From 7eff69d68065cd6c92389e17d016c2de931f34e0 Mon Sep 17 00:00:00 2001 From: Danny Staple Date: Mon, 1 Aug 2022 09:52:56 +0100 Subject: [PATCH] Chapter 10 code --- ch-10/1-proportional-distance-control/code.py | 2 + ch-10/2-pi-distance-control/code.py | 44 ++ .../pio_encoder.py | 0 .../robot.py | 4 +- ch-10/3-damping-with-derivative/code.py | 35 + .../pid_controller.py | 20 + .../3-damping-with-derivative/pio_encoder.py | 77 +++ ch-10/3-damping-with-derivative/robot.py | 52 ++ ch-10/3-wall-follow/pid.py | 39 -- ch-10/3-wall-follow/robot_wifi.py | 25 - ch-10/3-wall-follow/wall_follow.py | 104 --- ch-10/4-wall-follow/code.py | 60 ++ ch-10/4-wall-follow/pid_controller.py | 20 + ch-10/4-wall-follow/pio_encoder.py | 77 +++ ch-10/4-wall-follow/robot.FCStd | Bin 0 -> 316619 bytes ch-10/4-wall-follow/robot.py | 52 ++ ch-10/_figure_generator/error_plot.png | Bin 100688 -> 0 bytes ch-10/_figure_generator/error_values.png | Bin 106561 -> 0 bytes .../idealised-pid-response.ipynb | 77 +++ .../noisy_derivatives_graph.ipynb | 237 +++++++ ch-10/_figure_generator/slopes_on_wave.png | Bin 0 -> 8062 bytes ch-10/_figure_generator/slopes_on_wave.svg | 631 ++++++++++++++++++ .../tangent_on_sinewave.ipynb | 131 ++++ 23 files changed, 1517 insertions(+), 170 deletions(-) create mode 100644 ch-10/2-pi-distance-control/code.py rename ch-10/{3-wall-follow => 2-pi-distance-control}/pio_encoder.py (100%) rename ch-10/{3-wall-follow => 2-pi-distance-control}/robot.py (92%) create mode 100644 ch-10/3-damping-with-derivative/code.py create mode 100644 ch-10/3-damping-with-derivative/pid_controller.py create mode 100644 ch-10/3-damping-with-derivative/pio_encoder.py create mode 100755 ch-10/3-damping-with-derivative/robot.py delete mode 100644 ch-10/3-wall-follow/pid.py delete mode 100644 ch-10/3-wall-follow/robot_wifi.py delete mode 100644 ch-10/3-wall-follow/wall_follow.py create mode 100644 ch-10/4-wall-follow/code.py create mode 100644 ch-10/4-wall-follow/pid_controller.py create mode 100644 ch-10/4-wall-follow/pio_encoder.py create mode 100644 ch-10/4-wall-follow/robot.FCStd create mode 100755 ch-10/4-wall-follow/robot.py delete mode 100644 ch-10/_figure_generator/error_plot.png delete mode 100644 ch-10/_figure_generator/error_values.png create mode 100644 ch-10/_figure_generator/idealised-pid-response.ipynb create mode 100644 ch-10/_figure_generator/noisy_derivatives_graph.ipynb create mode 100644 ch-10/_figure_generator/slopes_on_wave.png create mode 100644 ch-10/_figure_generator/slopes_on_wave.svg create mode 100644 ch-10/_figure_generator/tangent_on_sinewave.ipynb diff --git a/ch-10/1-proportional-distance-control/code.py b/ch-10/1-proportional-distance-control/code.py index 5bef4b3..ba3bc85 100644 --- a/ch-10/1-proportional-distance-control/code.py +++ b/ch-10/1-proportional-distance-control/code.py @@ -25,6 +25,8 @@ while True: distance = robot.left_distance.distance error = distance_set_point - distance speed = distance_controller.calculate(error) + if abs(speed) < 0.2: + speed = 0 uart.write(f"{error},{speed}\n".encode()) print(f"{error},{speed}") robot.set_left(speed) diff --git a/ch-10/2-pi-distance-control/code.py b/ch-10/2-pi-distance-control/code.py new file mode 100644 index 0000000..d5ad54a --- /dev/null +++ b/ch-10/2-pi-distance-control/code.py @@ -0,0 +1,44 @@ +import time +import board +import busio +import robot + +uart = busio.UART(board.GP12, board.GP13, baudrate=9600) + +class PIController: + def __init__(self, kp, ki): + self.kp = kp + self.ki = ki + self.integral = 0 + + def calculate(self, error, dt): + self.integral += error * dt + return self.kp * error + self.ki * self.integral + + +## We'll set up a single distance sensor, and keep a set distance from an object +robot.left_distance.distance_mode = 1 +robot.left_distance.start_ranging() + +distance_set_point = 10 +distance_controller = PIController(-0.19, -0.005) + +prev_time = time.monotonic() +while True: + if robot.left_distance.data_ready: + distance = robot.left_distance.distance + error = distance_set_point - distance + + current_time = time.monotonic() + speed = distance_controller.calculate(error, current_time - prev_time) + prev_time = current_time + # Control the motors with the speed + if abs(speed) < 0.35: + speed = 0 + uart.write(f"{error},{speed}," + f"{distance_controller.integral}\n".encode()) + print(f"{error},{speed},{distance_controller.integral}") + robot.set_left(speed) + robot.set_right(speed) + robot.left_distance.clear_interrupt() + time.sleep(0.05) diff --git a/ch-10/3-wall-follow/pio_encoder.py b/ch-10/2-pi-distance-control/pio_encoder.py similarity index 100% rename from ch-10/3-wall-follow/pio_encoder.py rename to ch-10/2-pi-distance-control/pio_encoder.py diff --git a/ch-10/3-wall-follow/robot.py b/ch-10/2-pi-distance-control/robot.py similarity index 92% rename from ch-10/3-wall-follow/robot.py rename to ch-10/2-pi-distance-control/robot.py index a564a9b..2fc5e08 100755 --- a/ch-10/3-wall-follow/robot.py +++ b/ch-10/2-pi-distance-control/robot.py @@ -19,8 +19,8 @@ left_encoder = pio_encoder.QuadratureEncoder(board.GP26, board.GP27) i2c0 = busio.I2C(sda=board.GP0, scl=board.GP1) i2c1 = busio.I2C(sda=board.GP2, scl=board.GP3) -right_distance = adafruit_vl53l1x.VL53L1X(i2c0) -left_distance = adafruit_vl53l1x.VL53L1X(i2c1) +left_distance = adafruit_vl53l1x.VL53L1X(i2c0) +right_distance = adafruit_vl53l1x.VL53L1X(i2c1) def stop(): diff --git a/ch-10/3-damping-with-derivative/code.py b/ch-10/3-damping-with-derivative/code.py new file mode 100644 index 0000000..9056d7a --- /dev/null +++ b/ch-10/3-damping-with-derivative/code.py @@ -0,0 +1,35 @@ +import time +import board +import busio +import robot +from pid_controller import PIDController + +uart = busio.UART(board.GP12, board.GP13, baudrate=9600) + + +## We'll set up a single distance sensor, and keep a set distance from an object +robot.left_distance.distance_mode = 1 +robot.left_distance.start_ranging() + +distance_set_point = 10 +distance_controller = PIDController(-0.09, -0.02, -0.07) + +prev_time = time.monotonic() +while True: + if robot.left_distance.data_ready: + distance = robot.left_distance.distance + error = distance_set_point - distance + + current_time = time.monotonic() + speed = distance_controller.calculate(error, current_time - prev_time) + prev_time = current_time + # Control the motors with the speed + if abs(speed) < 0.35: + speed = 0 + uart.write(f"{error},{speed},{distance_controller.integral},{distance_controller.derivative}\n".encode()) + print(f"{error},{speed},{distance_controller.integral},{distance_controller.derivative}") + robot.set_left(speed) + robot.set_right(speed) + # reset the distance sensor + robot.left_distance.clear_interrupt() + time.sleep(0.05) diff --git a/ch-10/3-damping-with-derivative/pid_controller.py b/ch-10/3-damping-with-derivative/pid_controller.py new file mode 100644 index 0000000..1dfee94 --- /dev/null +++ b/ch-10/3-damping-with-derivative/pid_controller.py @@ -0,0 +1,20 @@ +class PIDController: + def __init__(self, kp, ki, kd, d_filter_gain=0.1): + self.kp = kp + self.ki = ki + self.kd = kd + self.d_filter_gain = d_filter_gain + + self.integral = 0 + self.error_prev = 0 + self.derivative = 0 + + def calculate(self, error, dt): + self.integral += error * dt + + # Add a low pass filter to the difference + difference = (error - self.error_prev) * self.d_filter_gain + self.error_prev += difference + self.derivative = difference / dt + + return self.kp * error + self.ki * self.integral + self.kd * self.derivative diff --git a/ch-10/3-damping-with-derivative/pio_encoder.py b/ch-10/3-damping-with-derivative/pio_encoder.py new file mode 100644 index 0000000..ffcc9f2 --- /dev/null +++ b/ch-10/3-damping-with-derivative/pio_encoder.py @@ -0,0 +1,77 @@ +import rp2pio +import adafruit_pioasm +import array + +program = """ +; use the osr for count +; input pins c1 c2 + + set y, 0 ; clear y + mov osr, y ; and clear osr +read: + ; x will be the old value + ; y the new values + mov x, y ; store old Y in x + in null, 32 ; Clear ISR - using y + in pins, 2 ; read two pins into y + mov y, isr + jmp x!=y, different ; Jump if its different + jmp read ; otherwise loop back to read + +different: + ; x has old value, y has new. + ; extract the upper bit of X. + in x, 31 ; get bit 31 - old p1 (remember which direction it came in) + in null, 31 ; keep only 1 bit + mov x, isr ; put this back in x + jmp !x, c1_old_zero + +c1_old_not_zero: + jmp pin, count_up + jmp count_down + +c1_old_zero: + jmp pin, count_down + ; fall through +count_up: + ; for a clockwise move - we'll add 1 by inverting + mov x, ~ osr ; store inverted OSR on x + jmp x--, fake ; use jump to take off 1 +fake: + mov x, ~ x ; invert back + jmp send +count_down: + ; for a clockwise move, just take one off + mov x, osr ; store osr in x + jmp x--, send ; dec and send +send: + ; send x. + mov isr, x ; send it + push noblock ; put ISR into input FIFO + mov osr, x ; put X back in OSR + jmp read ; loop back +""" + +assembled = adafruit_pioasm.assemble(program) + + +class QuadratureEncoder: + def __init__(self, first_pin, second_pin, reversed=False): + """Encoder with 2 pins. Must use sequential pins on the board""" + self.sm = rp2pio.StateMachine( + assembled, + frequency=0, + first_in_pin=first_pin, + jmp_pin=second_pin, + in_pin_count=2, + ) + self.reversed = reversed + self._buffer = array.array("i", [0]) + + def read(self): + while self.sm.in_waiting: + self.sm.readinto(self._buffer) + if self.reversed: + return -self._buffer[0] + else: + return self._buffer[0] diff --git a/ch-10/3-damping-with-derivative/robot.py b/ch-10/3-damping-with-derivative/robot.py new file mode 100755 index 0000000..2fc5e08 --- /dev/null +++ b/ch-10/3-damping-with-derivative/robot.py @@ -0,0 +1,52 @@ +import board +import pwmio +import pio_encoder +import busio +import adafruit_vl53l1x + + +motor_A1 = pwmio.PWMOut(board.GP17) +motor_A2 = pwmio.PWMOut(board.GP16) +motor_B1 = pwmio.PWMOut(board.GP18) +motor_B2 = pwmio.PWMOut(board.GP19) + +right_motor = motor_A1, motor_A2 +left_motor = motor_B1, motor_B2 + +right_encoder = pio_encoder.QuadratureEncoder(board.GP20, board.GP21, reversed=True) +left_encoder = pio_encoder.QuadratureEncoder(board.GP26, board.GP27) + +i2c0 = busio.I2C(sda=board.GP0, scl=board.GP1) +i2c1 = busio.I2C(sda=board.GP2, scl=board.GP3) + +left_distance = adafruit_vl53l1x.VL53L1X(i2c0) +right_distance = adafruit_vl53l1x.VL53L1X(i2c1) + + +def stop(): + motor_A1.duty_cycle = 0 + motor_A2.duty_cycle = 0 + motor_B1.duty_cycle = 0 + motor_B2.duty_cycle = 0 + + +def set_speed(motor, speed): + # Swap motor pins if we reverse the speed + if speed < 0: + direction = motor[1], motor[0] + speed = -speed + else: + direction = motor + speed = min(speed, 1) # limit to 1.0 + max_speed = 2 ** 16 - 1 + + direction[0].duty_cycle = int(max_speed * speed) + direction[1].duty_cycle = 0 + + +def set_left(speed): + set_speed(left_motor, speed) + + +def set_right(speed): + set_speed(right_motor, speed) diff --git a/ch-10/3-wall-follow/pid.py b/ch-10/3-wall-follow/pid.py deleted file mode 100644 index e1e7264..0000000 --- a/ch-10/3-wall-follow/pid.py +++ /dev/null @@ -1,39 +0,0 @@ -class PID: - def __init__(self, proportional_k, integral_k, differential_k, set_point): - self.proportional_k = proportional_k - self.integral_k = integral_k - self.differential_k = differential_k - self.set_point = set_point - - self.error_sum = 0 - self.last_value = 0 - self.min_output = -1 - self.max_output = 1 - - self.dead_zone = 0.3 - - def update(self, measurement, time_delta): - error_value = measurement - self.set_point - proportional = error_value * self.proportional_k - - # calculate integral - self.error_sum += error_value * time_delta - # clamp it - self.error_sum = min(self.max_output, self.error_sum) - self.error_sum = max(self.min_output, self.error_sum) - - integral = self.error_sum * self.integral_k - - differentiated_error = (error_value - self.last_value) / time_delta - differential = differentiated_error * self.differential_k - self.last_value = error_value - - output = proportional + integral + differential - # clamp output - if abs(output) < self.dead_zone: - output = 0 - else: - output = min(self.max_output, output) - output = max(self.min_output, output) - - return output diff --git a/ch-10/3-wall-follow/robot_wifi.py b/ch-10/3-wall-follow/robot_wifi.py deleted file mode 100644 index 7093914..0000000 --- a/ch-10/3-wall-follow/robot_wifi.py +++ /dev/null @@ -1,25 +0,0 @@ -import board -import busio -from digitalio import DigitalInOut -from adafruit_esp32spi import adafruit_esp32spi -from adafruit_esp32spi import adafruit_esp32spi_wifimanager - -try: - from secrets import secrets -except ImportError: - print("WiFi secrets are kept in secrets.py, please add them there!") - raise - - -def connect_to_wifi(): - esp32_cs = DigitalInOut(board.GP10) - esp32_ready = DigitalInOut(board.GP9) - esp32_reset = DigitalInOut(board.GP8) - - spi = busio.SPI(board.GP14, MOSI=board.GP11, MISO=board.GP12) - esp = adafruit_esp32spi.ESP_SPIcontrol(spi, esp32_cs, esp32_ready, esp32_reset) - esp.reset() - wifi = adafruit_esp32spi_wifimanager.ESPSPI_WiFiManager(esp, secrets) - wifi.connect() - - return wifi, esp diff --git a/ch-10/3-wall-follow/wall_follow.py b/ch-10/3-wall-follow/wall_follow.py deleted file mode 100644 index c8932f9..0000000 --- a/ch-10/3-wall-follow/wall_follow.py +++ /dev/null @@ -1,104 +0,0 @@ -import time -import json -import math - -from adafruit_esp32spi import adafruit_esp32spi_wsgiserver -from adafruit_wsgi.wsgi_app import WSGIApp - -import pid -import robot -import robot_wifi - - -class FollowWallApp: - def __init__(self) -> None: - self.speed = 0.6 - self.max_deflection = 0.4 - self.follow_pid = pid.PID(0.1, 0.5, 0, 15) - self.follow_pid.dead_zone = 0.6 - - self.wifi = None - self.server = None - - self.last_time = time.monotonic() - self.left_dist = 0 - self.pid_output = 0 - - def setup_robot(self): - robot.left_distance.distance_mode = 1 - - def setup_wifi(self, app): - print("Setting up wifi.") - self.wifi, esp = robot_wifi.connect_to_wifi() - self.server = adafruit_esp32spi_wsgiserver.WSGIServer(80, application=app) - adafruit_esp32spi_wsgiserver.set_interface(esp) - print("Starting server") - - self.server.start() - ip_int = ".".join(str(int(n)) for n in esp.ip_address) - print(f"IP Address is {ip_int}") - - def index(self, request): - return ( - 200, - [("Content-Type", "application/json")], - [ - json.dumps( - { - "last_value": self.follow_pid.last_value, - "pid_output": self.pid_output, - "time": self.last_time, - } - ) - ], - ) - - def movement_update(self): - # do we have data - if robot.left_distance.data_ready: - self.left_dist = robot.left_distance.distance - - # calculate time delta - new_time = time.monotonic() - time_delta = new_time - self.last_time - self.last_time = new_time - - # get turn from pid - self.pid_output = self.follow_pid.update(self.left_dist, time_delta) - deflection = self.pid_output * self.max_deflection - - # make movements - robot.set_left(self.speed - deflection) - robot.set_right(self.speed + deflection) - - # reset and loop - robot.left_distance.clear_interrupt() - - def main_loop(self): - robot.left_distance.start_ranging() - while True: - try: - self.movement_update() - self.server.update_poll() - except RuntimeError as e: - print(f"Server poll error: {type(e)}, {e}") - robot.stop() - print(f"Resetting ESP...") - self.wifi.reset() - print("Reset complete.") - - def start(self): - app = WSGIApp() - app.route("/")(self.index) - print("Starting") - try: - self.setup_robot() - self.setup_wifi(app) - self.main_loop() - finally: - robot.stop() - robot.left_distance.clear_interrupt() - robot.left_distance.stop_ranging() - - -FollowWallApp().start() diff --git a/ch-10/4-wall-follow/code.py b/ch-10/4-wall-follow/code.py new file mode 100644 index 0000000..d18ec4d --- /dev/null +++ b/ch-10/4-wall-follow/code.py @@ -0,0 +1,60 @@ +import time +import board +import busio +import robot +from pid_controller import PIDController + +uart = busio.UART(board.GP12, board.GP13, baudrate=9600) + + +robot.right_distance.distance_mode = 1 +robot.right_distance.start_ranging() + +speed = 0.7 +distance_set_point = 15 +distance_controller = PIDController(0.046, 0.0, 0) +print("Waiting for bytes on UART...") + +prev_time = time.monotonic() +motors_active = False +while True: + if robot.right_distance.data_ready: + distance = robot.right_distance.distance + error = distance_set_point - distance + + current_time = time.monotonic() + deflection = distance_controller.calculate(error, current_time - prev_time) + prev_time = current_time + uart.write(f"{error},{deflection}\n".encode()) # ,{distance_controller.derivative} + if motors_active: + robot.set_left(speed - deflection) + robot.set_right(speed + deflection) + # reset the distance sensor + robot.right_distance.clear_interrupt() + time.sleep(0.05) + if uart.in_waiting: + command = uart.readline().decode().strip() + if command.startswith("M"): + speed = float(command[1:]) + elif command == "O": + motors_active = not motors_active + robot.set_left(0) + robot.set_right(0) + distance_controller.integral = 0 + elif command.startswith("P"): + distance_controller.kp = float(command[1:]) + elif command.startswith("I"): + distance_controller.ki = float(command[1:]) + elif command.startswith("D"): + distance_controller.kd = float(command[1:]) + elif command.startswith("S"): + distance_set_point = float(command[1:]) + elif command.startswith("?"): + uart.write(f"P{distance_controller.kp:.3f}\n".encode()) + uart.write(f"I{distance_controller.ki:.3f}\n".encode()) + uart.write(f"D{distance_controller.kd:.3f}\n".encode()) + uart.write(f"S{distance_set_point:.3f}\n".encode()) + uart.write(f"M{speed:.1f}\n".encode()) + time.sleep(3) + elif command.startswith("R"): + distance_controller.integral = 0 diff --git a/ch-10/4-wall-follow/pid_controller.py b/ch-10/4-wall-follow/pid_controller.py new file mode 100644 index 0000000..1dfee94 --- /dev/null +++ b/ch-10/4-wall-follow/pid_controller.py @@ -0,0 +1,20 @@ +class PIDController: + def __init__(self, kp, ki, kd, d_filter_gain=0.1): + self.kp = kp + self.ki = ki + self.kd = kd + self.d_filter_gain = d_filter_gain + + self.integral = 0 + self.error_prev = 0 + self.derivative = 0 + + def calculate(self, error, dt): + self.integral += error * dt + + # Add a low pass filter to the difference + difference = (error - self.error_prev) * self.d_filter_gain + self.error_prev += difference + self.derivative = difference / dt + + return self.kp * error + self.ki * self.integral + self.kd * self.derivative diff --git a/ch-10/4-wall-follow/pio_encoder.py b/ch-10/4-wall-follow/pio_encoder.py new file mode 100644 index 0000000..ffcc9f2 --- /dev/null +++ b/ch-10/4-wall-follow/pio_encoder.py @@ -0,0 +1,77 @@ +import rp2pio +import adafruit_pioasm +import array + +program = """ +; use the osr for count +; input pins c1 c2 + + set y, 0 ; clear y + mov osr, y ; and clear osr +read: + ; x will be the old value + ; y the new values + mov x, y ; store old Y in x + in null, 32 ; Clear ISR - using y + in pins, 2 ; read two pins into y + mov y, isr + jmp x!=y, different ; Jump if its different + jmp read ; otherwise loop back to read + +different: + ; x has old value, y has new. + ; extract the upper bit of X. + in x, 31 ; get bit 31 - old p1 (remember which direction it came in) + in null, 31 ; keep only 1 bit + mov x, isr ; put this back in x + jmp !x, c1_old_zero + +c1_old_not_zero: + jmp pin, count_up + jmp count_down + +c1_old_zero: + jmp pin, count_down + ; fall through +count_up: + ; for a clockwise move - we'll add 1 by inverting + mov x, ~ osr ; store inverted OSR on x + jmp x--, fake ; use jump to take off 1 +fake: + mov x, ~ x ; invert back + jmp send +count_down: + ; for a clockwise move, just take one off + mov x, osr ; store osr in x + jmp x--, send ; dec and send +send: + ; send x. + mov isr, x ; send it + push noblock ; put ISR into input FIFO + mov osr, x ; put X back in OSR + jmp read ; loop back +""" + +assembled = adafruit_pioasm.assemble(program) + + +class QuadratureEncoder: + def __init__(self, first_pin, second_pin, reversed=False): + """Encoder with 2 pins. Must use sequential pins on the board""" + self.sm = rp2pio.StateMachine( + assembled, + frequency=0, + first_in_pin=first_pin, + jmp_pin=second_pin, + in_pin_count=2, + ) + self.reversed = reversed + self._buffer = array.array("i", [0]) + + def read(self): + while self.sm.in_waiting: + self.sm.readinto(self._buffer) + if self.reversed: + return -self._buffer[0] + else: + return self._buffer[0] diff --git a/ch-10/4-wall-follow/robot.FCStd b/ch-10/4-wall-follow/robot.FCStd new file mode 100644 index 0000000000000000000000000000000000000000..770b6b52fe3bbacf39dd2c06042f6c4877dc91e0 GIT binary patch literal 316619 zcmaI7V|*t;(=Hs_+!z~sW81d1v2AXwjcwci*tTukwodlGpYxpe)B9zrd+@ued#bLQ zs_v1O0tG_@0s?