Examining PID tuning essentials

I favor software to automatically identify the open loop dynamics. The step size must be five times or more greater than the valve and measurement resolution. However, open loop tests of runaway processes in the actual plant are unsafe because there is no steady state and there is a point of no return. For these processes and very slow processes that take days to reach a steady state, a relay oscillation method developed by Karl Astrom to find the ultimate gain and ultimate period provides a safer and faster alternative. This can be used in the actual process to help improve the dynamic simulation to find the frequently missing sources of dead time in simulations.

Now we get to the extremely argumentative stuff about tuning rules. Maybe turn on some of your favorite music, grab some beer, and toast what you have learned and accomplished.

There should be separate tuning rules for self-regulating, integrating, and runaway processes. 

Self-regulating process with a primary time constant greater than four times the total loop deadtime are termed near-integrating processes and integrating process tuning rules should be used. Often not realized there is a window of allowable gains for integrating and runaway processes where too low besides too high of a PID gain causes instability. If there are no runaway processes, modified lambda tuning rules are useful that have low limits on reset time to facilitate more proportional action and some derivative action included based on dead time besides secondary time constant. I personally like my Short Cut Method (SCM) based on estimations of the ultimate period and ultimate gain for all three types of processes documented in my book Tuning and Control Loop Performance Fourth Edition free to download.

Tuning for unmeasured load disturbances

Shinskey and I favor first tuning for unmeasured load disturbances. Tuning tests are done by simply putting the controller momentarily in manual, quickly making an output change similar in size to that used to identify the process dynamics and then immediately returning the PID to automatic. There is a tradeoff between performance and robustness, so tests should be done at different operating conditions to confirm that significant oscillations do not develop. Dynamic simulations can readily provide this ability. 

Once you have good tuning for rejecting unmeasured load disturbances, setpoint lead-lags or beta and gamma factors in a 2 degrees of freedom (2DOF) PID structure are used to provide a fast approach to setpoint with no significant overshoot. Setpoint feedforward can greatly help, For the fastest approach to setpoint, the controller output can be positioned and held by output tracking at a maximum value until a future value block prediction shows that in slightly more than a dead time, the PV will reach setpoint at which time the output is momentarily set to an estimated FRV and the controller returned to automatic.

Practical applications

Michael, how can we best address some practical application and safety issues?

Michael: First and foremost, in order to properly tune any PID controller, one must understand how the process actually behaves from both the steady state (open-loop gain) as well as dynamic (primary lag time and deadtime) perspectives: a distillation column behaves very differently from a reactor which is different from a compressor; this includes the behavior due to (un)measured disturbances and control element changes, as well as the disturbance and SP change response requirements for the controllers accounting for both safety and nominal operations. Nonlinear (steady state) process behavior is another factor that comes into consideration.

Your comments regarding exothermic reactor controller requirements, as well as your books/articles on pH control, illustrates this point quite clearly. Furthermore, knowing the form of the PID is also required because it affects how the three control terms—proportional, integral and derivative—interact with and affect each other. This understanding is handy when troubleshooting controller behavior. Finally, as you mentioned, one must know whether the control system uses percent-of-scale (PoS) versus engineering units (EU) in its PID calculation. Fortunately, most systems use PoS, but this practical aspect of control implementation is often overlooked in many PID control textbooks and training courses.

The debates around tuning rules ranges from “taste great, less filling” arguments to outright “holy wars.” I’m not going to promote one set of rules over the others. My recommendation is to choose the rules that produce the required response to disturbances and SP changes to satisfy safety and normal operations criteria. Along those lines, there are a few criteria for tuning rules that, I believe, are worth stating:

1. The response to both a disturbance rejection and SP change must never cause the PV or the OP to oscillate. For further clarity, “oscillate” for the PV means crossing SP more than once and for OP means crossing the final steady state value more than once during the response time frame. This recommendation is predicated on a single step-change in SP and the same for a hypothetical disturbance. 
2. Some overshoot of both PV (referenced to SP) and OP (referenced to final steady state value) are fine because it minimizes the error during the initial controller response period. For the OP, it represents the amount of energy the controller injects into the process and that energy will affect the process, so the controller response should be “balanced” appropriately to the process’s behavior.
3. In terms of achieving the final steady state values or FRV for both PV and OP, the response should “crisply” get to the final values (taking the above criteria into account) rather than asymptotically approach it (i.e., a long “laggy” approach). 

Taking a page from the book on distillation control that I co-authored (A Real-Time Approach to Distillation Process Control, Wiley, 2023), the purpose of Process control is:

To stably, robustly and predictably maintain Product Qualities in the face of Measure and Unmeasured Disturbances with the LEAST total and incremental energy-input (i.e., minimal movement) to the Process while satisfying Operating Constraints and Safety Limits.

