This week I completed a model with the help of Roger Reedy that allowed me to confirm some concepts besides detail how the design of the control system can cut a project cost almost in half by the use of 10,000 gallon instead of 40,000 gallon neutralization tanks. It wasn't an easy pH control application but not many of them are. The titration curve slope and the hence process gain changed by a factor of 1,000:1 from the extremes of the pH scale range to the neutral point. The influent pH could swing from 12 to 2 pH during the regeneration of a demineralization system or an area pump out. The disturbances could be fast because of plug flow, batch sequences, manual operations, and the stick-slip action of control valves. If pH control is not your thing and it is "High Time We Went" per the Joe Cocker song I am listening to, here is the escape clause.

"Besides embedded process models saving projects a chunk of money, improving plant performance, and justifying better controls and valves by studying the dynamics and integrated functionality of the process and automation system design, you can learn neat stuff like:"

(1) Speed besides size is important
(2) Feedforward signals can do more harm than good
(3) Feedforward head starts based on deltas can help
(4) Linearization of the process variable can be robust and useful
(5) Valve stick-slip can be the upset that keeps on giving

If you are caught within the gravitational pull of this study, I can't guarantee it is not a black hole that sucks you into another dimension.

A process model constructed and embedded in the DCS was used to study a conventional pH and a reagent demand control system with and without feedforward control. In all cases the control loop was in the recirculation line of a vessel to provide a fast feedback correction of abrupt and large disturbances. The feed and reagents were injected at the inlet of a static mixer just before the recirculation stream reentered the vessel. Middle signal selection of 3 pH electrodes was used to inherently ignore a single sensor failure of any type, reduce measurement noise, ignore spikes and slow sensors, and facilitate online diagnostics and calibration. The inline control loop was extremely fast. The transportation delay was only about 2 seconds. The largest potential source of deadtime was injection delay associated with opening and closing of the reagent control valves but this was minimized by coordinated action of close coupled isolation valves at the injection point. Insuring model fidelity for a pH system simply came down to matching the slopes of the model's titration curve with the slopes of the plant's lab titration curve. The following file shows the model and lab titration curves on slides 1 and 2 and the control system on slide 3. Not readable is the slope of 0.015 at 2 and 12 pH.
pH System02 Study Results

First you need to get good lab curves by taking samples of the influent at key times such as steps in a batch sequence when acids or bases are used or during unusual operations such as the pump out of containment areas. The samples should be at the process temperature and titrated with the same reagents used in the automation system. The sample time, temperature, and volume and reagent type and strength must be noted and reagent addition volumes and pH must be tabularized. The typical graphical plots of titration curves showing a vertical line between 3 and 11 pH are next to useless.

The feedforward signal and linearized process variable for reagent demand control were created by use of the same signal characterizer block where the input array was pH values and the output array were corresponding X-axis values per the titration curve. The X-axis was scaled 0 to 100% for the Y-axis and the pH measurement scale of 2 to 12 pH. The first input to the signal characterizer for feedforward control was influent pH. The first input to the signal characterizer for reagent demand (feedback control) was static mixer outlet pH. The second input to both signal characterizers was the pH set point.

Since influent pH measurement errors as small as 0.04 at 2 and 12 pH can cause feedforward errors of 20% or more per the titration curve, it was decided that continuous adjustment by means of a pH feedforward signal could be making large incorrect changes in the reagent flow. It was reasoned that large changes computed in feedforward signal due to large changes in influent flow or pH could be useful as a delta head start to pre-position the valves for the start of a large upset and then let the feedback controller do its thing. This proved to be the case although the feedforward was complicated by the blend of the recirculation stream with the influent at the inlet to the static mixer. Unfortunately, the accuracy of the feedforward curve depended on the accuracy of the titration curve.

Reagent demand control does not deteriorate significantly for changes in the titration curve because only relative changes in the slope are important for linearization and any information is usually better than no information about the shape of the curve. Reagent demand control uses the X-axis of the titration curve scaled as a 0-100% process variable and set point. This control ignores the pH fluctuations near neutrality because these correspond to very small changes in reagent demand due to the steep slope. Reagent demand control also recognizes the true distance of the influent from the set point, which is important for startup and well as disturbances.

Results of the auto tuner showed that the pH controller gain needed to be very low (e.g. 0.02) because of the high process gain from the steep slope of the titration curve at the 7 pH set point. The reagent demand controller gain could be 10 times larger (e.g. 0.25) - see slides 5 and 6 for screen prints of auto tuner results.

A comparison of the conventional pH and reagent demand control is shown on slide 7. The spikes in the static mixer pH are caused by 0.4% stick-slip of the water valves. If the resolution of the water valves was improved from 0.4% to 0.1%, the spikes went away. If the resolution of the acid and base valves upstream or at the static mixer deteriorated from the specified 0.1% to 0.4%, there were many more spikes from the limit cycles of these valves. Normally, a 0.5% resolution control is consider good. This is not so for high process gains. Neutralization systems with pH set points near neutrality are excellent indicators of actual valve resolution and a perpetual stick-slip limit cycle. If you want to know more, check out "Improving pH System Design and Performance" at the Emerson Global Users Exchange this September and the Chemical Processing article on control valves last October.
http://www.chemicalprocessing.com/articles/2007/200.html