PID controller affect on a differential driving robot when the parameters (Kp, Ki, and Kd) are increased individually. [full Q written below]

Question

Question: A PID controller has three parameters Kp, Ki and Kd which could affect the output performance. A differential driving robot is controlled by a PID controller. The heading information is sensed by a compass sensor. The moving forward speed is kept constant. The PID controller is able to control the heading information to follow a given direction. Explain the outcome on the differential driving robot performance when the three parameters are increased individually.

This is a question that has come up in a past paper but most likely won't show up this year but it still worries me. It's the only question that has me thinking for quite some time. I'd love an answer in simple terms. Most stuff i've read on the internet don't make much sense to me as it goes heavy into the detail and off topic for my case.

My take on this:

I know that the proportional term, Kp, is entirely based on the error and that, let's say, double the error would mean doubling Kp (applying proportional force). This therefore implies that increasing Kp is a result of the robot heading in the wrong direction so Kp is increased to ensure the robot goes on the right direction or at least tries to reduce the error as time passes so an increase in Kp would affect the robot in such a way to adjust the heading of the robot so it stays on the right path.

The derivative term, Kd, is based on the rate of change of the error so an increase in Kd implies that the rate of change of error has increased over time so double the error would result in double the force. An increase by double the change in the robot's heading would take place if the robot's heading is doubled in error from the previous feedback result. Kd causes the robot to react faster as the error increases.

An increase in the integral term, Ki, means that the error is increased over time. The integral accounts for the sum of error over time. Even a small increase in the error would increase the integral so the robot would have to head in the right direction for an equal amount of time for the integral to balance to zero.

I would appreciate a much better answer and it would be great to be confident for a similar upcoming question in the finals.

Side note: i've posted this question on the Robotics part earlier but seeing that the questions there are hardly ever noticed, i've also posted it here.

Answer 1

I would highly recommend reading this article PID Without a PhD it gives a great explanation along with some implementation details. The best part is the numerous graphs. They show you what changing the P, I, or D term does while holding the others constant.

And if you want real world Application Atmel provides example code on their site (for 8 bit MCU) that perfectly mirrors the PID without a PhD article. It follows this code from AVR's website exactly (they make the ATMega32p microcontroller chip on the Arduino UNO boards) PDF explanation and Atmel Code in C

But here is a general explanation the way I understand it.

Proportional: This is a proportional relationship between the error and the target. Something like Pk(target - actual) Its simply a scaling factor on the error. It decides how quickly the system should react to an error (if it is of any help, you can think of it like amplifier slew rate). A large value will quickly try to fix errors, and a slow value will take longer. With Higher values though, we get into an overshoot condition and that's where the next terms come into play

Integral: This is meant to account for errors in the past. In fact it is the sum of all past errors. This is often useful for things like a small dc/constant offset that a Proportional controller can't fix on its own. Imagine, you give a step input of 1, and after a while the output settles at .9 and its clear its not going anywhere. The integral portion will see this error is always ~.1 too small so it will add it back in, to hopefully bring control closer to 1. THis term usually helps to stabilize the response curve. Since it is taken over a long period of time, it should reduce noise and any fast changes (like those found in overshoot/ringing conditions). Because it's aggregate, it is a very sensitive measurement and is usually very small when compared to other terms. A lower value will make changes happen very slowly, and create a very smooth response(this can also cause "wind-up" see the article)

Derivative: This is supposed to account for the "future". It uses the slope of the most recent samples. Remember this is the slope, it has nothing to do with the position error(current-goal), it is previous measured position - current measured position. This is most sensitive to noise and when it is too high often causes ringing. A higher value encourages change since we are "amplifying" the slope.

I hope that helps. Maybe someone else can offer another viewpoint, but that's typically how I think about it.