<filename>neclib/controllers/antenna_pid.py
r"""PID controller for telescope main dish.

Optimum control parameter is calculated using a simple function consists of
Proportional, Integral and Derivative terms:

.. math::

    u(t) = K_\mathrm{p} \, e(t)
    + K_\mathrm{i} \int e(\tau) \, \mathrm{d}\tau
    + K_\mathrm{d} \frac{ \mathrm{d}e(t) }{ \mathrm{d}t }

where :math:`K_\mathrm{p}, K_\mathrm{i}` and :math:`K_\mathrm{d}` are non-negative
constants, :math:`u(t)` is the controller's objective parameter, and :math:`e(t)` is the
error between desired and actual values of explanatory parameter.

.. note::

    This script will be executed in high frequency with no vectorization, and there are
    many arrays updated frequently. These mean that the use of Numpy may not be the best
    choice to speed up the calculation. Measure the execution time first, then
    implement.

"""

__all__ = ["PIDController"]

import time
from typing import ClassVar, Dict, Tuple, Union

import astropy.units as u
import numpy as np

from .. import utils
from ..typing import AngleUnit, Literal
from ..utils import ParameterList


# Indices for parameter lists.
Last = -2
Now = -1


# Default values for PIDController.
DefaultK_p = 1.0
DefaultK_i = 0.5
DefaultK_d = 0.3
DefaultMaxSpeed = 2 << u.deg / u.s
DefaultMaxAcceleration = 2 << u.deg / u.s ** 2
DefaultErrorIntegCount = 50
DefaultThreshold = {
    "cmd_coord_change": 100 << u.arcsec,
    "accel_limit_off": 20 << u.arcsec,
    "target_accel_ignore": 2 << u.deg / u.s ** 2,
}
ThresholdKeys = Literal["cmd_coord_change", "accel_limit_off", "target_accel_ignore"]


class PIDController:
    """PID controller for telescope antenna.

    PID controller, a classical but sophisticated controller for system which has some
    delay on response to some input. This controller handles only 1 device, so use 2
    instances for Az-El control of telescope antenna.

    Parameters
    ----------
    pid_param
        Coefficients for PID formulation, list of [K_p, K_i, K_d].
    max_speed
        Maximum speed for telescope motion.
    max_acceleration
        Maximum acceleration for telescope motion.
    error_integ_count
        Number of error data to be stored for integral term calculation.
    threshold
        Thresholds for conditional executions. Interpreted keys are:

        - ``cmd_coord_change`` (angle)
            If separation between new command coordinate and last one is larger than
            this value, this controller assumes the target coordinate has been changed
            and resets the error integration.
        - ``accel_limit_off`` (angle)
            If separation between encoder reading and command coordinate is smaller than
            this value, this controller stops applying acceleration limit for quick
            convergence of drive.
        - ``target_accel_ignore`` (angular acceleration)
            If acceleration of target coordinate exceeds this value, the
            ``target_speed`` term is ignored as such commands most likely caused by
            software bug or network congestion.

    Attributes
    ----------

    k_p: float
        Proportional term coefficient.
    k_i: float
        Integral term coefficient.
    k_d: float
        Derivative term coefficient.
    max_speed: float
        Upper limit of drive speed in [``ANGLE_UNIT`` / s].
    max_acceleration: float
        Upper limit of drive acceleration in [``ANGLE_UNIT`` / s^2].
    error_integ_count: int
        Number of data stored for error integration.
    threshold: Dict[str, u.Quantity]
        Thresholds for conditional controls.
    cmd_speed: ParameterList[float]
        List of last 2 PID calculation results in unit [``ANGLE_UNIT`` / s].
    time: ParameterList[float]
        List of last ``error_integ_count`` UNIX timestamps the calculations are done.
    cmd_coord: ParameterList[float]
        List of last 2 command coordinates in [``ANGLE_UNIT``].
    enc_coord: ParameterList[float]
        List of last 2 encoder readings in [``ANGLE_UNIT``].
    error: ParameterList[float]
        List of last ``error_integ_count`` deviation values between ``cmd_coord`` and
        ``enc_coord``.
    target_speed: ParameterList[float]
        List of last 2 rate of change of command coordinates in [``ANGLE_UNIT`` / s].

    Notes
    -----
    This controller adds constant term to the general PID formulation. This is an
    attempt to follow constant motions such as raster scanning and sidereal motion
    tracking. ::

        speed = target_speed
            + (k_p * error)
            + (k_i * error_integral)
            + (k_d * error_derivative)

    This class keeps last 50 error values (by default) for integral term. This causes
    optimal PID parameters to change according to PID calculation frequency, as the time
    interval of the integration depends on the frequency.

