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Measuring multivariable

controller performanceHow to tell if your multivariable controlleris doing a good job

By Steven Obermann

2015 May/June Issue


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Multivariable controllers have been in use in manufacturing and production systems formany years. Multivariable controllers typically cost from $60,000 to more than $500,000,and they can deliver savings that are many times their cost. Yet the full benets of these

controllers are often not realized. Even worse, manufacturing sites may be completelyunaware that the performance of the controllers is subpar. This article describes effectiveways to measure and improve the performance of these powerful advanced controls.

Introduction to multivariable controlsMultivariable control technology has two benets: reduced

variability and operation closer to constraints. Reduced variabilityin the production process translates to energy and raw materialsavings, improved quality, and fewer production losses relatedto process trips. It is also the precursor for driving the productionprocess closer to constraints to achieve greater overall productionefciency and protability.

Multivariable controller performance issues come from fourgeneral areas:

Multivariable controller implementation

Regulatory layer controls Operator actions Process changes and disturbances

To ensure the performance of the full multivariable control system, we must have metricsto detect and resolve each of the performance issues.

Measuring performanceAssessing the performance of a multivariable controller

requires producing metrics that reveal problems, impairment, and loss of benets.

Metrics for the controller itselfOne early metric applied to multi-variable controllers is time in service (on or off). Thismetric has proven to be of limited use, because functionality can be signicantly

impaired while the controller is still technically on. Measuring performance this way isakin to assessing an individuals performance based on how long the ofce light is on.

Do not discard this metric completely, however; a low time in service is usually not good

Measuring multivariable controller

performanceHow to tell if your multivariable controller is doing a good jobBy Steven Obermann

Fast Forward

Many multivariable

controllers are notoperating at their best.

Simple metrics can be

used to identify the issues.

Automated software

systems track performanceand provide diagnostics.


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and should instigate an investigation to get to the root cause. But, if there are nosupporting metrics to help set the direction of that investigation, it could be timeconsuming, involving operator interviews and trend analysis. Good supporting metrics helpanalysts get to the root cause sooner. Good supporting metrics are more important in theopposite scenario, where the multivariable controller has high time in service, but otherimpairments exist.

Supporting metrics can be high-level metrics or detail metrics. A

high-level metric is one that ags a performance issue. It can be

a combination of several detail metrics. The previously discussedtime-in-service metric can be made more useful by rolling thestate of all the controller variables into the metric. If a low time-in-service condition occurs, it is easy to identify the controller vari-ables that are responsible. A detail metric gives information on a

specic behavior or condition. They are generally applied to

individual controller variables; an example is time at limit. An

important requirement of a good metric is that it registers

deviation from what is normal or optimal. Considering the time-at-limit metric, it would be good to know if being at a limit was goodor bad, and this can vary from variable to variable. Good metricsalert us to a performance issue without making us scan historicaltrends and apply personal and possibly inconsistent interpreta-tions to the information. When a performance issue is identied,

a good metric provides information that leads us to the source ofthe problem.

Regulatory control metrics

Regulatory layer control issues consist of controller tuning changes and measurement andvalve problems. A multivariable controller relies on measurements collected by the

regulatory layer. If those values are erroneous or upset (e.g., oscillation caused by valvesticking), they can cause less than optimal behavior from the multivariable controller. A

multivariable controller is tuned to manage a production process. Regulatory layercontroller tuning is embedded in the production process model the multivariable

controller uses.

Another source of multivariable controller

impairment comes from operatoractivity. This consists of actions taken to

turn variables on or off or to change limitson variables. Some limit changes restrictthe controller from achieving a moreoptimal operating condition; others can setup infeasible conditions, severelyimpairing the controller. Finally, there areprocess changes. These can be seasonalor product quality/grade changes. They

could be raw-material related: a different type of catalyst or a different grade or purity of

additive. Changes that affect a process over time include heat exchanger fouling and

Detail metrics

CV prediction error(avg, abs avg, standarddeviation)

MV available range

CV and MV oscillatingcondition

CV and MV time at limit

High-level metrics Number of operatorchanges

Objective function & value

Percent of time in service

Percent of variables constrained


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catalyst deactivation. There are also physical changes like switching to packed internals in anoriginally trayed column or bypassing equipment and vessels.

