van_der_pol.cc

#include "drake/examples/van_der_pol/van_der_pol.h"

#include "drake/common/default_scalars.h"
#include "drake/systems/analysis/simulator.h"
#include "drake/systems/framework/basic_vector.h"
#include "drake/systems/framework/diagram_builder.h"
#include "drake/systems/framework/system_constraint.h"
#include "drake/systems/primitives/signal_logger.h"

namespace drake {
namespace examples {
namespace van_der_pol {

template <typename T>
VanDerPolOscillator<T>::VanDerPolOscillator()
    : systems::LeafSystem<T>(systems::SystemTypeTag<VanDerPolOscillator>{}) {
  // State is (q,q̇).
  this->DeclareContinuousState(1, 1, 0);

  // First output, y₁ = q, for interesting estimation problems.
  this->DeclareVectorOutputPort(systems::BasicVector<T>(1),
                                &VanDerPolOscillator::CopyPositionToOutput);

  // Second output, y₂ = [q,q̇]', for e.g. visualizing the full state.
  this->DeclareVectorOutputPort(systems::BasicVector<T>(2),
                                &VanDerPolOscillator::CopyFullStateToOutput);

  // Single parameter, μ, with default μ=1.
  this->DeclareNumericParameter(systems::BasicVector<T>(Vector1<T>(1.0)));

  // Declare μ≥0 constraint.
  systems::ContextConstraintCalc<T> mu = [](const systems::Context<T>& context,
                                            VectorX<T>* value) {
    // Extract μ from the parameters.
    *value = Vector1<T>(context.get_numeric_parameter(0).GetAtIndex(0));
  };
  this->DeclareInequalityConstraint(mu, {Vector1d(0), std::nullopt}, "mu ≥ 0");
}

template <typename T>
Eigen::Matrix2Xd VanDerPolOscillator<T>::CalcLimitCycle() {
  systems::DiagramBuilder<double> builder;

  auto vdp = builder.AddSystem<VanDerPolOscillator<double>>();
  auto logger = LogOutput(vdp->get_full_state_output_port(), &builder);
  auto diagram = builder.Build();

  systems::Simulator<double> simulator(*diagram);

  // The following initial state was pre-computed (by running the simulation
  // with μ=1 long enough for it to effectively reach the steady-state limit
  // cycle).
  simulator.get_mutable_context().SetContinuousState(
      Eigen::Vector2d{-0.1144, 2.0578});

  // Simulate for the approximate period (acquired by inspection of numerical
  // simulation results) of the cycle for μ=1.
  simulator.AdvanceTo(6.667);

  return logger->data();
}

// q̈ + μ(q² - 1)q̇ + q = 0
template <typename T>
void VanDerPolOscillator<T>::DoCalcTimeDerivatives(
    const systems::Context<T>& context,
    systems::ContinuousState<T>* derivatives) const {
  const T q =
      context.get_continuous_state().get_generalized_position().GetAtIndex(0);
  const T qdot =
      context.get_continuous_state().get_generalized_velocity().GetAtIndex(0);
  const T mu = context.get_numeric_parameter(0).GetAtIndex(0);

  using std::pow;
  const T qddot = -mu * (q * q - 1) * qdot - q;

  derivatives->get_mutable_generalized_position().SetAtIndex(0, qdot);
  derivatives->get_mutable_generalized_velocity().SetAtIndex(0, qddot);
}

template <typename T>
void VanDerPolOscillator<T>::CopyPositionToOutput(
    const systems::Context<T>& context, systems::BasicVector<T>* output) const {
  output->SetAtIndex(
      0,
      context.get_continuous_state().get_generalized_position().GetAtIndex(0));
}

template <typename T>
void VanDerPolOscillator<T>::CopyFullStateToOutput(
    const systems::Context<T>& context, systems::BasicVector<T>* output) const {
  output->SetFromVector(context.get_continuous_state_vector().CopyToVector());
}

}  // namespace van_der_pol
}  // namespace examples
}  // namespace drake

DRAKE_DEFINE_CLASS_TEMPLATE_INSTANTIATIONS_ON_DEFAULT_SCALARS(
    class ::drake::examples::van_der_pol::VanDerPolOscillator)