text: import time
  
  ###############################################################
  
  ######################
  ### PID CONTROLLER ###
  ######################
  
  class PID_ctrl:
      """PID Controller"""
  
      def __init__(self, P=0.2, I=0.0, D=0.0, current_time=None):
  
          self.Kp = P
          self.Ki = I
          self.Kd = D
  
          self.sample_time = 0.00
          self.current_time = current_time if current_time is not None else time.time()
          self.last_time = self.current_time
  
          self.clear()
  
      def clear(self):
          """Clears PID computations and coefficients"""
          self.SetPoint = 0.0
  
          self.PTerm = 0.0
          self.ITerm = 0.0
          self.DTerm = 0.0
          self.last_error = 0.0
  
          # Windup Guard
          self.int_error = 0.0
          self.windup_guard = 20.0
  
          self.output = 0.0
  
      def update(self, feedback_value, current_time=None):
          """Calculates PID value for given reference feedback
          .. math::
              u(t) = K_p e(t) + K_i \int_{0}^{t} e(t)dt + K_d {de}/{dt}
          .. figure:: images/pid_1.png
             :align:   center
             Test PID with Kp=1.2, Ki=1, Kd=0.001 (test_pid.py)
          """
          error = self.SetPoint - feedback_value
  
          self.current_time = current_time if current_time is not None else time.time()
          delta_time = self.current_time - self.last_time
          delta_error = error - self.last_error
  
          if (delta_time >= self.sample_time):
              self.PTerm = self.Kp * error
              self.ITerm += error * delta_time
  
              if (self.ITerm < -self.windup_guard):
                  self.ITerm = -self.windup_guard
              elif (self.ITerm > self.windup_guard):
                  self.ITerm = self.windup_guard
  
              self.DTerm = 0.0
              if delta_time > 0:
                  self.DTerm = delta_error / delta_time
  
              # Remember last time and last error for next calculation
              self.last_time = self.current_time
              self.last_error = error
  
              self.output = self.PTerm + (self.Ki * self.ITerm) + (self.Kd * self.DTerm)
  
      def setKp(self, proportional_gain):
          """Determines how aggressively the PID reacts to the current error with setting Proportional Gain"""
          self.Kp = proportional_gain
  
      def setKi(self, integral_gain):
          """Determines how aggressively the PID reacts to the current error with setting Integral Gain"""
          self.Ki = integral_gain
  
      def setKd(self, derivative_gain):
          """Determines how aggressively the PID reacts to the current error with setting Derivative Gain"""
          self.Kd = derivative_gain
  
      def setWindup(self, windup):
          """Integral windup, also known as integrator windup or reset windup,
          refers to the situation in a PID feedback controller where
          a large change in setpoint occurs (say a positive change)
          and the integral terms accumulates a significant error
          during the rise (windup), thus overshooting and continuing
          to increase as this accumulated error is unwound
          (offset by errors in the other direction).
          The specific problem is the excess overshooting.
          """
          self.windup_guard = windup
  
      def setSampleTime(self, sample_time):
          """PID that should be updated at a regular interval.
          Based on a pre-determined sampe time, the PID decides if it should compute or return immediately.
          """
          self.sample_time = sample_time
  
  ###############################################################
  