pid Algorithm

/**
 * PID Controller
 * 
 * The PID controller is a linear control algorithm that has three terms:
 *  - Proportional: A simple scaling of the error value by a gain kP
 *  - Integral: Integration of the error value over time, then multipled by gain kI
 *  - Derivative: Rate of change of the error value over time, multiplied by gain kD
 * 
 * Terms of the controller can be removed by setting their gain to 0, creating a PI (kD = 0)
 * or PD (kI = 0) controller. Depending on the control problem at hand, some terms may not
 * increase the performance of the system, or may have a negative effect.
 * 
 * For a more mathematical expanation of the PID Controller, see https://en.wikipedia.org/wiki/PID_controller
 * 
 * Limitations of this implementation:
 *  - Since this implementation is just for demonstration, the pid_step function takes the 
 *    dt as a parameter, and it can be provided by the user in main(). This allows deterministic
 *    experimentation with the algorithm, rather than using time(NULL) which would make the function
 *    non-deterministic.
 * 
 * Inputs: e(t) - Current error at time t. For example, how far a servo is off the desired angle
 * Output: u(t) - Controller output at time t.
 */
#include <stdio.h>

struct pid {
    // Controller gains
    float kP;
    float kI;
    float kD;

    // State variables
    float lastError;
    float integral;
};

float pid_step(struct pid* controller, float dt, float error) {
    // Calculate p term
    float p = error * controller->kP;

    // Calculate i term
    controller->integral += error * dt * controller->kI;

    // Calculate d term, taking care to not divide by zero
    float d = dt == 0 ? 0 : ((error - controller->lastError) / dt) * controller->kD;
    controller->lastError = error;

    return p + controller->integral + d;
}

int main() {
    printf("PID Controller Example\n");

    struct pid controller = {
        .lastError = 0,
        .integral = 0
    };

    // Take the controller gains from the user
    printf("Please enter controller gains in format kP, kI, KD. For example, \"1.2 2.1 3.2\"\n> ");
    scanf("%f %f %f", &controller.kP, &controller.kI, &controller.kD);
    printf("Using kP: %f, kI: %f, kD: %f\n", controller.kP, controller.kI, controller.kD);

    // How often the pid_step algorithm expects to be called. In a real life scenario this would
    // be provided by calling time(NULL) - last_time, or by calling the function reliably at X Hz (using a timer or RTOS etc)
    // For demonstration of this algorithm though, it is defined below as 1 second, allowing easy testing of integral
    // and derivative terms.
    float time_step = 1;

    float error_value;
    while (1) {
        printf("Enter error value\n>");
        scanf("%f", &error_value);

        float output = pid_step(&controller, time_step, error_value);
        printf("Output: %f\n", output);
    }
}