This change gives the equation a better relationship to its physical meaning and allows the units to work out properly to a unitless number: We can also replace K i and K d with 1/T i and T d, respectively. K p, K i, and K d are constants that tune how the system reacts to each factor: P, I, and D are represented by the three terms that add together here.
We can express PID control mathematically with the following equation. While limit-based control can get you in the ballpark, your system will tend to act somewhat erratically. In this example, they would prevent a car's speed from bouncing from an upper to a lower limit, and we can apply the same concept to a variety of control situations. These more subtle effects are what the I and D terms consider mathematically.