{pYIc89mL36fg*XNRdPzeBg8M!zY-{LjZEWL2=Vonn-mw<9)*Q#` z(Um3GMy5L6Wym_lO@MpwlCRy^hG$5x)>hWB?!A{oQYN`Ur643>v!p!%I<7Pse-0*b zO#%caF0WX+tzNr|0gM8M8rGkjs;B$DMSvJF^F*OBwRceN%QE@kizhNB!JSEerTcN_ z!Zi2p`_c9F*%a|5HuuTukt{s3aF9Ne?gsD@T&K?@sFvB3v4`B}zy(4{pAX@Jhnw*;YDl)f|@=BhW*yr_t>e@GCubUEGlJH6n 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"import numpy as np\n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# create a time linspace - up to 8 pi\n", + "t = np.linspace(0, 8 * np.pi, 1000)\n", + "# use this to make the idealised pid response graph, with a little overshoot and undershoot\n", + "error = np.sin(t) * 0.125\n", + "for n in range(1, 63, 2):\n", + " error = np.sin(t / n)+ error\n", + "plt.plot(t, error)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.4 ('.venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.4" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "97190208b4a6552dc9493965a1caf8d39c9d1897fe9495f2fe88af90c5a07bd6" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/ch-10/_figure_generator/noisy_derivatives_graph.ipynb b/ch-10/_figure_generator/noisy_derivatives_graph.ipynb new file mode 100644 index 0000000..0b677b6 --- /dev/null +++ b/ch-10/_figure_generator/noisy_derivatives_graph.ipynb @@ -0,0 +1,237 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "# create a sinewave with a frequency of 1Hz\n", + "t = np.arange(0, 4, 0.01)\n", + "pure = np.sin(2 * np.pi * t)\n", + "\n", + "# add random noise to the sinewave\n", + "noise = np.random.normal(0, 0.1, len(t))\n", + "noisy = pure + noise" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the sinewave\n", + "plt.plot(t, pure, label='pure')\n", + "plt.plot(t, noisy, label='noisy')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def derivative(x, y, gain=0.1):\n", + " return np.gradient(y, x) * gain" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot derivative of pure sinewave\n", + "plt.plot(t, derivative(t, pure, 1), label='derivative')\n", + "# plot derivative of noisy sinewave\n", + "plt.plot(t, derivative(t, noisy, 1), label='derivative')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# low pass filter on the noisy sinewave\n", + "filtered = np.convolve(noisy, np.ones(10)/10, mode='same')\n", + "# plot filtered noisy\n", + "plt.plot(t, filtered, label='filtered')\n", + "# plot derivative of filtered noisy\n", + "plt.plot(t, derivative(t, filtered, 1), label='filtered derivative')\n", + "# # plot derivative of original noisy\n", + "# plt.plot(t, derivative(t, noisy, 1), label='noisy derivative')\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Create pseudo-derivative function\n", + "def pseudo_derivative(x, y, gain=0.1):\n", + " # apply a low pass filter to x\n", + " filtered = np.convolve(y, np.ones(10)/10, mode='same')\n", + " # now take the derivative of x_filt\n", + " return np.gradient(filtered, x) * gain" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the pseudo-derivative of noisy sinewave\n", + "plt.plot(t, pseudo_derivative(t, noisy, 1), label='pseudo-derivative')\n", + "\n", + "# plot derivative of noisy sinewave\n", + "# plt.plot(t, derivative(t, noisy, 1), label='derivative')\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# try a