    .. note::

        All methods assume the argument is given in ``ANGLE_UNIT``, and return the
        results in that unit. If you need to change it, substitute ``ANGLE_UNIT`` before
        instantiating this class.

    Examples
    --------
    >>> neclib.controllers.PIDController.ANGLE_UNIT
    deg
    >>> controller = neclib.controllers.PIDController(
    ...     pid_param=[1.5, 0, 0],
    ...     max_speed="1000 arcsec/s",
    ...     max_acceleration="1.6 deg/s",
    ... )
    >>> target_coordinate, encoder_reading = 30, 10  # deg
    >>> controller.get_speed(target_coordinate, encoder_reading)
    1.430511474609375e-05  # deg/s
    >>> controller.get_speed(target_coordinate, encoder_reading)
    0.20356178283691406  # deg/s

    """

    ANGLE_UNIT: ClassVar[AngleUnit] = "deg"
    """Unit in which all public functions accept as its argument and return."""

    def __init__(
        self,
        *,
        pid_param: Tuple[float, float, float] = [DefaultK_p, DefaultK_i, DefaultK_d],
        max_speed: Union[str, u.Quantity] = DefaultMaxSpeed,
        max_acceleration: Union[str, u.Quantity] = DefaultMaxAcceleration,
        error_integ_count: int = DefaultErrorIntegCount,
        threshold: Dict[ThresholdKeys, Union[str, u.Quantity]] = DefaultThreshold,
    ) -> None:
        self.k_p, self.k_i, self.k_d = pid_param
        self.max_speed = utils.parse_quantity(max_speed, unit=self.ANGLE_UNIT).value
        self.max_acceleration = utils.parse_quantity(
            max_acceleration, unit=self.ANGLE_UNIT
        ).value
        self.error_integ_count = error_integ_count
        _threshold = DefaultThreshold.copy()
        _threshold.update(threshold)
        self.threshold = {
            k: utils.parse_quantity(v, unit=self.ANGLE_UNIT).value
            for k, v in _threshold.items()
        }

        # Initialize parameter buffers.
        self._initialize()

    @property
    def dt(self) -> float:
        """Time interval of last 2 PID calculations."""
        return self.time[Now] - self.time[Last]

    @property
    def error_integral(self) -> float:
        """Integral of error."""
        _time, _error = np.array(self.time), np.array(self.error)
        dt = _time[1:] - _time[:-1]
        error_interpolated = (_error[1:] + _error[:-1]) / 2
        return np.nansum(error_interpolated * dt)

    @property
    def error_derivative(self) -> float:
        """Derivative of error."""
        return (self.error[Now] - self.error[Last]) / self.dt

    def _set_initial_parameters(self, cmd_coord: float, enc_coord: float) -> None:
        """Initialize parameters, except necessity for continuous control."""
        self._initialize()

        if np.isnan(self.cmd_speed[Now]):
            self.cmd_speed.push(0)
        self.time.push(time.time())
        self.cmd_coord.push(cmd_coord)
        self.enc_coord.push(enc_coord)
        self.error.push(cmd_coord - enc_coord)
        self.target_speed.push(0)

    def _initialize(self) -> None:
        """Define control loop parameters."""
        if not hasattr(self, "cmd_speed"):
            self.cmd_speed = ParameterList.new(2)
        self.time = ParameterList.new(2 * int(self.error_integ_count / 2))
        self.cmd_coord = ParameterList.new(2)
        self.enc_coord = ParameterList.new(2)
        self.error = ParameterList.new(2 * int(self.error_integ_count / 2))
        self.target_speed = ParameterList.new(2)

    def get_speed(
        self,
        cmd_coord: float,
        enc_coord: float,
        stop: bool = False,
    ) -> float:
        """Modulated drive speed.

        Parameters
        ----------
        cmd_coord
            Instructed Az/El coordinate.
        enc_coord
            Az/El encoder reading.
        stop
            If ``True``, the telescope won't move regardless of the inputs.

