Best PID tuning methods explained for level loops: Part 2

In this blog we are going to compare different tuning techniques used to tune the level loops in a distillation column. The tuning methods under consideration are Lambda, the Zak Friedman tuning rules and AptiTune. The idea is to obtain a tuning based on engineering specifications like maximum deviations, minimal gain and dead-time margin.

The following distillation column example illustrates the tuning strategies that can be applied when designing the controller for level loops. A debutaniser is used to separate the C4 (isobutane, n-butane) from a natural gas liquids stream (NGL). In this example, there are 4 cascade loops, for the column pressure, the top temperature, and the column bottom and reflux drum levels. There are also single loops for the feed and steam flow. The piping and instrumentation diagram is presented the figure below:

The process, PID tuning methods and PID loops

The two loops we are interested in here are:

• LC Column: the column is subjected to changes in the feed stream, and bottom flow should be set to vary as smooth as possible to reduce the impact on the downstream process.
• LC Reflux drum: the reflux drum is small, and it is easy to lose the level if top temperature or pressure is changed and tight control is required.

A simulation of the column in a proprietary tool was used to evaluate the three different tuning approaches presented in the first blog on level control. The PID tuning methods:

• Lambda
• Zak Friedman tuning rules,
• AptiTune. 

Different criteria were used for each PID method, response time (l) for Lambda, maximum allowed fluctuation in the level (LD) for Zak Friedman, and two others for AptiTune, the PV deviation (PVD), equivalent to LD, and the gain and dead-time margins (GM/DM) for a robust set for the reflux drum loop.

The distillate and condensate flows were stepped on the outflow (LC OPs) to generate the data needed for the tuning from the simulation. The models were identified on AptiTune and are presented in the figure above. The integrating gains are shown in blue in the upper right. Note that gain for the reflux drum is 5 times higher, corresponding to a surface area 5 times smaller than for the column. Another important aspect here is the time delay observed in the two systems, around 30s. This behavior could be related to a transportation delay, the tuning of the slave loops, or the measurement principle, for example, which should be considered when designing the controller.

A smoother design of PID loops

The table below presents the tuning sets found for the three different approaches (PID tuning methods), Zak Friedman, and Lambda tuning rules, and AptiTune. Note that a PI structure was selected for both controllers.

The figure below shows the PV and OP behavior for the LC Column loop with the three sets. After a unit step disturbance in the OP, the column level moved smoothly for the three methods, with slow variations in the OP, which would represent a more stable downstream operation as desired.
It can be noticed that only AptiTune achieved the specified tuning criteria of 20% maximum PV deviation.

The reflux drum level response is less straightforward as seen in the next figure. Due to its lower volume (and surface area), the process dead-time plays a major role here since the controller is meant to react more quickly for a strict level loop. This dynamic characteristic affects the maximum aggressiveness of the loop, which can easily lead to unstable behaviors when not considered in the design. This limitation shows up through the oscillations on both PV and OP. Even though the Lambda rule considers the time delay on the calculation of both gain and integral parameters, it presented the worst response with the disturbance taking almost the 40 minutes window to disappear. AptiTune again met the tuning criteria, PVD: 5%, with a less oscillatory response, but still aggressive indicating we are missing something here: the loop robustness.

The best PID loop robust response

Gain Margin (GM) and Dead-time Margin (DM) are two measures used to translate the robustness of a loop. These parameters refer to the amount of gain, and dead-time, which can be added to the process without making the system unstable. The greater the margins, the greater the stability. The figure below presents an additional set for the tuning of the reflux drum level when we include a GM of 2 and DM of 5 as engineering specifications in AptiTune. The new tuning is also available in Table 1.

As expected, the new set allows a larger error on the PV in exchange for a higher robustness for the system.

The most important feature of AptiTune is its ability to design PID loops that will meet a robustness criterion, remaining stable and well damped even if the process conditions change substantially. As result of a tuning calculation, the tool returns the Stability Robustness Plot, also shown in the figure above (right) after the optimization. The y-axis plot denotes the process gain ratio with which the process gain is multiplied (GM), and the x-axis refers to the dead-time added to the open loop model (DM).

The violet stability line indicates what combinations of gain and dead-time will lead the loop to the instability. The region beyond (above and to the right of) this violet line is the unstable region. The red block serves as a guideline and it is recommended to design the controllers such that they are at least stable in this red area, that means the block should not be crossed by the stability line. The actual process gain and dead time lie at the GM of 1 and DM of 0, in the center of the block.

In the example, a gain ratio of 2 and dead time addition of 5 samples (5 sec = 0.08 min) could be added to the process, marked as the combined robustness spec with the blue line. The tuning settings found are just within the design constraints, and the closed loop system would get marginally stable at the given specification.

The simulated response to a disturbance in the inlet flow of the Distillation column is presented below for the level two loops, considering the best tuning for each, both given by AptiTune. It is possible to see the variation on the LC Column of 20%, as chosen in the tuning criteria on the tool, which is translated into a slow variation in the condensate flow. The reflux drum level control responds quicker and a change of only 2.5% is observed, showing a good compromise between performance and robustness, as defined by the gain and dead-time margins specification.

AptiTune: the best PID tuning method for level loops

Tuning level loops can be a demanding activity specially because of its integrating characteristic. Poor tuning can easily lead to oscillations and instability, and de-tuning the parameters found from the conventional rules cannot guarantee that engineering specifications are met.

With the AptiTune you guarantee that every aspect of the tuning process is considered when tuning a level loop. From the evaluation of different tuning sets and disturbances, to the automatic conversion of the parameters to the DCS algorithm, the tool finds the best tuning set for your level loop.

Choose AptiTune for level loops and you get: 

• The best responses for both strict and smooth level control
• Performance and robustness design criteria
• Easy evaluation of scenarios

Do you want to learn more about using AptiTune for level control tuning? Request a 30-minute live demo and gain insights into what you can achieve with INCA Tools PID Tuning. It is all you need to get your PID controllers’ algorithm right the first time.

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