Modeling and Control

The process variable of greatest interest in a process stream is generally concentration. If the final concentration is not right, not much else matters. Yet online analyzers are few and far between. Plant analyzer groups have been cut back or allowed to disappear through attrition. While I think the staffing of these groups would be more than justified, given the current situation analyzers are needed more than ever that can be maintained and supported without special expertise.

Coriolis mass flow meters offer exceptionally accurate mass flow and density measurement with minimal maintenance when properly selected and installed. Many compositions can be better controlled by a more accurate mass flow ratio and the stream density can be used to provide an inference of changes in the stream composition. For specialty chemical and pharmaceutical, the potential number of Coriolis flow meters is quite large because the pipe sizes are small and the value of the product is high.

We loose sight figuratively and literally that the concentration in any stream does not usually match what is listed on the process flow diagram. The concentrations are quite variable due to fluctuations or unknowns in the raw materials and in the unit operations and from cycling introduced by poor controller tuning and final element resolution. The effect of most of these disturbances is typically unmeasured. Often not considered is the capability offered by the Coriolis meter to track down a disturbance. For example, if the temperature corrected density of a feed has changed, it probably means the concentration of a raw material or intermediate has changed.

The extended use of Coriolis meters on feed, recycle, and product streams in any industry with reasonable pipe sizes for both continuous and batch operations seems to me to be one of the biggest straightforward opportunities.

One of the best kept secrets is that a good portion of the benefits from the application of advanced process control (APC) originates from the improvements made to the basic control system as part of the APC project. While Model Predictive Control (MPC) and Neural Networks (NN), and Real Time Optimization (RTO) are glamorous and powerful, a much more extensive aspect of process control improvement involves the control valves, measurements, and PID controllers that form the foundation supporting the performance of any APC technology. A good APC team will use a person experienced in basic control to take a good look at the location and types of sensors and valves and the tuning and configuration of the PID controllers at the get go. To help locate and verify improvements, the set points of PID controllers used by the APC system are stepped in both directions and the dynamics and tuning of the PID loops are identified. The basic improvements on then put in place before process testing and data are used to build and verify MPC, NN, or RTO models. Instead of waiting for an APC project, why not get a head start on the benefits of better basic control now by checking the following? The values listed below are for a 2% required change in controller output, a 1% allowable control error, a process dead time of 10 seconds, a process time constant of 10 seconds, process gain of 1, and a disturbance time constant of 1 minute.

(1) Does the control valve quickly respond to the required changes in the controller output (e.g. half deadband and resolution < 0.2% and response time < 5 seconds)?
(2) Is the sensor noise and repeatability error less than 1/10 the allowable control error (e.g. noise and repeatability error < 0.1%)?
(3) Is the delay and lag of the measurement less than 1/10 the process dead time and process time constant (e.g. measurement delay and lag < 1 second)?
(4) Is the execution time of the controller less than 1/5 the process dead time and process time constant (e.g. control module execution time < 2 seconds)?
(5) Is the controller tuned to provide a standard deviation of the controlled variable less than 1/5 the allowable error (e.g. std dev < 0.2%)?

The additional dead time introduced by the automation system can be approximated here as the summation of the delay and lags introduced by the valve, sensor, and controller. The delay from the valve is the pre-stroke dead time and the delay from the dead band and resolution limit per equation 2-50 in Advanced Control Unleashed. The valve lag is roughly 1/4 of its response time minus the delay. The dead time from the controller is on the average 1/2 of the control module execution time. Adhering to the check list above should provide a peak error less than allowable control error for the case cited but results must be confirmed by loop performance monitoring in the plant.

In analyzing loops in the control room, the story for me was more in the controller output. Yet data analytics tend to focus mostly on primary process variables.

The clues to the significance of the controller output as a source of information are in its job and its action. The job of a feedback controller is to transfer variability and offsets in the controlled variable (process variable) to its manipulated variable (controller output) whether they originate in the sensor, process, or valve. The PID controller output is the result of proportional, integral, and possibly derivative action. Thus the trend of the PID output can contain information on the duration of a shift, approach to set point, and the rate of change of the process variable. Several examples help illustrate this concept.

A trend of a pressure controller’s output showed it varied significant from day to night. It was later confirmed that there was a day to night temperature induced shift in the calibration of the transmitter.

The shifts in the steady state value of the reflux to feed ratio manipulated by a column temperature controller and the reagent to influent feed ratio manipulated by a pH controller were found to coincide with the replacement of the sensors.

For a batch reactor, a larger and earlier dip in manipulated jacket inlet temperature and peak in manipulated vent flow corresponded to a higher heat release and secondary product vapor flow from a more concentrated reactant. In other cases, a higher makeup coolant flow manipulated by the jacket temperature controller coincided with a higher cooling tower temperature.

