The following technical discussion is part of an occasional series showcasing the ISA Mentor Program, authored by Greg McMillan, industry consultant, author of numerous process control books, 2010 ISA Life Achievement Award recipient and retired Senior Fellow from Solutia Inc. (now Eastman Chemical). Greg will be posting questions and responses from the ISA Mentor Program, with contributions from program participants.

In the previous post on bumpless transfer, it was mentioned that there are ways to optimize the immediate change you get in the PID output for a setpoint change. For a structure of PID on error, there is a step from the proportional mode and a kick from the derivative mode in the PID output.

This fast and immediate change in PID output makes the setpoint response faster but operators and other loops may get upset by the large abrupt change in PID output. A gradual and smooth response of the PID output for a setpoint change may increase the time to reach setpoint by a matter of seconds for pressure loops and minutes for temperature loops but this may be inconsequential.

Also, the prevention of setpoint overshoot is more easily achievable when there is no proportional step. For bioreactor temperature and pH control, overshoot must be totally eliminated and increases in setpoint response time are insignificant because the batch cycle times are days to weeks. Additionally, for many gas unit operations in hydrocarbon processes, abrupt changes and overshoot of final resting value by the PID output must be avoided at all costs due to severe interactions from heat integration and recycle streams.

Brian Hrankowsky, an ISA Mentor Program resource, has found several equivalent methods that give the user a lot of options to totally eliminate the proportional step and derivative kick for a setpoint change without affecting load response. His use of Laplace transforms not only provides conclusive proof but shows that this knowledge gained in university control theory courses has considerable practical value. Laplace transforms are effectively used by Brian here to provide a unified view and a valuable perspective showing that the user has a lot of ways of achieving this objective.

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Brian Hrankowsky’s derivation of equivalent methods

Vendors provide PID features in various combinations that often are intended to address the same control problem or objective. It is not always clear how to translate or compare these features from one vendor PID algorithm to another. The purpose of these derivations is to illustrate that several methods for eliminating or controlling the proportional step and derivative kick in a PID output resulting from a change of setpoint are equivalent by seeing they end up with the same Laplace transform equations.

All algorithms below are based on the ISA standard form. To identify control actions taken on process value vs. error, a hyphen is used to separate the two. Actions to the left of the hyphen are taken on error. Actions to the right are taken on PV. For example, a PID controller with a structure of proportional and integral on error and derivative on PV is shown as “PI-D” and a structure with integral on error with proportional and derivative on PV is shown as “I-PD”.

Setting a setpoint filter equal to the reset time


Setting the PID algorithm to use a proportional and derivative on PV structure



Setting the PID Algorithm to Two Degrees of Freedom (2DOF) Structure with Beta and Gamma Set to Zero


After setting beta and gamma to zero, the Laplace transform is the same as the one for “I-PD” structure previously shown so there is no need to repeat the remaining equations.

Setting the setpoint lead-lag (SPLLAG) factor to zero

Some controllers use a setpoint lead and lag where the lag is automatically set to the RESET time and the lead is a factor of the reset time between zero and one inclusive. Below, I’ve used beta to represent the factor.



The resulting equation is the same as for the 2DOF with beta and gamma set equal to zero.

We see that there are four equivalent methods of eliminating the proportional step and derivative kick from a setpoint change. Since not all PID controllers have a built in option for adding a lead-lag or filter to the setpoint or a structure with Integral action on error and proportional and derivative action on the process variable or two degrees freedom, this recognition of equivalent functionality has significant practical value as it allows the control engineer to achieve the desired result with whichever of the options are available for the particular control system. The user can readily eliminate abrupt changes in the PID output and prevent overshoot of the setpoint by the PV and overshoot of the final resting value by the PID output when required.

Any change that is to be made to a control system must be thoroughly functionally tested by realistic simulations of the process’s dynamic response. The ability of the control system improvement to deal with abnormal besides normal operating conditions must be verified. The commissioning and performance of improvements should be closely monitored to ensure they meet plant requirements.

Additional Mentor Program Resources

See the ISA book 101 Tips for a Successful Automation Career that grew out of this Mentor Program to gain concise and practical advice. See the InTech magazine feature article Enabling new automation engineers for candid comments from some of the original program participants. See the Control Talk column How to effectively get engineering knowledge with the ISA Mentor Program protégée Keneisha Williams on the challenges faced by young engineers today, and the column How to succeed at career and project migration with protégé Bill Thomas on how to make the most out of yourself and your project. Providing discussion and answers besides Greg McMillan and co-founder of the program Hunter Vegas (project engineering manager at Wunderlich-Malec) are resources Mark Darby (principal consultant at CMiD Solutions), Brian Hrankowsky (consultant engineer at a major pharmaceutical company), Michel Ruel (executive director, engineering practice at BBA Inc.), Leah Ruder (director of global project engineering at the Midwest Engineering Center of Emerson Automation Solutions), Nick Sands (ISA Fellow and Manufacturing Technology Fellow at DuPont), Bart Propst (process control leader for the Ascend Performance Materials Chocolate Bayou plant), Angela Valdes (automation manager of the Toronto office for SNC-Lavalin), and Daniel Warren (senior instrumentation/electrical specialist at D.M.W. Instrumentation Consulting Services, Ltd.).

About the Author
Gregory K. McMillan, CAP, is a retired Senior Fellow from Solutia/Monsanto where he worked in engineering technology on process control improvement. Greg was also an affiliate professor for Washington University in Saint Louis. Greg is an ISA Fellow and received the ISA Kermit Fischer Environmental Award for pH control in 1991, the Control magazine Engineer of the Year award for the process industry in 1994, was inducted into the Control magazine Process Automation Hall of Fame in 2001, was honored by InTech magazine in 2003 as one of the most influential innovators in automation, and received the ISA Life Achievement Award in 2010. Greg is the author of numerous books on process control, including Advances in Reactor Measurement and Control and Essentials of Modern Measurements and Final Elements in the Process Industry. Greg has been the monthly "Control Talk" columnist for Control magazine since 2002. Presently, Greg is a part time modeling and control consultant in Technology for Process Simulation for Emerson Automation Solutions specializing in the use of the virtual plant for exploring new opportunities. He spends most of his time writing, teaching and leading the ISA Mentor Program he founded in 2011.

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