PID

[Tanaythan]

PID (stands for proportional, integral, and derivative) is a control loop where the feedback is used as an adjustment for the next iteration. It takes in a setpoint that the loop will try to adjust for and the sensors that you stated will give you back a current value. You can subtract your current from your setpoint to get your error.

The way that most people understand PID is thinking about it as a function graph where the x-axis is the number of iterations and the y-axis is your error (setpoint - current). Now this function (let's call it f(x)) is your basic function for your error versus iterations that is constantly growing as your PID loop continues. Your proportional value will be a constant (kP) multiplied by f(b) where b is equal to your last iteration. The integral (if you have not taken calculus) is the area underneath the curve of the function, which can be simply done by adding all the error terms. Then, you can multiply your constant (kI) by the sum of your error to find your integral constant. The derivative term is the slope of the function and is given by your point slope formula: (f(b) - f(a)) / (b - a). The derivative value is given by multiplying this slope and the constant (kD). You add all of these together to get a PID value to send to your motor.

Now, the proportional value is pretty self-explanatory. It decreases as the error becomes smaller or as you approach your setpoint. Thus, it gives a huge boost at the beginning and reduces its effectiveness as the error decreases. A P-only loop will result in oscillation. The integral term provides an extra boost that will get the PID loop to the setpoint required. Since it is the sum of the errors, it can "predict" where the power level will go next and try to compensate. The derivative portion speeds up (or slows down if your constant is negative) the loop because it multiplies a constant by your slope and adds it to the system.