import time def _clamp(value, limits): lower, upper = limits if value is None: return None elif (upper is not None) and (value > upper): return upper elif (lower is not None) and (value < lower): return lower return value try: # Get monotonic time to ensure that time deltas are always positive _current_time = time.ticks_ms except AttributeError: # time.monotonic() not available (using python < 3.3), fallback to time.time() _current_time = time.ticks_ms class PID(object): """A simple PID controller.""" def __init__( self, Kp=1.0, Ki=0.0, Kd=0.0, setpoint=0, sample_time=0.1, output_limits=(None, None), auto_mode=True, proportional_on_measurement=False, differetial_on_measurement=False, error_map=None, ): """ Initialize a new PID controller. :param Kp: The value for the proportional gain Kp :param Ki: The value for the integral gain Ki :param Kd: The value for the derivative gain Kd :param setpoint: The initial setpoint that the PID will try to achieve :param sample_time: The time in seconds which the controller should wait before generating a new output value. The PID works best when it is constantly called (eg. during a loop), but with a sample time set so that the time difference between each update is (close to) constant. If set to None, the PID will compute a new output value every time it is called. :param output_limits: The initial output limits to use, given as an iterable with 2 elements, for example: (lower, upper). The output will never go below the lower limit or above the upper limit. Either of the limits can also be set to None to have no limit in that direction. Setting output limits also avoids integral windup, since the integral term will never be allowed to grow outside of the limits. :param auto_mode: Whether the controller should be enabled (auto mode) or not (manual mode) :param proportional_on_measurement: Whether the proportional term should be calculated on the input directly rather than on the error (which is the traditional way). Using proportional-on-measurement avoids overshoot for some types of systems. :param differetial_on_measurement: Whether the differential term should be calculated on the input directly rather than on the error (which is the traditional way). :param error_map: Function to transform the error value in another constrained value. """ self.Kp, self.Ki, self.Kd = Kp, Ki, Kd self.setpoint = setpoint self.sample_time = sample_time self._min_output, self._max_output = None, None self._auto_mode = auto_mode self.proportional_on_measurement = proportional_on_measurement self.differetial_on_measurement = differetial_on_measurement self.error_map = error_map self._proportional = 0 self._integral = 0 self._derivative = 0 self._last_time = None self._last_output = None self._last_error = None self._last_input = None self.output_limits = output_limits self.reset() def __call__(self, input_, dt=None): """ Update the PID controller. Call the PID controller with *input_* and calculate and return a control output if sample_time seconds has passed since the last update. If no new output is calculated, return the previous output instead (or None if no value has been calculated yet). :param dt: If set, uses this value for timestep instead of real time. This can be used in simulations when simulation time is different from real time. """ if not self.auto_mode: return self._last_output now = _current_time()/1000 if dt is None: dt = now - self._last_time if (now - self._last_time) else 1e-16 elif dt <= 0: raise ValueError('dt has negative value {}, must be positive'.format(dt)) if self.sample_time is not None and dt < self.sample_time and self._last_output is not None: # Only update every sample_time seconds return self._last_output # Compute error terms error = self.setpoint - input_ d_input = input_ - (self._last_input if (self._last_input is not None) else input_) d_error = error - (self._last_error if (self._last_error is not None) else error) # Check if must map the error if self.error_map is not None: error = self.error_map(error) # Compute the proportional term if not self.proportional_on_measurement: # Regular proportional-on-error, simply set the proportional term self._proportional = self.Kp * error else: # Add the proportional error on measurement to error_sum self._proportional -= self.Kp * d_input # Compute integral and derivative terms self._integral += self.Ki * error * dt self._integral = _clamp(self._integral, self.output_limits) # Avoid integral windup if self.differetial_on_measurement: self._derivative = -self.Kd * d_input / dt else: self._derivative = self.Kd * d_error / dt # Compute final output output = self._proportional + self._integral + self._derivative output = _clamp(output, self.output_limits) # Keep track of state self._last_output = output self._last_input = input_ self._last_error = error self._last_time = now return output def __repr__(self): return ( '{self.__class__.__name__}(' 'Kp={self.Kp!r}, Ki={self.Ki!r}, Kd={self.Kd!r}, ' 'setpoint={self.setpoint!r}, sample_time={self.sample_time!r}, ' 'output_limits={self.output_limits!r}, auto_mode={self.auto_mode!r}, ' 'proportional_on_measurement={self.proportional_on_measurement!r}, ' 'differetial_on_measurement={self.differetial_on_measurement!r}, ' 'error_map={self.error_map!r}' ')' ).format(self=self) @property def components(self): """ The P-, I- and D-terms from the last computation as separate components as a tuple. Useful for visualizing what the controller is doing or when tuning hard-to-tune systems. """ return self._proportional, self._integral, self._derivative @property def tunings(self): """The tunings used by the controller as a tuple: (Kp, Ki, Kd).""" return self.Kp, self.Ki, self.Kd @tunings.setter def tunings(self, tunings): """Set the PID tunings.""" self.Kp, self.Ki, self.Kd = tunings @property def auto_mode(self): """Whether the controller is currently enabled (in auto mode) or not.""" return self._auto_mode @auto_mode.setter def auto_mode(self, enabled): """Enable or disable the PID controller.""" self.set_auto_mode(enabled) def set_auto_mode(self, enabled, last_output=None): """ Enable or disable the PID controller, optionally setting the last output value. This is useful if some system has been manually controlled and if the PID should take over. In that case, disable the PID by setting auto mode to False and later when the PID should be turned back on, pass the last output variable (the control variable) and it will be set as the starting I-term when the PID is set to auto mode. :param enabled: Whether auto mode should be enabled, True or False :param last_output: The last output, or the control variable, that the PID should start from when going from manual mode to auto mode. Has no effect if the PID is already in auto mode. """ if enabled and not self._auto_mode: # Switching from manual mode to auto, reset self.reset() self._integral = last_output if (last_output is not None) else 0 self._integral = _clamp(self._integral, self.output_limits) self._auto_mode = enabled @property def output_limits(self): """ The current output limits as a 2-tuple: (lower, upper). See also the *output_limits* parameter in :meth:`PID.__init__`. """ return self._min_output, self._max_output @output_limits.setter def output_limits(self, limits): """Set the output limits.""" if limits is None: self._min_output, self._max_output = None, None return min_output, max_output = limits if (None not in limits) and (max_output < min_output): raise ValueError('lower limit must be less than upper limit') self._min_output = min_output self._max_output = max_output self._integral = _clamp(self._integral, self.output_limits) self._last_output = _clamp(self._last_output, self.output_limits) def reset(self): """ Reset the PID controller internals. This sets each term to 0 as well as clearing the integral, the last output and the last input (derivative calculation). """ self._proportional = 0 self._integral = 0 self._derivative = 0 self._integral = _clamp(self._integral, self.output_limits) self._last_time = _current_time()/1000 self._last_output = None self._last_input = None