CONTROL SYSTEMS

On-Off (Bang-Bang) Control

In our previous lesson, we explored open-loop control systems. Today, we'll dive into closed-loop control systems, focusing on the simplest form: on-off control, also known as bang-bang control.

Closed-Loop Control Systems

Closed-loop control systems use feedback to adjust their output. They constantly compare the actual output with the desired output (setpoint) and make corrections based on the difference (error).

Key Components:

Input (Setpoint): The desired value or state of the system

Controller: The decision-making component that determines what action to take

Plant (System being controlled): The physical system or process being controlled

Output: The actual value or state of the system

Sensor: Measures the output and converts it into a signal the controller can understand

Feedback loop: The path that brings output information back to the controller

On-Off Control Algorithm

On-off control, or bang-bang control, is the simplest form of closed-loop control. The output switches between two states based on whether the measured value is above or below the setpoint.

How It Works:

• The system has a setpoint (desired value)

• The sensor measures the current value

• If the measured value is below the setpoint, the controller turns the system ON

• If the measured value is above the setpoint, the controller turns the system OFF

Real-World Examples:

Advantages and Limitations of On-Off Control:

Maqueen Robot Line Following Sensors:

The Maqueen robot uses Infrared (IR) reflective sensors for line detection. Here's how they work:

Working Principle:

• The sensor has an IR emitter and an IR receiver.

• The emitter sends out IR light.

• The light reflects off the surface below the robot.

• The receiver detects the amount of reflected light.

• Dark surfaces (like a black line) absorb more light, resulting in less reflection.

• Light surfaces (like a white background) reflect more light.

Sensor Values:

• The sensors return analog values ranging from 0 to 1023.

• Lower values indicate darker surfaces (more light absorbed).

• Higher values indicate lighter surfaces (more light reflected).

The Maqueen has 5 of these sensors, but we'll focus on the three centered at the front:

• Left sensor (L1)

• Center sensor (M)

• Right sensor (R1)

Challenge 1: Sensor Calibration

Objective: Determine appropriate threshold values to distinguish between the line and the background.

Materials:

• Maqueen robot

• micro:bit

• Line following mat (white background with black line)

Code:

from microbit import *

from maqueenplusv2 import *

init_maqueen()

while True:

    center = read_line_sensor(M)  

    print("Center: {}".format(center))

    sleep(500)

Run this program and observe the values when:

1. The sensor is over the white background

2. The sensor is over the black line

3. The sensor is partially on the line

Choose a threshold value that reliably distinguishes between the line and background.

Bang-Bang Control in Line Following:

Now that we understand how the sensors work, let's break down how bang-bang control applies to line following:

• Setpoint: The robot should stay centered on the line. Our "setpoint" is the center sensor detecting the line while the side sensors do not.

• Sensor Input: Readings from left, center, and right sensors, compared against our chosen threshold.

• Error: Deviation from the center of the line. This is detected when either the left or right sensor sees the line instead of the center sensor.

• Control Action: Adjust wheel speeds to turn towards the line.

Control Logic:

We'll use our threshold value to determine if a sensor is "ON" (detecting the line) or "OFF" (detecting the background):

• ON state: Sensor value < threshold (detecting dark line)

• OFF state: Sensor value ≥ threshold (detecting light background)

Control decisions:

• If center sensor ON, left and right OFF: Move forward (on the line)

• If left sensor ON, others OFF: Turn right (line is to the left)

• If right sensor ON, others OFF: Turn left (line is to the right)

This creates a zig-zag motion along the line:

• When the robot veers left, the right sensor detects the line, causing a right turn.

• When it veers right, the left sensor detects the line, causing a left turn.

• These continuous corrections keep the robot following the line.

Challenge 2: Implement Line Following

Now that we understand how the sensors work and how to interpret their data, your challenge is to implement the line following algorithm using bang-bang control. Write a MicroPython program that allows the Maqueen robot to follow a black line on a white background using the three front line sensors (L1, M, R1).

Starter Code:

from microbit import *

from maqueenplusv2 import *

init_maqueen()

# Your threshold value from Challenge 1

THRESHOLD = 500  # Adjust this based on your calibration results

while True:

    # Your code here

    sleep(10)  # Small delay to prevent overwhelming the micro:bit

Hints:

• read_line_sensor(sensor) returns a single analog reading from the sensor chosen. Sensor can be L2, L1, M, R1, R2.

• drive(speed) will drive straight.

• spin_left(speed) spins the robot left.

• spin_right(speed) spins the robot right.

• motors(left speed, left direction, right speed, right direction) gives you finer control over both motors