DiscreteComponents.Sampler() {}
  sp = DiscreteComponents.Sampler() {}
  zoh = DiscreteComponents.ZeroOrderHold() {}
  ref = BlockComponents.Sources.Constant(k = 1.0) {}
  price = BlockComponents.Sources.Sine(amplitude = 0.5, frequency = 0.2, offset = 0.5) {}
  mpc = MPCComponents.LinearMPCController(dynamics = plant, inputs = ["u"], outputs = ["y"], state_variables = ["x"], Ts = 0.1, Q1 = [1.0], Q2 = [0.01], Eu = [[1.0]], umin = [0.0], umax = [2.0], Np = 8, R1 = [0.01], R2 = [0.01]) {}
  "Plant output"
  variable y1::Real
  "Control signal"
  variable u1::Real
relations
  y1 = plant.y
  u1 = mpc.u[1]
  connect(zoh.y, plant.u)
  connect(plant.y, s1.u)
  connect(s1.y, mpc.y[1], periodicclock.y)
  connect(ref.y, sr.u)
  connect(sr.y, mpc.r[1])
  connect(price.y, sp.u)
  connect(sp.y, mpc.p[1])
  connect(mpc.u[1], zoh.u)
metadata {"Dyad": {"tests": {"case1": {"stop": 10}}, "doc": {"behavior": false}}}
end


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