Once you get the GUI up and running, the next thing you'll want to do is tune your multirotor. The MultiWii GUI uses PID values in order to attain a stable state. Below is a simplified explanation of how PID theory works and hopefully it will help you tune your multirotor.
The PID loop is a systematical method used to stabilize many different systems; in this case a multirotor. PID stands for Proportional, Integral and Derivate. These terms represent the 3 basic components needed to stabilize a multirotor. The Proportional (P) component focuses on correcting for present errors, the Integral (I) component focuses on correcting for past errors and the Derivative (D) component focuses on predicting future errors. For more information on how these components work together to stabilize a multirotor, read below.
Proportional is the first component of the PID loop and it focuses on correcting present errors in multirotor stabilization. In order to understand how the proportional component of the loop works, we're going to assume it is the only part of the PID loop and that the integral (I) and derivative (D) components don't exist. Now, let's assume that your multirotor is completely stable and hovering perfectly still in the air. Let's say that some outside force (wind or someone pulling on it) causes the the multirotor to tilt in one direction. The gyros on the board will sense this change and it will know how many degrees the multirotor has tilted in that particular direction. Knowing this degree of change, the controller board can tell the motors to output a force in the opposite direction of the tilt.
The amount of force that the controller board tells the motors to use is proportional to how much the multirotor is tilted. This proportional force is intended to return the multirotor back to its initial position, but in reality it causes the multirotor to overshoot it's initial position and start tilting in the opposite direction. Once this happens, the multirotor will keep tilting back and forth between these two opposite positions indefinitely. This is a problem that occurs when you have only the proportional (P) component in the loop (see animation below). Now we're going to see how adding the integral (I) and derivative (D) components to the loop fixes this problem.
Integral (I) is the second component of the PID loop and it focuses on correcting past errors in multirotor stabilization. Recall the original scenario when you had only a proportional (P) component in the PID loop and the multirotor was indefinitely tilting back and forth between two opposite positions. This is where the integral (I) component comes into play.
When your multirotor tilts in any direction, the controller board will measure how many degrees it tilted (just like the P component) but it will also measure how long the tilt lasted for. The controller board will then integrate this tilt (in degrees) over the amount of time it measured for the tilt. The resulting integral (I) tells the controller board how much of an overshoot has been occurring in the past. Once the controller board knows this, it can then instruct the motors to compensate for the overshoot and help stabilize the multirotor.
The integral (I) component will bring the multirotor closer to equilibrium, however, there is one more issue. The integral (I) term uses the measurement of time to calculate erros made in the past. Due to this fact, there is a natural delay between when the controller board starts making measurements and when it finally implements a change. This delay can eventually result in the multirotor failing to reach equilibrium and this is where the derivative (D) component comes in to solve the problem.
The derivative (D) component of the PID loop focuses on predicting future erros in multirotor stabilization. The derivative (D) component uses the same type of measurement as the integral (I) component. It measures the degree of tilt the multirotor is experiencing as well as the duration of the tilt, however, instead of integrating these two terms, it takes their derivative. Once this derivative (D) is calculated, the controller board knows the rate of change of the tilt and it can then predict where the next overshoot will occur. Knowing where the next error will occur, counteracts any issues that may occur with the integral (I) component of the loop and helps bring the multirotor to a final, stable position.
These three components of the PID loop all work together in order to fully stabilize a multirotor. Due to the fact that each component has to perfectly balance out with the other two components, it is sometimes necessary to have to "tune" the PID parameters. All this means is that the user must adjust the relative amount of P gain, I gain and D gain in the loop so that no single component overwhelms the rest.