Each element has a constant K value in front (K p, K i, and K d), which signifies each element's weight as they form u(t), or the control output at a specific time. And while it never hurts, you don't even have to be able to do calculus.īreaking the first equation down, we produce u(t)-the unitless controller output on the left-hand side of the equation-by adding three mathematical elements on the right-hand side of the equal sign: P, I, and D. The good news is that you don't have to dig out your Modeling and Analysis of Dynamic Systems textbook to understand what's going on here. One advantage of this form is that we can adjust the overall K p constant for the whole equation at one time:Īll of this may look a bit intimidating, perhaps even to someone who graduated with an engineering degree. We can also transpose the equation to extract the K p value and apply it to the entire equation, in what's known as the standard form. 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.
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