Definition

Control Systems are the methods used to achieve some desired physical result, based on logical input. I.e. Control systems get from something like 'go forward at a speed of x' to the actual control signals that go to the motor controllers. This includes any safety/protection systems - such as to prevent the motors from shorting out from too much acceleration, as well as making the system human controllable (avoiding sudden jerks and such).

PID

PID controllers are very common throughout many different industries due to the simple philosophy behind them. PID stands for Proportional Integral Derivative. Basically it just breaks the controller into these three parts and then sums the results. These controllers are usually designed in the Laplace domain using the root locus philosophy. You may be familiar with the Laplace domain if you have taken a differential equations class (where they make you solve it by changing the variable to s using tables). Another way these controllers can be designed is in the frequency domain using Bode plots but we will not be using this as it requires a deeper understanding of the theory.

P (Proportional)

This part of the controller works by multiplying the Error by Kp.

I (Integral)

This part of the controller works by integrating the Error and then multiplying it by Ki.

D (Derivative)

This part of the controller works by multiplying the derivative of the Error by Kd.

Results

Note that Kp, Ki, and Kd are just regular numbers. Integrating and taking the derivative of the Error may sound complicated but really they are just basic math. The integral is just summing the Error over time and the derivative is just the rate of change of the error. By changing these three numbers you can drastically change how your system responds. Also you don't always want or need all three components. PI controllers (Kd=0) are the most commonly used.