        """
        delta_cmd_coord = cmd_coord - self.cmd_coord[Now]
        if np.isnan(self.time[Now]) or (
            abs(delta_cmd_coord) > self.threshold["cmd_coord_change"]
        ):
            self._set_initial_parameters(cmd_coord, enc_coord)
            # Set default values on initial run or on detection of sudden jump of error,
            # which may indicate a change of command coordinate.
            # This will give too small `self.dt` later, but that won't propose any
            # problem, since `current_speed` goes to 0, and too large target_speed will
            # be ignored in `_calc_pid`.

        current_speed = self.cmd_speed[Now]
        # Encoder readings cannot be used, due to the lack of stability.

        self.time.push(time.time())
        self.cmd_coord.push(cmd_coord)
        self.enc_coord.push(enc_coord)
        self.error.push(cmd_coord - enc_coord)
        self.target_speed.push((cmd_coord - self.cmd_coord[Now]) / self.dt)

        # Calculate and validate drive speed.
        speed = self._calc_pid()
        if abs(self.error[Now]) > self.threshold["accel_limit_off"]:
            # When error is small, smooth control delays the convergence of drive.
            # When error is large, smooth control can avoid overshooting.
            max_diff = self.max_acceleration * self.dt
            # 0.2 clipping is to avoid large acceleration caused by large dt.
            speed = utils.clip(
                speed, current_speed - max_diff, current_speed + max_diff
            )  # Limit acceleration.
        speed = utils.clip(speed, absmax=self.max_speed)  # Limit speed.

        if stop:
            self.cmd_speed.push(0)
        else:
            self.cmd_speed.push(speed)

        return self.cmd_speed[Now]

    def _calc_pid(self) -> float:
        # Speed of the move of commanded coordinate. This includes sidereal motion, scan
        # speed, and other non-static component of commanded value.
        target_acceleration = (
            self.target_speed[Now] - self.target_speed[Last]
        ) / self.dt
        if abs(target_acceleration) > self.threshold["target_accel_ignore"]:
            self.target_speed[Now] = 0

        return (
            self.target_speed[Now]
            + self.k_p * self.error[Now]
            + self.k_i * self.error_integral
            + self.k_d * self.error_derivative
        )

<filename>neclib/controllers/antenna_pid.py
r"""PID controller for telescope main dish.

Optimum control parameter is calculated using a simple function consists of
Proportional, Integral and Derivative terms:

.. math::

    u(t) = K_\mathrm{p} \, e(t)
    + K_\mathrm{i} \int e(\tau) \, \mathrm{d}\tau
    + K_\mathrm{d} \frac{ \mathrm{d}e(t) }{ \mathrm{d}t }

where :math:`K_\mathrm{p}, K_\mathrm{i}` and :math:`K_\mathrm{d}` are non-negative
constants, :math:`u(t)` is the controller's objective parameter, and :math:`e(t)` is the
error between desired and actual values of explanatory parameter.

.. note::

    This script will be executed in high frequency with no vectorization, and there are
    many arrays updated frequently. These mean that the use of Numpy may not be the best
    choice to speed up the calculation. Measure the execution time first, then
    implement.

"""

__all__ = ["PIDController"]

import time
from typing import ClassVar, Dict, Tuple, Union

import astropy.units as u
import numpy as np

from .. import utils
from ..typing import AngleUnit, Literal
from ..utils import ParameterList


# Indices for parameter lists.
Last = -2
Now = -1


# Default values for PIDController.
DefaultK_p = 1.0
DefaultK_i = 0.5
DefaultK_d = 0.3
DefaultMaxSpeed = 2 << u.deg / u.s
DefaultMaxAcceleration = 2 << u.deg / u.s ** 2
DefaultErrorIntegCount = 50
DefaultThreshold = {
    "cmd_coord_change": 100 << u.arcsec,
    "accel_limit_off": 20 << u.arcsec,
    "target_accel_ignore": 2 << u.deg / u.s ** 2,
}
ThresholdKeys = Literal["cmd_coord_change", "accel_limit_off", "target_accel_ignore"]


class PIDController:
    """PID controller for telescope antenna.

    PID controller, a classical but sophisticated controller for system which has some
    delay on response to some input. This controller handles only 1 device, so use 2
    instances for Az-El control of telescope antenna.

    Parameters
    ----------
    pid_param
        Coefficients for PID formulation, list of [K_p, K_i, K_d].
    max_speed
        Maximum speed for telescope motion.
    max_acceleration
        Maximum acceleration for telescope motion.
    error_integ_count
        Number of error data to be stored for integral term calculation.
    threshold
        Thresholds for conditional executions. Interpreted keys are:

        - ``cmd_coord_change`` (angle)
            If separation between new command coordinate and last one is larger than
            this value, this controller assumes the target coordinate has been changed
            and resets the error integration.
        - ``accel_limit_off`` (angle)
            If separation between encoder reading and command coordinate is smaller than
            this value, this controller stops applying acceleration limit for quick
            convergence of drive.
        - ``target_accel_ignore`` (angular acceleration)
            If acceleration of target coordinate exceeds this value, the
            ``target_speed`` term is ignored as such commands most likely caused by
            software bug or network congestion.

