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2-PID Control In CelciuXº


Objectives
This Technical Note is to demonstrate the use of 2-PID in CelciuXº
Introduction
Response for PID controller
Content
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 non-zero 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.
 

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 graph

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.
 

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.

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.

Summary
This demonstrates the effectiveness of Omron 2-PID algorithm. The major advantage of using this is that
  • It allows independent tuning for setpoint changes and disturbances
  • It can operate across a range of temperatures
  • 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.
 
References
 
Glossary
 



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Created 2008-12-04
Modified 2008-12-04
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