PID control is the cornerstone of modern robotics, enabling precise movement, stability, and responsiveness. This advanced guide will take you beyond the basics and show you how to implement sophisticated PID controllers for your robotics projects, with real-world examples from our Maze Master 3000 robot.

Understanding PID Control

PID stands for Proportional, Integral, and Derivative control. It's a feedback control mechanism that continuously calculates an error value as the difference between a desired setpoint and a measured process variable, then applies a correction based on proportional, integral, and derivative terms.

Output = Kp × e(t) + Ki × ∫e(t)dt + Kd × de(t)/dt

Proportional (P)

Current error correction

Integral (I)

Past error accumulation

Derivative (D)

Future error prediction

Implementing PID in Arduino

Here's a basic PID controller implementation in Arduino. This code provides a framework you can adapt for various robotics applications:

class PIDController {
  public:
    // PID gains
    float Kp, Ki, Kd;
    
    // Variables for PID calculation
    float error, lastError, integral, derivative;
    
    // Time variables
    unsigned long currentTime, previousTime;
    float elapsedTime;
    
    // Constructor
    PIDController(float Kp, float Ki, float Kd) {
        this->Kp = Kp;
        this->Ki = Ki;
        this->Kd = Kd;
        lastError = 0;
        integral = 0;
        previousTime = millis();
    }
    
    // Calculate PID output
    float compute(float setpoint, float input) {
        // Calculate error
        error = setpoint - input;
        
        // Calculate time difference
        currentTime = millis();
        elapsedTime = (currentTime - previousTime) / 1000.0; // Convert to seconds
        
        // Proportional term
        float Pout = Kp * error;
        
        // Integral term with anti-windup
        integral += error * elapsedTime;
        // Apply integral limits to prevent windup
        integral = constrain(integral, -100, 100);
        float Iout = Ki * integral;
        
        // Derivative term (using derivative on measurement)
        derivative = (input - lastError) / elapsedTime;
        float Dout = Kd * derivative;
        
        // Calculate total output
        float output = Pout + Iout - Dout; // Note: D term subtracted for derivative on measurement
        
        // Remember values for next iteration
        lastError = input;
        previousTime = currentTime;
        
        return output;
    }
};

// Example usage for motor speed control
PIDController speedPID(0.8, 0.05, 0.1); // Kp, Ki, Kd values

void setup() {
    // Initialize your motor controllers and sensors
}

void loop() {
    float desiredSpeed = 100; // RPM
    float currentSpeed = readMotorSpeed(); // Implement this function
    
    float controlSignal = speedPID.compute(desiredSpeed, currentSpeed);
    
    // Apply control signal to motor
    setMotorSpeed(controlSignal); // Implement this function
    
    delay(20); // Control loop timing
}

Tuning PID Parameters

Proper PID tuning is critical for optimal performance. Here's our systematic approach:

  1. Start with P only: Set Ki and Kd to zero. Increase Kp until the system oscillates, then reduce to 50% of that value.
  2. Add Integral term: Increase Ki until the system reaches the setpoint with minimal steady-state error. Too much Ki causes overshoot.
  3. Add Derivative term: Increase Kd to reduce overshoot and settling time. Too much Kd causes system instability.
  4. Fine-tune all parameters: Make small adjustments to all parameters for optimal performance.

Advanced PID Techniques

For complex robotics systems, consider these advanced techniques:

  • Cascade Control: Use two PID controllers where the output of one becomes the setpoint of another
  • Feedforward Control: Predict control output based on system model to complement PID
  • Gain Scheduling: Change PID parameters dynamically based on operating conditions
  • Fuzzy Logic Adaptation: Use fuzzy rules to adjust parameters in real-time

Case Study: Maze Master 3000

Our Maze Master 3000 robot uses a sophisticated dual PID system for navigation:

// Maze Master 3000 PID Implementation
PIDController headingPID(1.2, 0.01, 0.3);
PIDController wallFollowPID(0.7, 0.001, 0.15);

void navigateMaze() {
    // Read sensors
    float currentHeading = readCompass();
    float leftDistance = readLeftDistanceSensor();
    float rightDistance = readRightDistanceSensor();
    
    // Wall-following PID (maintain equal distance to walls)
    float wallError = leftDistance - rightDistance;
    float wallCorrection = wallFollowPID.compute(0, wallError);
    
    // Heading PID (maintain desired heading)
    float headingCorrection = headingPID.compute(desiredHeading, currentHeading);
    
    // Combine corrections
    float leftMotorSpeed = baseSpeed - headingCorrection - wallCorrection;
    float rightMotorSpeed = baseSpeed + headingCorrection + wallCorrection;
    
    // Apply motor speeds
    setLeftMotorSpeed(leftMotorSpeed);
    setRightMotorSpeed(rightMotorSpeed);
}

Common Challenges & Solutions

When implementing PID in robotics, watch for these common issues:

  • Integral Windup: Use clamping or back-calculation to limit integral accumulation
  • Noise Amplification: Add low-pass filtering to derivative term
  • Nonlinear Systems: Implement gain scheduling or adaptive control
  • Computational Limits: Optimize code and use fixed-point arithmetic

Mastering PID control will transform your robotics projects, enabling precise and stable movement in complex environments. Start with simple implementations and gradually add complexity as you gain experience.