Specifications

Synergy Nano Technical Manual, Revision -
Page 51
PID
As mentioned previously, PID stands for Proportional, Integral, and Derivative and is a popular
control algorithm. PID controllers are used to regulate a process variable (temperature, humidity,
etc) at a setpoint. The setpoint is the desired level of the process variable. The control variable is
equal to the output of the controller. The output of a PID controller changes in response to a change
in process value or setpoint.
PID Output = Proportional + Integral + Derivative
The Proportional Band, Reset and Rate constants control the calculation of the PIDs.
P Proportional Band = 100/gain
I Integral = 1/reset (units of time)
D Derivative = rate (units of time)
Error – Err
Error is the difference between setpoint and actual value.
Error = setpoint – actual value (measurement)
Proportional Band
The proportional band is the range of error that forces the output from 1 to 100%. In the proportional
band, the proportional controller output is proportional to the error. Decreasing the proportional band
increases the controller gain; however, increasing the controller gain can make the process less
stable.
If error < the proportional band
Proportional Output = (error)*100/(proportional band)
Else
Proportional Output = 100%.
Integral – In
With integral action, the integral portion of the controller output is proportional to the integral of the
error. Integral action is used to eliminate the steady state error of a strictly proportional control.
Increasing the reset (the integral gain) can destabilize the response, decreasing the reset can
stabilize and slow the system response.
Integral Output =
∫ (100/proportional band * Reset * Error)
Derivative – Dn
The derivative portion of the controller output is proportional to the rate of change of the error.
Derivative Output = 100/(proportional band) * Rate * d(error) / dt
Proportional Output – Pn
Proportional output is the difference between setpoint and actual value divided by the proportional
band. As an example: if the proportional band is 10 and the actual temperature is 90C and the
setpoint is 100 then the Pn term is 100%. When the actual value reaches 95 degrees the Pn term is
at 50%, at 99C the Pn term is 10%, at 100C the Pn term is 0%.