text: import math
  import numpy as np
  
  from common.numpy_fast import clip
  from common.realtime import DT_CTRL
  from cereal import log
  from selfdrive.controls.lib.drive_helpers import get_steer_max
  
  
  class LatControlLQR():
    def __init__(self, CP):
      self.scale = CP.lateralTuning.lqr.scale
      self.ki = CP.lateralTuning.lqr.ki
  
      self.A = np.array(CP.lateralTuning.lqr.a).reshape((2, 2))
      self.B = np.array(CP.lateralTuning.lqr.b).reshape((2, 1))
      self.C = np.array(CP.lateralTuning.lqr.c).reshape((1, 2))
      self.K = np.array(CP.lateralTuning.lqr.k).reshape((1, 2))
      self.L = np.array(CP.lateralTuning.lqr.l).reshape((2, 1))
      self.dc_gain = CP.lateralTuning.lqr.dcGain
  
      self.x_hat = np.array([[0], [0]])
      self.i_unwind_rate = 0.3 * DT_CTRL
      self.i_rate = 1.0 * DT_CTRL
  
      self.sat_count_rate = 1.0 * DT_CTRL
      self.sat_limit = CP.steerLimitTimer
  
      self.reset()
  
    def reset(self):
      self.i_lqr = 0.0
      self.sat_count = 0.0
  
    def _check_saturation(self, control, check_saturation, limit):
      saturated = abs(control) == limit
  
      if saturated and check_saturation:
        self.sat_count += self.sat_count_rate
      else:
        self.sat_count -= self.sat_count_rate
  
      self.sat_count = clip(self.sat_count, 0.0, 1.0)
  
      return self.sat_count > self.sat_limit
  
    def update(self, active, CS, CP, VM, params, last_actuators, desired_curvature, desired_curvature_rate):
      lqr_log = log.ControlsState.LateralLQRState.new_message()
  
      steers_max = get_steer_max(CP, CS.vEgo)
      torque_scale = (0.45 + CS.vEgo / 60.0)**2  # Scale actuator model with speed
  
      # Subtract offset. Zero angle should correspond to zero torque
      steering_angle_no_offset = CS.steeringAngleDeg - params.angleOffsetAverageDeg
  
      desired_angle = math.degrees(VM.get_steer_from_curvature(-desired_curvature, CS.vEgo, params.roll))
  
      instant_offset = params.angleOffsetDeg - params.angleOffsetAverageDeg
      desired_angle += instant_offset  # Only add offset that originates from vehicle model errors
      lqr_log.steeringAngleDesiredDeg = desired_angle
  
      # Update Kalman filter
      angle_steers_k = float(self.C.dot(self.x_hat))
      e = steering_angle_no_offset - angle_steers_k
      self.x_hat = self.A.dot(self.x_hat) + self.B.dot(CS.steeringTorqueEps / torque_scale) + self.L.dot(e)
  
      if CS.vEgo < 0.3 or not active:
        lqr_log.active = False
        lqr_output = 0.
        output_steer = 0.
        self.reset()
      else:
        lqr_log.active = True
  
        # LQR
        u_lqr = float(desired_angle / self.dc_gain - self.K.dot(self.x_hat))
        lqr_output = torque_scale * u_lqr / self.scale
  
        # Integrator
        if CS.steeringPressed:
          self.i_lqr -= self.i_unwind_rate * float(np.sign(self.i_lqr))
        else:
          error = desired_angle - angle_steers_k
          i = self.i_lqr + self.ki * self.i_rate * error
          control = lqr_output + i
  
          if (error >= 0 and (control <= steers_max or i < 0.0)) or \
             (error <= 0 and (control >= -steers_max or i > 0.0)):
            self.i_lqr = i
  
        output_steer = lqr_output + self.i_lqr
        output_steer = clip(output_steer, -steers_max, steers_max)
  
      check_saturation = (CS.vEgo > 10) and not CS.steeringRateLimited and not CS.steeringPressed
      saturated = self._check_saturation(output_steer, check_saturation, steers_max)
  
      lqr_log.steeringAngleDeg = angle_steers_k
      lqr_log.i = self.i_lqr
      lqr_log.output = output_steer
      lqr_log.lqrOutput = lqr_output
      lqr_log.saturated = saturated
      return output_steer, desired_angle, lqr_log
  