The short version can be described as the “Goldilocks Rule”: Not too hot (aggressive), not too cold (sluggish), but just right!  And “just right” is entirely dependent upon the specifics of the process behavior, thus it can’t be completely generalized or reduced to a single arbitrary response curve. 

I will also add this: I’ve often heard people comment that PID control is not a “model-based” controller. While I understand how this perception came about, it is completely wrong: BOTH the process model (how it really works), the controller response, as well as the PID Form, are imbedded in the tuning constants which are generated from the process characteristics and the intended controller response; thus, even Ziegler-Nichols tuning is “model-based”. This is why PID can address both Integrating as well as Self-Regulating processes without any additional manipulations or “features” (as is required for most multivariable controllers (MVCs)).

As to explicitly limiting output moves with rate-of-change (RoC) or maximum change clamps, I’m averse to implementing or using such features as it can and often does hide or disguise controller behavior and poor/inappropriate tuning. For example, I was engaged with a client and found one controller that had the output RoC clamps so tight that the craziest tuning didn’t change the behavior one bit: the controller hardly moved the output at all. It was only after I stumbled upon the output clamp settings (which were on a different “page” from the tuning constants) that I realized what was (not) happening. 

Along these same lines, there is a natural Output limit that results from the mechanical/process design based on the range of the final control elements (FCEs)—usually a flow control valve—relative to the PV it’s intended to control.  If the full operating range available from a FCE is based only on steady state considerations and not the controller’s required dynamic behavior into account, particularly for disturbance rejection and/or feed forward control, the FCE could very well be too small. I highly recommend a relative gain analysis (RGA) be performed on all regulatory controllers, both inventory (level and pressure) and quality controls using PoS values, which normalizes them to all to the same basis regardless of EUs. Doing this exercise before the process design is completed will reveal deficient controller and/or mechanical designs which should be addressed before proceeding with the equipment ordering and fabrication. A rule-of-thumb that I’ve described is that any PID controller that has a PoS (normalized) open-loop gain (OLG) or process gain (usually designated as Kp) that is less than 0.2 should be evaluated for a change in mechanical design and/or modifying the manipulated variable-controlled variable (MV-CV) Pairings between controllers in close proximity to each other. Doing so before the equipment is commissioned will save a LOT of grief once the plant is running. A plot of PoS controller gain versus OLG will reveal the reasoning behind this recommendation: to address a 1% change in PV, the controller that has a PoS OLG of 0.2 must make a 6X change in OP at steady state to address that change in PV; as the PoS OLG gets smaller, the controller response gets exponentially larger!  And this analysis looks ONLY at the Steady State response: the dynamic response may require a much larger change in Output. 

To summarize, there are three things one must understand very clearly and to a high degree of certainty to have a “properly behaving” PID controller:

1. Process characteristics: open-loop gain, primary lag time and deadtime (as well as any potential nonlinear steady state behavior);
2. PID form; and
3. Controller (disturbance and SP change) response requirements

On a related note to your question of “safety issues”, there are a couple of additional comments that are warranted.

One must realize that a SIS is a backstop to address known or expected sources of safety limit excursions. Furthermore, Safety instrument functions (SIFs) are typically designed around single-source failures or excursion sources. It’s impossible to predict a priori all the possible combinations of potential excursion sources (some physical/mechanical, others organizational) that can come together in unanticipated or unexpected ways (e.g., “that can never happen here.”). That’s why I always advocate for controls designs to be visually intuitive to the operator so that when he needs to intervene manually, it’s obvious where and how he needs to do that, as opposed to going behind the curtain to find some esoteric parameter to adjust to prevent the plant from blowing up.

Secondly, from an organizational perspective, both operators and (instrument/mechanical) technicians must be trained in the specific hazards of their processes, so that when they receive a job assignment to repair, diagnose or calibrate something, they understand not only the what (the procedure to follow) but the reason why it—the equipment or instrument--exists; that is, understanding the hazard (to which they ARE potentially exposed) this equipment, SIF or instrument is intended to mitigate. This kind of understanding is what is lacking in so much of the typical safety training that is found throughout the process industries and why we continue to have incidents which are labelled the result of human error. 

Greg: “Uffda” is a Scandinavian term I learned since my grandparents are Norwegian. Uffda defies exact translation. It is a heart-rendering expression of feelings at particularly poignant moments. Everybody has had such occasions in their lives. Some days you may feel as though you have had more than your fair share. The following list is dedicated to all of us who have had one or more of those "uffda" days.