frc971/control_loops/c2d.h

#ifndef FRC971_CONTROL_LOOPS_C2D_H_
#define FRC971_CONTROL_LOOPS_C2D_H_

#include <chrono>

#include <Eigen/Dense>
// We need to include MatrixFunctions for the matrix exponential.
#include "unsupported/Eigen/MatrixFunctions"

namespace frc971 {
namespace controls {

template <typename Scalar, int num_states, int num_inputs>
void C2D(const ::Eigen::Matrix<Scalar, num_states, num_states> &A_continuous,
         const ::Eigen::Matrix<Scalar, num_states, num_inputs> &B_continuous,
         ::std::chrono::nanoseconds dt,
         ::Eigen::Matrix<Scalar, num_states, num_states> *A,
         ::Eigen::Matrix<Scalar, num_states, num_inputs> *B) {
  // Trick from
  // https://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models
  // to solve for A and B more efficiently.
  Eigen::Matrix<Scalar, num_states + num_inputs, num_states + num_inputs>
      M_state_continuous;
  M_state_continuous.setZero();
  M_state_continuous.template block<num_states, num_states>(0, 0) =
      A_continuous *
      ::std::chrono::duration_cast<::std::chrono::duration<Scalar>>(dt).count();
  M_state_continuous.template block<num_states, num_inputs>(0, num_states) =
      B_continuous *
      ::std::chrono::duration_cast<::std::chrono::duration<Scalar>>(dt).count();

  Eigen::Matrix<Scalar, num_states + num_inputs, num_states + num_inputs>
      M_state = M_state_continuous.exp();
  *A = M_state.template block<num_states, num_states>(0, 0);
  *B = M_state.template block<num_states, num_inputs>(0, num_states);
}

template <typename Scalar, int num_states>
void DiscretizeQ(
    const Eigen::Matrix<Scalar, num_states, num_states> &Q_continuous,
    const Eigen::Matrix<Scalar, num_states, num_states> &A_continuous,
    ::std::chrono::nanoseconds dt,
    Eigen::Matrix<Scalar, num_states, num_states> *Q_d) {
  Eigen::Matrix<Scalar, num_states, num_states> Qtemp =
      (Q_continuous + Q_continuous.transpose()) / static_cast<Scalar>(2.0);
  Eigen::Matrix<Scalar, 2 * num_states, 2 * num_states> M_gain;
  M_gain.setZero();
  // Set up the matrix M = [[-A, Q], [0, A.T]]
  M_gain.template block<num_states, num_states>(0, 0) = -A_continuous;
  M_gain.template block<num_states, num_states>(0, num_states) = Qtemp;
  M_gain.template block<num_states, num_states>(num_states, num_states) =
      A_continuous.transpose();

  Eigen::Matrix<Scalar, 2 * num_states, 2 *num_states> phi =
      (M_gain *
       ::std::chrono::duration_cast<::std::chrono::duration<Scalar>>(dt)
           .count()).exp();

  // Phi12 = phi[0:num_states, num_states:2*num_states]
  // Phi22 = phi[num_states:2*num_states,
  // num_states:2*num_states]
  Eigen::Matrix<Scalar, num_states, num_states> phi12 =
      phi.block(0, num_states, num_states, num_states);
  Eigen::Matrix<Scalar, num_states, num_states> phi22 =
      phi.block(num_states, num_states, num_states, num_states);

  *Q_d = phi22.transpose() * phi12;
  *Q_d = (*Q_d + Q_d->transpose()) / static_cast<Scalar>(2.0);
}

}  // namespace controls
}  // namespace frc971

#endif  // FRC971_CONTROL_LOOPS_C2D_H_