For a continuous reactor, a larger variability in the vent valve position at higher rates was discovered to be caused by a significant flattening of the installed characteristic of the butterfly valve above 50% open.

Sustained equal amplitude saw tooth and sinusoidal oscillation in the controller output were deduced to be indicative of a limit cycle from stick-slip in a self-regulating loop and deadband in an integrating loop, respectively.

A study of the control of reactor feed flow showed that an inadvertent change in the time interval used for the calculation of the loss in weight flow measurement created a shift in the feed controller output (manipulated speed of the positive displacement pump).

If the controller gain is higher than one or rate action is used, noise in the process variable will be amplified in the controller output. If the peak to peak noise in the controller output exceeds the dead band and resolution of the valve, the controller is inflicting disturbances upon itself or other loops.

Noise also makes it more difficult to see the change in the pattern of the controller output due top changes in process inputs. Thus, whether the analysis of the controller output is done visually or by multivariate statistical process control, the reduction of noise by better doing tuning and filtering is important for batch and continuous analytics.

When there are set point changes, there is also significant information in the pattern of the process variable (e.g. approach, overshoot, and settling of reactor temperature). In a way this consideration is consistent with the above concept in that the set point and thus the process variable is being manipulated by a batch or startup sequence. Similarly, the process variables of loops manipulated by cascade or model predictive control are important.

Unfortunately most of the examples in literature for batch analytics are for process variables of manual or missing controllers. For example, a significant downward trend in dissolved oxygen (DO) is often shown for batch analytics of a fermentor when in fact DO would be controlled at a set point and the story would be in the manipulated air flow.

The concept of transfer of variability from controlled variables to manipulated variables for analysis of batch profiles is emphasized in the book New Directions in Bioprocess Modeling and Control (ISA, 2006).

A controller with just the right tuning is a rare bird but knowing when tuning is important is the real game. While it is nice to say that all loops should be tuned better, what are the benefits and issues? New software can identify the process dynamics but the user is still left with the question - how fast or slow should I tune the controller? This choice comes up as a relative specification (fast or slow) as a menu choice or slider bar or a numerical specification, such as Lambda (closed loop time constant), or a Lambda factor (ratio of the closed loop time constant to the process time constant).

Controller tuning that is too slow (controller gain too low and/or too reset time high) may transfer insufficient variability from the controlled variable (primary process variable) to the manipulated variable (e.g. final element or secondary loop set point). Slower tuning results in larger standard deviations of the controlled variable during upsetting times, startups, grade changes, and batch operation. During quiet operation of continuous self-regulating processes with good control valves (minimal stick-slip) the standard deviation may be negligible so slower tuning does not always mean a problem. Furthermore, the value of reducing the standard deviation depends upon the economic importance of the process variable, blending, and control in downstream equipment. Column, crystallizer, evaporator, extruder, dryer, kiln, and reactor temperatures are indicators of composition and thus generally important. However, if the oscillation period is much faster than the downstream blend time of surge or storage tanks or is much slower than the Lambda of concentration control loops downstream, the effect may be negligible. For example, an opportunity assessment of continuous polymerization line with plug flow reactors showed there was an opportunity for better polymer temperature and pressure control both of which was important for product quality. However, the process engineers placed no economic value on a reduction of the standard deviation because fluctuations from an individual polymer production line were averaged out by the huge storage tank downstream. A similar state of affairs occurred for the temperature of a purification column train. A fair question is why not take out the storage or run at a lower level? Well in this case many lines or trains dumped into the same tank so the tank had to be large enough to accommodate a dynamic unbalance between supply and demand. Less inventory translates to more changes in production rate to match changes in customer and distribution requirements, which means transferring more variability from sales and transportation to production.

My general experience is that temperature loops on large agitated or boiling volumes (e.g. columns, evaporators, fermenters, and stirred reactors) are tuned too slow because the appropriate Lamdda factor is in the range of 0.05 to 0.5 whereas users are comfortable with Lambda factors of 1 to 10 that are suitable for volumes without much back mixing (e.g. extruders, heat exchangers, kilns, pipelines, plug flow reactors, sheet lines, and static mixers) and for flow loops. Similarly, gas pressure control requires lambda factors an order of magnitude lower than liquid pressure control loops. Thus, reactor gas pressure controllers are often tuned too slow. An important point to remember is that variability in a manipulated variable, such as steam, coolant, or vent flow, is usually not as important as decreasing a variability in the controlled variable that is an inference of product composition.

Stay tuned for Part 2 on the signs and consequences of a loop tuned too fast, Part 3 on the quantitative assessment of slow tuning, and finally Part 4 on suggested tools.