    Attributes
    ----------

    k_p: float
        Proportional term coefficient.
    k_i: float
        Integral term coefficient.
    k_d: float
        Derivative term coefficient.
    max_speed: float
        Upper limit of drive speed in [``ANGLE_UNIT`` / s].
    max_acceleration: float
        Upper limit of drive acceleration in [``ANGLE_UNIT`` / s^2].
    error_integ_count: int
        Number of data stored for error integration.
    threshold: Dict[str, u.Quantity]
        Thresholds for conditional controls.
    cmd_speed: ParameterList[float]
        List of last 2 PID calculation results in unit [``ANGLE_UNIT`` / s].
    time: ParameterList[float]
        List of last ``error_integ_count`` UNIX timestamps the calculations are done.
    cmd_coord: ParameterList[float]
        List of last 2 command coordinates in [``ANGLE_UNIT``].
    enc_coord: ParameterList[float]
        List of last 2 encoder readings in [``ANGLE_UNIT``].
    error: ParameterList[float]
        List of last ``error_integ_count`` deviation values between ``cmd_coord`` and
        ``enc_coord``.
    target_speed: ParameterList[float]
        List of last 2 rate of change of command coordinates in [``ANGLE_UNIT`` / s].

    Notes
    -----
    This controller adds constant term to the general PID formulation. This is an
    attempt to follow constant motions such as raster scanning and sidereal motion
    tracking. ::

        speed = target_speed
            + (k_p * error)
            + (k_i * error_integral)
            + (k_d * error_derivative)

    This class keeps last 50 error values (by default) for integral term. This causes
    optimal PID parameters to change according to PID calculation frequency, as the time
    interval of the integration depends on the frequency.

    .. note::

        All methods assume the argument is given in ``ANGLE_UNIT``, and return the
        results in that unit. If you need to change it, substitute ``ANGLE_UNIT`` before
        instantiating this class.

    Examples
    --------
    >>> neclib.controllers.PIDController.ANGLE_UNIT
    deg
    >>> controller = neclib.controllers.PIDController(
    ...     pid_param=[1.5, 0, 0],
    ...     max_speed="1000 arcsec/s",
    ...     max_acceleration="1.6 deg/s",
    ... )
    >>> target_coordinate, encoder_reading = 30, 10  # deg
    >>> controller.get_speed(target_coordinate, encoder_reading)
    1.430511474609375e-05  # deg/s
    >>> controller.get_speed(target_coordinate, encoder_reading)
    0.20356178283691406  # deg/s

    """

    ANGLE_UNIT: ClassVar[AngleUnit] = "deg"
    """Unit in which all public functions accept as its argument and return."""

    def __init__(
        self,
        *,
        pid_param: Tuple[float, float, float] = [DefaultK_p, DefaultK_i, DefaultK_d],
        max_speed: Union[str, u.Quantity] = DefaultMaxSpeed,
        max_acceleration: Union[str, u.Quantity] = DefaultMaxAcceleration,
        error_integ_count: int = DefaultErrorIntegCount,
        threshold: Dict[ThresholdKeys, Union[str, u.Quantity]] = DefaultThreshold,
    ) -> None:
        self.k_p, self.k_i, self.k_d = pid_param
        self.max_speed = utils.parse_quantity(max_speed, unit=self.ANGLE_UNIT).value
        self.max_acceleration = utils.parse_quantity(
            max_acceleration, unit=self.ANGLE_UNIT
        ).value
        self.error_integ_count = error_integ_count
        _threshold = DefaultThreshold.copy()
        _threshold.update(threshold)
        self.threshold = {
            k: utils.parse_quantity(v, unit=self.ANGLE_UNIT).value
            for k, v in _threshold.items()
        }

        # Initialize parameter buffers.
        self._initialize()

    @property
    def dt(self) -> float:
        """Time interval of last 2 PID calculations."""
        return self.time[Now] - self.time[Last]

    @property
    def error_integral(self) -> float:
        """Integral of error."""
        _time, _error = np.array(self.time), np.array(self.error)
        dt = _time[1:] - _time[:-1]
        error_interpolated = (_error[1:] + _error[:-1]) / 2
        return np.nansum(error_interpolated * dt)

