2-PID Control in CelciuXº
Technology Note
Objective: Demonstrate the use of 2-PID in CelciuXº
Components used:
EJ1_-TC__-__
Description:
Omron uses a well tried and tested technology for PID control referred to as 2 degrees of freedom
PID (or 2-PID) in short. This means that the controller allows the response to setpoint changes and
disturbances to be tailored independently.
Typically, if one tunes the controller for good disturbance rejection (eg. Ziegler-Nichols rules for
quarter decay ratio) then setpoint responses have large overshoots. Conversely, if PID is set to
give response with no overshoot to setpoint changes then the disturbance rejection is also very
slow.
Through the use of setpoint feed forward and scaling via a normalised parameter alpha it is
possible to tune the response accordingly. By default Omron temperature controllers have a nonzero value of alpha (0.65) which gives an effective combination
With CelciuXº the parameter alpha can be changed while control is running during commissioning
while in the previous controllers this could only be done as part of configuration while control was
stopped.
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Operation of 2-PID
One of the major problems in tuning PID controllers for thermal systems is dealing with the
problem of overshoot during the initial warm-up period of a furnace or an oven.
It is common practice to warm the furnace or the oven up to a set temperature before starting the
programmed heat treatment process. In this instance the setpoint is usually fixed and it is expected
that the unit reaches the setpoint as quickly as possible and with as small an overshoot as
practicable.
Temperature
Warm-up
phase
Heat treatment phase
Cool down
phase
Time
The main reason for the overshoot is the accumulation of the additional integral term during the
warm-up phase where the controller output is saturated at maximum heating. Different
manufacturer’s deal with this phenomenon differently.
Omron uses the more generic two degree of freedom PID algorithm (2-PID) which allows separate
tuning of setpoint response and disturbances. This means that there is a parameter alpha which
only affects the behaviour of setpoint response and has no effect on overall stability or reaction to
disturbances. Alpha is set between 0 and 1. A default value of alpha of 0.65 is used in all
instruments. But this value can be changed to suit the process. A value of 0.0 has minimum
influence on overshoot response while a value of 1.0 gives maximum effect to reduce overshoot.
The following section shows the effect of alpha on a simulated oven. The behaviour shown is
typical of how these parameters work.
Alpha = 0
PV, SP, OP
400
300
200
100
0
0
50
100
150
Time in Seconds
Alpha = 0.65
200
250
0
50
100
150
Time in Seconds
200
250
PV, SP, OP
400
300
200
100
0
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The above example shows a case where PID parameters are tuned to cope with a 20%
disturbance at a setpoint of 300 degrees but the settings cause an overshoot for setpoint response.
It can be seen that the default value of 0.65 gives a very reasonable setpoint response and the
disturbance response is totally unaffected. The default value of 0.65 works well for many cases but
if needed the user can change the value of alpha to suit the application. Increasing the value
towards 1.0 will suppress overshoot while reducing it towards zero will make the control more
responsive to setpoint changes.
Alpha = 0.65
350
300
300
250
250
PV, Setpoint, Output
PV, Setpoint, Output
Alpha = 0
350
200
150
200
150
100
100
50
50
0
0
0
50
100
150
Time in Seconds
200
250
0
50
100
150
Time in Seconds
200
250
The next example shows the effect of alpha in reducing the overshoot at the end of ramped
setpoints. The graph on the left hand side is with alpha set to zero and the graph on the right hand
side has alpha set to 0.65.
Conclusions
This demonstrates the effectiveness of Omron 2-PID algorithm. The major advantage of using this
is that
1. It allows independent tuning for setpoint changes and disturbances
2. It can operate across a range of temperatures
3. It improves overshoot response to ramps and soaks as well as step changes
The default value of 0.65 is quite effective in many applications but can be adjusted by the user to
suit the application.
1A