frc971/control_loops/python/controls.py

#!/usr/bin/python

"""
Control loop pole placement library.

This library will grow to support many different pole placement methods.
Currently it only supports direct pole placement.
"""

__author__ = 'Austin Schuh (austin.linux@gmail.com)'

import numpy
import slycot

class Error (Exception):
  """Base class for all control loop exceptions."""


class PolePlacementError(Error):
  """Exception raised when pole placement fails."""


# TODO(aschuh): dplace should take a control system object.
# There should also exist a function to manipulate laplace expressions, and
# something to plot bode plots and all that.
def dplace(A, B, poles, alpha=1e-6):
  """Set the poles of (A - BF) to poles.

  Args:
    A: numpy.matrix(n x n), The A matrix.
    B: numpy.matrix(n x m), The B matrix.
    poles: array(imaginary numbers), The poles to use.  Complex conjugates poles
      must be in pairs.

  Raises:
    ValueError: Arguments were the wrong shape or there were too many poles.
    PolePlacementError: Pole placement failed.

  Returns:
    numpy.matrix(m x n), K
  """
  # See http://www.icm.tu-bs.de/NICONET/doc/SB01BD.html for a description of the
  # fortran code that this is cleaning up the interface to.
  n = A.shape[0]
  if A.shape[1] != n:
    raise ValueError("A must be square")
  if B.shape[0] != n:
    raise ValueError("B must have the same number of states as A.")
  m = B.shape[1]

  num_poles = len(poles)
  if num_poles > n:
    raise ValueError("Trying to place more poles than states.")

  out = slycot.sb01bd(n=n,
                      m=m,
                      np=num_poles,
                      alpha=alpha,
                      A=A,
                      B=B,
                      w=numpy.array(poles),
                      dico='D')

  A_z = numpy.matrix(out[0])
  num_too_small_eigenvalues = out[2]
  num_assigned_eigenvalues = out[3]
  num_uncontrollable_eigenvalues = out[4]
  K = numpy.matrix(-out[5])
  Z = numpy.matrix(out[6])

  if num_too_small_eigenvalues != 0:
    raise PolePlacementError("Number of eigenvalues that are too small "
                             "and are therefore unmodified is %d." %
                             num_too_small_eigenvalues)
  if num_assigned_eigenvalues != num_poles:
    raise PolePlacementError("Did not place all the eigenvalues that were "
                             "requested. Only placed %d eigenvalues." %
                             num_assigned_eigenvalues)
  if num_uncontrollable_eigenvalues != 0:
    raise PolePlacementError("Found %d uncontrollable eigenvlaues." %
                             num_uncontrollable_eigenvalues)

  return K