PID tuning





The setting up of PID controllers is complex and contains many varaibles. Following are two examples of methods that may be adopted

Ziegler-Nichols Closed Loop (Hunt) Method

    1. Set up the system in closed loop i.e. with the controller in auto mode
    2. Remove integral and derivative action
    3. Increase the gain (reduce proportional band) untill the controller just begins a steady hunt
    4. record the Proportional Band setting as value P
    5. Record the periodic time of the sinusoidal hunt as value T

    • For Proportional only- Proportional Band = 2 x P
    • For Proportional + integral- Proportional band = 2.2 x P, Integral Action Time = T/2
    • For Proportional + Integral + Derivative- Proportional band = 1.67 x P, Integral Action Time = T/2, Derivative action time = T/8

Ziegler-Nichols Open Loop Method

    1. Switch controller to manual ensuring that the system is open loop. i.e. that the controller is disconnected from the controlling unit which can be manually adjusted
    2. Rapidly alter manual regulator to cause a stepped change in the control valve by a set amount. Record the movement of the control valve as a percentage of total travel. Record this as δR

      In the above example the valve has moved by 12 out of a total 20mm therefore is has move 60% of its total travel.δR = 60
    3. Record the system open loop resonse. That is record the intial valve from the measured valve transmitter, initiate the stepped input then record how the measure valve responds in relation to this
    4. Change the vertical axis of the response graph so that it is scaled as a percentage of the measure value range ( which from above we see is 20m).
    5. From the grap dtermine values as best as possible for dv (distance-velocity- time between controller output signal being generated and contolled element receiving it) lag T[s]and the maximum slope N[%/s]

    • For Proportional only- Proportional Band = N xT/δR x 100%
    • For Proportional + integral- Proportional band = N x T/δR x 110%, Integral Action Time = 3.33 x T
    • For Proportional + Integral + Derivative- Proportional band = N x T/δR x 83%, Integral Action Time = 2 x T, Derivative action time = 0.5 x T
For the above worked example this would give the following results
Proportional only
PB = N x T/δR * 100 = 17.8 x 1.5 / 60 * 100 = 44.5%
Proportional + Integral Action
PB = N x T/δR * 110 = 17.8 x 1.5 / 60 * 110 = 49%
IAT = 3.33 x T = 3.33 x 1.5 = 5 [s]
Proportional + Integral Action + Derivative Action
PB = N x T/δR * 83 = 17.8 x 1.5 / 60 * 83 = 37%
IAT = 2 x T = 2 x 1.5 = 3 [s]
DAT = 0.5 x T = o.5 * 1.5 = 0.75 [s]

System responses

Effects of changing Proportinal Band on P controller

Effects of changing Integral Action Time on P + I controller

Effects of changing Derivative Action Time on P + I + D controller