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								import numpy as np
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								from numbers import Number
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								from common.numpy_fast import clip, interp
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								class PIDController():
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								  def __init__(self, k_p, k_i, k_f=0., k_d=0., pos_limit=1e308, neg_limit=-1e308, rate=100):
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								    self._k_p = k_p
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								    self._k_i = k_i
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								    self._k_d = k_d
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								    self.k_f = k_f   # feedforward gain
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								    if isinstance(self._k_p, Number):
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								      self._k_p = [[0], [self._k_p]]
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								    if isinstance(self._k_i, Number):
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								      self._k_i = [[0], [self._k_i]]
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								    if isinstance(self._k_d, Number):
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								      self._k_d = [[0], [self._k_d]]
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								    self.pos_limit = pos_limit
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								    self.neg_limit = neg_limit
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								    self.i_unwind_rate = 0.3 / rate
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								    self.i_rate = 1.0 / rate
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								    self.speed = 0.0
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								    self.reset()
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								  @property
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								  def k_p(self):
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								    return interp(self.speed, self._k_p[0], self._k_p[1])
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								  @property
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								  def k_i(self):
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								    return interp(self.speed, self._k_i[0], self._k_i[1])
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								  @property
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								  def k_d(self):
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								    return interp(self.speed, self._k_d[0], self._k_d[1])
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								  @property
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								  def error_integral(self):
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								    return self.i/self.k_i
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								  def reset(self):
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								    self.p = 0.0
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								    self.i = 0.0
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								    self.d = 0.0
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								    self.f = 0.0
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								    self.control = 0
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								  def update(self, error, error_rate=0.0, speed=0.0, override=False, feedforward=0., freeze_integrator=False):
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								    self.speed = speed
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								    self.p = float(error) * self.k_p
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								    self.f = feedforward * self.k_f
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								    self.d = error_rate * self.k_d
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								    if override:
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								      self.i -= self.i_unwind_rate * float(np.sign(self.i))
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								    else:
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								      i = self.i + error * self.k_i * self.i_rate
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								      control = self.p + i + self.d + self.f
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								      # Update when changing i will move the control away from the limits
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								      # or when i will move towards the sign of the error
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								      if ((error >= 0 and (control <= self.pos_limit or i < 0.0)) or
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								          (error <= 0 and (control >= self.neg_limit or i > 0.0))) and \
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								         not freeze_integrator:
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								        self.i = i
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								    control = self.p + self.i + self.d + self.f
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								    self.control = clip(control, self.neg_limit, self.pos_limit)
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								    return self.control
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