Bueno, como dijo Jason S, esta pregunta es antigua :). Pero a continuación es mi enfoque. He implementado esto en un PIC16F616 que se ejecuta en un oscilador interno de 8MHz, usando el compilador XC8. El código debería explicarse en los comentarios, si no, pregúntame. Además, puedo compartir todo el proyecto, como lo haré en mi sitio web más adelante.
/*
* applyEncoder Task:
* -----------------
* Calculates the PID (proportional-integral-derivative) to set the motor
* speed.
*
* PID_error = setMotorSpeed - currentMotorSpeed
* PID_sum = PID_Kp * (PID_error) + PID_Ki * ∫(PID_error) + PID_Kd * (ΔPID_error)
*
* or if the motor is speedier than it is set;
*
* PID_error = currentMotorSpeed - setMotorSpeed
* PID_sum = - PID_Kp * (PID_error) - PID_Ki * ∫(PID_error) - PID_Kd * (ΔPID_error)
*
* Maximum value of PID_sum will be about:
* 127*255 + 63*Iul + 63*255 = 65500
*
* Where Iul is Integral upper limit and is about 250.
*
* If we divide by 256, we scale that down to about 0 to 255, that is the scale
* of the PWM value.
*
* This task takes about 750us. Real figure is at the debug pin.
*
* This task will fire when the startPID bit is set. This happens when a
* sample is taken, about every 50 ms. When the startPID bit is not set,
* the task yields the control of the CPU for other tasks' use.
*/
void applyPID(void)
{
static unsigned int PID_sum = 0; // Sum of all PID terms.
static unsigned int PID_integral = 0; // Integral for the integral term.
static unsigned char PID_derivative = 0; // PID derivative term.
static unsigned char PID_error; // Error term.
static unsigned char PID_lastError = 0; // Record of the previous error term.
static unsigned int tmp1; // Temporary register for holding miscellaneous stuff.
static unsigned int tmp2; // Temporary register for holding miscellaneous stuff.
OS_initializeTask(); // Initialize the task. Needed by RTOS. See RTOS header file for the details.
while (1)
{
while (!startPID) // Wait for startPID bit to be 1.
{
OS_yield(); // If startPID is not 1, yield the CPU to other tasks in the mean-time.
}
DebugPin = 1; // We will measure how much time it takes to implement a PID controller.
if (currentMotorSpeed > setMotorSpeed) // If the motor is speedier than it is set,
{
// PID error is the difference between set value and current value.
PID_error = (unsigned char) (currentMotorSpeed - setMotorSpeed);
// Integrate errors by subtracting them from the PID_integral variable.
if (PID_error < PID_integral) // If the subtraction will not underflow,
PID_integral -= PID_error; // Subtract the error from the current error integration.
else
PID_integral = 0; // If the subtraction will underflow, then set it to zero.
// Integral term is: Ki * ∫error
tmp1 = PID_Ki * PID_integral;
// Check if PID_sum will overflow in the addition of integral term.
tmp2 = 0xFFFF - tmp1;
if (PID_sum < tmp2)
PID_sum += tmp1; // If it will not overflow, then add it.
else
PID_sum = 0xFFFF; // If it will, then saturate it.
if (PID_error >= PID_lastError) // If current error is bigger than last error,
PID_derivative = (unsigned char) (PID_error - PID_lastError);
// then calculate the derivative by subtracting them.
else
PID_derivative = (unsigned char) (PID_lastError - PID_error);
// Derivative term is : Kd * d(Δerror)
tmp1 = PID_Kd * PID_derivative;
// Check if PID_sum will overflow in the addition of derivative term.
if (tmp1 < PID_sum) // Check if subtraction will underflow PID_sum
PID_sum -= tmp1;
else PID_sum = 0; // If the subtraction will underflow, then set it to zero.
// Proportional term is: Kp * error
tmp1 = PID_Kp * PID_error; // Calculate the proportional term.
if (tmp1 < PID_sum) // Check if subtraction will underflow PID_sum
PID_sum -= tmp1;
else PID_sum = 0; // If the subtraction will underflow, then set it to zero.
}
else // If the motor is slower than it is set,
{
PID_error = (unsigned char) (setMotorSpeed - currentMotorSpeed);
// Proportional term is: Kp * error
PID_sum = PID_Kp * PID_error;
PID_integral += PID_error; // Add the error to the integral term.
if (PID_integral > PID_integralUpperLimit) // If we have reached the upper limit of the integral,
PID_integral = PID_integralUpperLimit; // then limit it there.
// Integral term is: Ki * ∫error
tmp1 = PID_Ki * PID_integral;
// Check if PID_sum will overflow in the addition of integral term.
tmp2 = 0xFFFF - tmp1;
if (PID_sum < tmp2)
PID_sum += tmp1; // If it will not overflow, then add it.
else
PID_sum = 0xFFFF; // If it will, then saturate it.
if (PID_error >= PID_lastError) // If current error is bigger than last error,
PID_derivative = (unsigned char) (PID_error - PID_lastError);
// then calculate the derivative by subtracting them.
else
PID_derivative = (unsigned char) (PID_lastError - PID_error);
// Derivative term is : Kd * d(Δerror)
tmp1 = PID_Kd * PID_derivative;
// Check if PID_sum will overflow in the addition of derivative term.
tmp2 = 0xFFFF - tmp1;
if (PID_sum < tmp2)
PID_sum += tmp1; // If it will not overflow, then add it.
else
PID_sum = 0xFFFF; // If it will, then saturate it.
}
// Scale the sum to 0 - 255 from 0 - 65535 , dividing by 256, or right shifting 8.
PID_sum >>= 8;
// Set the duty cycle to the calculated and scaled PID_sum.
PWM_dutyCycle = (unsigned char) PID_sum;
PID_lastError = PID_error; // Make the current error the last error, since it is old now.
startPID = 0; // Clear the flag. That will let this task wait for the flag.
DebugPin = 0; // We are finished with the PID control block.
}
}