Show HN: 2D PID controller simulation (opens in new tab)

Proportional-integral-derivative (PID) controller is a feedback loop algorithm for control. You give some desired goal (in this case is to reach a position) and it moves to that goal by iteratively attempting to minimise the error (in this case distance).

A real life example is the stabilisation of quadcopters ("drones" eugh I hate that word). Where instead of attempting to reach a location the target is to maintain a specific angle relative to the ground.

As always wikipedia is your friend http://en.wikipedia.org/wiki/PID_controller.

- Brown ball is physically simulated (has inertia)

- A program controls the ball only via two thrusters (x/y), force represented as orange bars

- Program's goal is to deliver the ball to a given point (last click position)

There is a link in the footer: https://en.wikipedia.org/wiki/PID_controller which explains what's a PID controller in this case.

PID is a way to minimize error in a system. Its usually used in industrial settings to control mechanical devices. An example would be you want an electric motor to rotate at a constant N degrees/second. If you just apply a voltage to the motor, you probably won't get an accurate movement because of the variable characteristics of the motor, the load on the motor, and other factors. To fix this, you can add a sensor that can determine how fast the motor is currently moving or how much the motor has moved (a rotary encoder). You then compute the error and use PID control to fix the error.

There are limitations of PID and what it can and cant be used for. There are also other ways of controlling systems (like state feedback).

I might have made some errors in the above statements because I haven't done control theory in a long time, but any control theory course at a university would cover PID control.

In relation to what the post is about, it seems like they've tuned a PID control loop to perform PID error calculations based on where you click and where the circle currently is, then move the circle to that position with a force (/acceleration) determined by the controller.

PID is the hello world of Control Theory which can be used to solve very complex control requirements by iteratively processing feedback. For example these quad-copters juggling use CT even though you may think this is only possible with some kind of machine learning algo.

https://www.youtube.com/watch?v=3CR5y8qZf0Y

This is how cruise control in your car works, in almost all cases.

Yes. Reformulate the systems transfer function into a state space representation, and then solve the algebraic ricatti equation to find an optimal gain matrix. This is know and the LQR problem.

http://en.m.wikipedia.org/wiki/Linear-quadratic_regulator

Switching the output from 100% to -100% is another viable approach, known as bang-bang control, but it is not necessarily optimal

slightly relevant: I've just built a lighting desk that uses motorised faders for some of the control input. To get the PID values for the faders I built a genetic algorithm tool that would evolve the right numbers. Worked a treat but the first half hour of running had the fader slamming about like nobody's business: I burnt one out during testing... But the really interesting thing I found was that you really need a genetic algorithm tool to evolve the correct set of parameters for the goodness function: different goodness functions produced different results in different timeframes.

For some definition of "optimal". I expect you can reach the "5% deviation from target" region much faster if you allow a bit of overshoot.

That's a good idea, I'll add them.

Edit: Done.

Your comment regarding the gravity was really insightful for me (I didn't learn PID formally). When I put large values for i, the ball just oscillated and I couldn't see how i is useful. After I added gravity (in my local build, not published), I began to see how the integral affects the control. That's awesome!

One way to make the integral term useful would be to add some static friction to the simulation, that would be interesting.

Yeah, I didn't put anything there yet, but thanks for the heads-up.

Make it neutrally stable, e.g. Kp = 1, Kd = 0, Ki = 0;

Click x to the right of its standstill position. When it is halfway there click x below its current position.