PID Control Fundamentals

1. Introduction

PID control is a widely used control loop feedback mechanism in industrial control systems and robotics. PID stands for Proportional, Integral, and Derivative, which are the three terms that make up the controller's calculation.

The PID controller continuously calculates an error value as the difference between a desired setpoint and a measured process variable. The controller attempts to minimize this error by adjusting the process control inputs.

2. PID Parameters

The PID controller consists of three parameters:

• Proportional (P): The proportional term produces an output value that is proportional to the current error value. It helps reduce the overall error.
• Integral (I): The integral term is concerned with the accumulation of past errors. It integrates the error over time to eliminate residual steady-state error.
• Derivative (D): The derivative term predicts future error based on its rate of change. It dampens the system response and helps to prevent overshoot.

3. PID Control Algorithm

The output of a PID controller is calculated using the formula:

output(t) = Kp * error(t) + Ki * ∫error(t)dt + Kd * (d(error)/dt)

Where:

• output(t): Control output at time t.
• error(t): The difference between the setpoint and the process variable.
• Kp, Ki, Kd: Tuning constants for proportional, integral, and derivative terms.

4. Tuning Methods

Tuning a PID controller involves adjusting the parameters Kp, Ki, and Kd to achieve the desired response. Common tuning methods include:

1. Ziegler-Nichols Method: A heuristic tuning method based on the reaction curve of the system.
2. Trial and Error: Manually adjusting parameters based on system behavior.
3. Software Tools: Utilizing software simulations to model and tune the PID controller.

5. Implementation

Implementing a PID controller in code can be done using the following C-like structure:

float Kp = 1.0; // Proportional gain
float Ki = 0.1; // Integral gain
float Kd = 0.01; // Derivative gain

float integral = 0; 
float previous_error = 0;

void loop() {
    float setpoint = 100; // Desired value
    float measured_value = readSensor(); // Function to read sensor value
    float error = setpoint - measured_value;
    
    integral += error; // Accumulate the integral
    float derivative = error - previous_error; // Calculate derivative
    
    // PID output
    float output = Kp * error + Ki * integral + Kd * derivative;
    
    // Apply output to actuator
    applyOutput(output);
    
    previous_error = error; // Store error for next iteration
}
            

6. Best Practices

When implementing a PID controller, consider the following best practices:

• Start with Kp and set Ki and Kd to zero before tuning.
• Adjust Ki to eliminate steady-state error once Kp is set.
• Finally, adjust Kd to improve stability and response time.
• Continuously monitor system performance and adjust parameters as needed.

7. FAQ