    @property
    def error_derivative(self) -> float:
        """Derivative of error."""
        return (self.error[Now] - self.error[Last]) / self.dt

    def _set_initial_parameters(self, cmd_coord: float, enc_coord: float) -> None:
        """Initialize parameters, except necessity for continuous control."""
        self._initialize()

        if np.isnan(self.cmd_speed[Now]):
            self.cmd_speed.push(0)
        self.time.push(time.time())
        self.cmd_coord.push(cmd_coord)
        self.enc_coord.push(enc_coord)
        self.error.push(cmd_coord - enc_coord)
        self.target_speed.push(0)

    def _initialize(self) -> None:
        """Define control loop parameters."""
        if not hasattr(self, "cmd_speed"):
            self.cmd_speed = ParameterList.new(2)
        self.time = ParameterList.new(2 * int(self.error_integ_count / 2))
        self.cmd_coord = ParameterList.new(2)
        self.enc_coord = ParameterList.new(2)
        self.error = ParameterList.new(2 * int(self.error_integ_count / 2))
        self.target_speed = ParameterList.new(2)

    def get_speed(
        self,
        cmd_coord: float,
        enc_coord: float,
        stop: bool = False,
    ) -> float:
        """Modulated drive speed.

        Parameters
        ----------
        cmd_coord
            Instructed Az/El coordinate.
        enc_coord
            Az/El encoder reading.
        stop
            If ``True``, the telescope won't move regardless of the inputs.

        """
        delta_cmd_coord = cmd_coord - self.cmd_coord[Now]
        if np.isnan(self.time[Now]) or (
            abs(delta_cmd_coord) > self.threshold["cmd_coord_change"]
        ):
            self._set_initial_parameters(cmd_coord, enc_coord)
            # Set default values on initial run or on detection of sudden jump of error,
            # which may indicate a change of command coordinate.
            # This will give too small `self.dt` later, but that won't propose any
            # problem, since `current_speed` goes to 0, and too large target_speed will
            # be ignored in `_calc_pid`.

        current_speed = self.cmd_speed[Now]
        # Encoder readings cannot be used, due to the lack of stability.

        self.time.push(time.time())
        self.cmd_coord.push(cmd_coord)
        self.enc_coord.push(enc_coord)
        self.error.push(cmd_coord - enc_coord)
        self.target_speed.push((cmd_coord - self.cmd_coord[Now]) / self.dt)

        # Calculate and validate drive speed.
        speed = self._calc_pid()
        if abs(self.error[Now]) > self.threshold["accel_limit_off"]:
            # When error is small, smooth control delays the convergence of drive.
            # When error is large, smooth control can avoid overshooting.
            max_diff = self.max_acceleration * self.dt
            # 0.2 clipping is to avoid large acceleration caused by large dt.
            speed = utils.clip(
                speed, current_speed - max_diff, current_speed + max_diff
            )  # Limit acceleration.
        speed = utils.clip(speed, absmax=self.max_speed)  # Limit speed.

        if stop:
            self.cmd_speed.push(0)
        else:
            self.cmd_speed.push(speed)

        return self.cmd_speed[Now]

    def _calc_pid(self) -> float:
        # Speed of the move of commanded coordinate. This includes sidereal motion, scan
        # speed, and other non-static component of commanded value.
        target_acceleration = (
            self.target_speed[Now] - self.target_speed[Last]
        ) / self.dt
        if abs(target_acceleration) > self.threshold["target_accel_ignore"]:
            self.target_speed[Now] = 0

        return (
            self.target_speed[Now]
            + self.k_p * self.error[Now]
            + self.k_i * self.error_integral
            + self.k_d * self.error_derivative
        )

