Enter the PID output, proportional gain, error, integral gain, integral of error, derivative gain, and derivative of error into the calculator to determine the missing variable.
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PID Coefficient Formula
The following formula is used to calculate the PID output for given values of proportional gain, error, integral gain, integral of error, derivative gain, and derivative of error.
PID = (Kp * e) + (Ki * Ie) + (Kd * De)
Variables:
- PID is the PID output
- Kp is the proportional gain
- e is the error
- Ki is the integral gain
- Ie is the integral of error
- Kd is the derivative gain
- De is the derivative of error
To calculate the PID output, multiply the proportional gain by the error, add the product of the integral gain and the integral of error, and then add the product of the derivative gain and 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.
How to Calculate PID Coefficients?
The following steps outline how to calculate the PID coefficients.
- First, determine the proportional gain (Kp).
- Next, determine the error (e).
- Next, determine the integral gain (Ki).
- Next, determine the integral of error (Ie).
- Next, determine the derivative gain (Kd).
- Next, determine the derivative of error (De).
- Finally, calculate the PID output using the formula PID = (Kp * e) + (Ki * Ie) + (Kd * De).
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Proportional Gain (Kp) = 2
Error (e) = 5
Integral Gain (Ki) = 1
Integral of Error (Ie) = 3
Derivative Gain (Kd) = 0.5
Derivative of Error (De) = 4