PID Coefficient Calculator

Formula

The formula to calculate the PID output is:

\[ PID = (K_p \cdot e) + (K_i \cdot I_e) + (K_d \cdot D_e) \]

Where:

\( PID \) is the PID output
\( K_p \) is the proportional gain
\( e \) is the error
\( K_i \) is the integral gain
\( I_e \) is the integral of error
\( K_d \) is the derivative gain
\( D_e \) is the derivative of error

What is a PID Controller?

A PID controller (Proportional-Integral-Derivative controller) is a control loop feedback mechanism widely used in industrial control systems. A PID controller continuously calculates an error value as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms. The controller attempts to minimize the error by adjusting the process control inputs. The proportional term produces an output value that is proportional to the current error value. The integral term is concerned with the accumulation of past errors, and the derivative term is a prediction of future error, based on its rate of change. By tuning the three constants in the PID controller algorithm, the controller can provide control action designed for specific process requirements.

Example Calculation

Let's assume the following values:

Proportional Gain (K_p) = 2
Error (e) = 5
Integral Gain (K_i) = 1
Integral of Error (I_e) = 4
Derivative Gain (K_d) = 0.5
Derivative of Error (D_e) = 3

Using the formula to calculate the PID output:

\[ PID = (2 \cdot 5) + (1 \cdot 4) + (0.5 \cdot 3) = 10 + 4 + 1.5 = 15.5 \]

The PID output is 15.5.