PID controller for telescope main dish.  Optimum control parameter is calculated using a simple function consists of Proportional, Integral and Derivative terms:  .. math::      u(t) = K_\mathrm{p} \, e(t)     + K_\mathrm{i} \int e(\tau) \, \mathrm{d}\tau     + K_\mathrm{d} \frac{ \mathrm{d}e(t) }{ \mathrm{d}t }  where :math:`K_\mathrm{p}, K_\mathrm{i}` and :math:`K_\mathrm{d}` are non-negative constants, :math:`u(t)` is the controller's objective parameter, and :math:`e(t)` is the error between desired and actual values of explanatory parameter.  .. note::      This script will be executed in high frequency with no vectorization, and there are     many arrays updated frequently. These mean that the use of Numpy may not be the best     choice to speed up the calculation. Measure the execution time first, then     implement. # Indices for parameter lists. # Default values for PIDController. PID controller for telescope antenna.      PID controller, a classical but sophisticated controller for system which has some     delay on response to some input. This controller handles only 1 device, so use 2     instances for Az-El control of telescope antenna.      Parameters     ----------     pid_param         Coefficients for PID formulation, list of [K_p, K_i, K_d].     max_speed         Maximum speed for telescope motion.     max_acceleration         Maximum acceleration for telescope motion.     error_integ_count         Number of error data to be stored for integral term calculation.     threshold         Thresholds for conditional executions. Interpreted keys are:          - ``cmd_coord_change`` (angle)             If separation between new command coordinate and last one is larger than             this value, this controller assumes the target coordinate has been changed             and resets the error integration.         - ``accel_limit_off`` (angle)             If separation between encoder reading and command coordinate is smaller than             this value, this controller stops applying acceleration limit for quick             convergence of drive.         - ``target_accel_ignore`` (angular acceleration)             If acceleration of target coordinate exceeds this value, the             ``target_speed`` term is ignored as such commands most likely caused by             software bug or network congestion.      Attributes     ----------      k_p: float         Proportional term coefficient.     k_i: float         Integral term coefficient.     k_d: float         Derivative term coefficient.     max_speed: float         Upper limit of drive speed in [``ANGLE_UNIT`` / s].     max_acceleration: float         Upper limit of drive acceleration in [``ANGLE_UNIT`` / s^2].     error_integ_count: int         Number of data stored for error integration.     threshold: Dict[str, u.Quantity]         Thresholds for conditional controls.     cmd_speed: ParameterList[float]         List of last 2 PID calculation results in unit [``ANGLE_UNIT`` / s].     time: ParameterList[float]         List of last ``error_integ_count`` UNIX timestamps the calculations are done.     cmd_coord: ParameterList[float]         List of last 2 command coordinates in [``ANGLE_UNIT``].     enc_coord: ParameterList[float]         List of last 2 encoder readings in [``ANGLE_UNIT``].     error: ParameterList[float]         List of last ``error_integ_count`` deviation values between ``cmd_coord`` and         ``enc_coord``.     target_speed: ParameterList[float]         List of last 2 rate of change of command coordinates in [``ANGLE_UNIT`` / s].      Notes     -----     This controller adds constant term to the general PID formulation. This is an     attempt to follow constant motions such as raster scanning and sidereal motion     tracking. ::          speed = target_speed             + (k_p * error)             + (k_i * error_integral)             + (k_d * error_derivative)      This class keeps last 50 error values (by default) for integral term. This causes     optimal PID parameters to change according to PID calculation frequency, as the time     interval of the integration depends on the frequency.      .. note::          All methods assume the argument is given in ``ANGLE_UNIT``, and return the         results in that unit. If you need to change it, substitute ``ANGLE_UNIT`` before         instantiating this class.      Examples     --------     >>> neclib.controllers.PIDController.ANGLE_UNIT     deg     >>> controller = neclib.controllers.PIDController(     ...     pid_param=[1.5, 0, 0],     ...     max_speed="1000 arcsec/s",     ...     max_acceleration="1.6 deg/s",     ... )     >>> target_coordinate, encoder_reading = 30, 10  # deg     >>> controller.get_speed(target_coordinate, encoder_reading)     1.430511474609375e-05  # deg/s     >>> controller.get_speed(target_coordinate, encoder_reading)     0.20356178283691406  # deg/s Unit in which all public functions accept as its argument and return. # Initialize parameter buffers. Time interval of last 2 PID calculations. Integral of error. Derivative of error. Initialize parameters, except necessity for continuous control. Define control loop parameters. Modulated drive speed.          Parameters         ----------         cmd_coord             Instructed Az/El coordinate.         enc_coord             Az/El encoder reading.         stop             If ``True``, the telescope won't move regardless of the inputs. # Set default values on initial run or on detection of sudden jump of error, # which may indicate a change of command coordinate. # This will give too small `self.dt` later, but that won't propose any # problem, since `current_speed` goes to 0, and too large target_speed will # be ignored in `_calc_pid`. # Encoder readings cannot be used, due to the lack of stability. # Calculate and validate drive speed. # When error is small, smooth control delays the convergence of drive. # When error is large, smooth control can avoid overshooting. # 0.2 clipping is to avoid large acceleration caused by large dt. # Limit acceleration. # Limit speed. # Speed of the move of commanded coordinate. This includes sidereal motion, scan # speed, and other non-static component of commanded value.