kalman filter on the noisy sinewave\n", + "\n", + "def kalman_filtered(x, kalman_gain=0.05):\n", + " current_value = x[0]\n", + " kalman_output = [current_value]\n", + " for item in x[1:]:\n", + " current_value = current_value + kalman_gain * (item - current_value)\n", + " kalman_output.append(current_value)\n", + " return kalman_output\n", + "\n", + "# plot kalman filtered noisy\n", + "plt.plot(t, kalman_filtered(noisy), label='lp filtered')\n", + "plt.plot(t, noisy, label='noisy')\n", + "plt.plot(t, pure, label='pure')\n", + "plt.plot(t, np.gradient(pure), label='pure derivative')\n", + "plt.plot(t, pseudo_derivative(t, noisy, 1), label='pseudo-derivative')\n", + "# plot derivative of kalman filtered noisy\n", + "plt.plot(t, derivative(t, kalman_filtered(noisy), 1), label='lp filtered derivative')\n", + "plt.legend()\n", + "plt.show()" + ] + } + ], + 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2022-07-18T20:12:56.773432 + image/svg+xml + + + Matplotlib v3.5.1, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/ch-10/_figure_generator/tangent_on_sinewave.ipynb b/ch-10/_figure_generator/tangent_on_sinewave.ipynb new file mode 100644 index 0000000..6de7b51 --- /dev/null +++ b/ch-10/_figure_generator/tangent_on_sinewave.ipynb @@ -0,0 +1,131 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from matplotlib import pyplot as plt\n", + "import numpy as np\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# create a decaying sinewave, 8 cycles with decaying amplitude\n", + "t = np.linspace(0, 8, 1000)\n", + "decaying_sine = np.sin(t * np.pi) * 0.8 * np.exp(-t * np.pi / 4) + np.log(1 + t**0.25)\n", + "\n", + "# graph the decaying sinewave \n", + "plt.plot(t, decaying_sine)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n", + "1.0\n", + "1.0\n", + "1.0\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "def plot_graph_tangent_at_time(graph, t, t_index, label='slope'):\n", + " # Get the slope of graph at that location\n", + " slope = np.gradient(graph, t)[t_index]\n", + " tangent = np.arctan(1/slope)\n", + " line_length = 1\n", + " line_w = np.sin(tangent) * line_length\n", + " line_h = np.cos(tangent) * line_length\n", + " # recalculate the length of the line\n", + " line_length = np.sqrt(line_w**2 + line_h**2)\n", + " print(line_length)\n", + "\n", + " # Add a line to the graph\n", + " plt.scatter(t[t_index], graph[t_index], color='C1', linewidth=2)\n", + " plt.plot([t[t_index] - line_w, t[t_index] + line_w], [graph[t_index] - line_h, graph[t_index] + line_h], 'C1--', label=label)\n", + "\n", + "# PLot the last graph again\n", + "plt.plot(t, decaying_sine, label='decaying sine wave')\n", + "\n", + "plot_graph_tangent_at_time(decaying_sine, t, 100)\n", + "plot_graph_tangent_at_time(decaying_sine, t, 165)\n", + "plot_graph_tangent_at_time(decaying_sine, t, 500)\n", + "plot_graph_tangent_at_time(decaying_sine, t, 700)\n", + "# plt.legend()\n", + "plt.axis('equal')\n", + "# set y axis range from 2 to 0\n", + "plt.ylim(0, 2)\n", + "\n", + "plt.savefig(\"slopes_on_wave.png\", bbox_inches=\"tight\")\n", + "plt.savefig(\"slopes_on_wave.svg\", bbox_inches=\"tight\", format=\"svg\")\n", + "plt.show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.4 ('.venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.4" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "97190208b4a6552dc9493965a1caf8d39c9d1897fe9495f2fe88af90c5a07bd6" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}