The PID controller (an abbreviation of Proportional Integral Differential) is the most widely applied feedback control formula/algorithm. It is applied in a huge variety of 'things' to automate them, such as planes, drones, cars, coffeemakers, wind turbines, furnaces, and manufacturing units. It is fair to say that the PID controller is the work horse for automation. The PID formula has three parameters that must be set or tuned in the right way and that is what is the PID Tuner is used for. In this article we will explain a suitable way to program a PID controller yourself (if you do not want to use standard libaries), and we present some background on different tuning methods.
The PID Controller has three parameters that should be tuned. The proportional term (Kp), the integral term (Ti) and the differential term (Td). The figure below shows the effects of varying Kp and Ti.
The equations below present a PID formula that can be programmed in a control computer (note that we define the output of the PID controller as MV or u, and the controlled variable as PV):
\( \Delta u_k = K_p \left( e_k - e_{k-1} + \frac{T_s}{T_i}e_k + \frac{T_d}{T_s} \left( e_k - 2 e_{k-1} + e_{k-2} \right) \right) \)Various methods exist to tune a PID Controller:
Table 1: PID Open Loop Tuning Rules based on [1]
Kp | Ti | Td | |
---|---|---|---|
P | -- | -- | -- |
PI | 0.35*Tp / (Tdt * K) | min( 8*Tdt, Tp) | -- |
PID | 0.5*Tp / (Tdt*K) | min( 8*Tdt , Tp ) | 0.5*Tdt |
Table 2: Closed Loop PI Tuning Rules (Tuning rules for PID are not reliable to our opinion).
Kp | Ti | Td | |
---|---|---|---|
PI | 0.45*Ku | T0/1.2 | 0 |
if u < 0 u = 0 end if u > 100 u = 100 end
du = min( du, 3) du = max( du, -3)
if du < -1 du = 0 end if du > 1 du = 0 end
Having tuned many PID controllers, we developed the PID Tuner - a 'toolbox'. You can try out a demo of the PID Tuner for free.
If you are interested in this software, a training in PID tuning, or if you want help, send us a mail at info@dotxcontrol.com
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