Multivariable controller model inaccuracy can also lead to cycling. As discussed before, the

process itself can change over time. A detail metric like controller prediction error can help get to

the root cause for this type of change. This is an indication it is time to perform maintenance onthe multivariable controller. Maintaining an average prediction error detail metric for each con-

trolled variable permits the identication of the subset of variables most affected by the processchanges. A trend of the average prediction error for a controlled variable provides some guidance

on the direction a model update should take. For example, if the prediction error (actual predicted) is consistently negative, this means one or more of the models affecting this controlledvariable should have a decrease in gain. It may also be possible to address the over predictionwith adjustments to model time constants. This may be less desirable, however, because it maynecessitate additional adjustments to the overall controller time horizons.

The absolute value of the prediction error can help with two pieces of information. If the predictionerror is alternating between over and under predictions, the average prediction error could end upnear zeroleading us to assume there are no concerns. The average absolute value of theprediction error highlights the magnitude of the prediction error and provides an alert if theaverage prediction ends up close to zero. Taking the standard deviation of the prediction erroris a measure of the dispersion of the error condition. It is not necessarily a bad situation when acontrolled variable has a prediction error. A steady consistent prediction error causes little harm

to controller performance. The opposite is true for a prediction error that is bouncing around. Thiscondition could make it difcult for the controller to keep the variables within limits and very likely

will reduce optimizing time. The prediction error standard deviation identies this situation.

When operating in its best condition, a multivariable controller can return many times its originalinvestment. Perhaps when the multivariable controller was rst implemented there was an audit of

the benets achieved. The company made an effort to justify the original investment in thetechnology. As the previous paragraphs have shown, there are many ways a multivariable

controller can suffer performance losses. These conditions will reduce the return on the originalinvestment. To advocate effectively for funds to maintain the controller, point out the losses inbenets when the controller is not functioning optimally. We have discussed several technical

measures to identify performance problems, but an economic indicator may well be the best toolto help justify when a company should conduct maintenance. One common way to establish thevalue added by the multivariable controller is to compare production protability from a period

when the multivariable controller was not in use to the current protability while the controller is

in use. Should that difference in protability start to get smaller, investigate the reasons for that

decline. When the reason for the difference is identied, use the difference in protability to justify

the expense of correcting the problem.

Measuring operator actionsSometimes operator actions reduce the effectiveness of a multivariable controller. A good high-

level metric is a count of times any variable is turned off or on, or a limit value is changed.Referencing this count against a norm alerts us to the possibility that the operators are havingdifculty with the behavior of the multivariable controller. Drilling into the detailed metrics for the

count values of the individual variables reveals what variable or part of the controller is of concern.Just because there was an excursion in operator activity does not mean the multivariablecontroller is impaired. Adding another piece of detailed information, like the available operating


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range of the variables, ags a situation where the operator change restricted the exibility of the

controller. Possibly the worst case is where a feasible operating point does not exist, and themultivariable controller simply saturates at several limits. A high-level metric to monitor the

number of constrained variables and the individual time-at-limit metric for those variables wouldalso ag an impaired controller.

A combination of the three metrics, number of changes, operating range, and constrained

variables, provides a good screening tool to identify multivariable controllers that needattention. A person responsible for the performance of half-a-dozen or more multivariable

controllers could spend quite some time looking through trends to determine if a controller is outof normal condition. It is much more efcient to have a screening tool point out specic

multivariable controllers not meeting their expected performance metrics.

Measuring process changes and disturbancesThe components of the production process (pumps, vessels, motors, and control systems) needto be evaluated and monitored to maintain operating performance. Bearings arelubricated, valves are repacked, and heat exchangers are cleaned to achieve their expected

lifetimes and avoid sudden failures, accidents, and disruption to business. The hard or physicalcomponents of our systems generally get the care required; these are components that we cantouch (bearing is too hot) or that we can see (leaks from a seal). There tends to be less attentionto the soft components of the production process, because the metrics to assess condition arenot as obvious. Multivariable controllers and control systems in general fall into the softcomponent category. It is similar to evaluating the condition of your home heating and cooling. Ifthe thermostat setting (metric) is being achieved, is everything good? Not necessarily, the system

might be turning on and off more frequently or for longer periods of time. The performance metricsneed to be more sophisticated. Power consumption, outside temperature, and air ow together

give a better picture of the condition of the system.

Another important metric is oscillation identication; after all, one of the purposes of a

multivariable controller is to reduce variability. Oscillation condition is a high-level metric. Ingeneral, it needs some supporting metrics to qualify if a particular cycle is a problem (gure 1).

Using the amplitude of the cycle is one way to sort out small, insignicant behavior. Compare the

amplitude of the cycling variable to the operating range the operator has allowed. If the amplitudeis as large as the span of the operator limits, perhaps someone has overly constrained thecontroller, and it is just moving from lower bound to upper bound. Has the variance of thatvariable changed? Some multivariable controllers have an optimizing function that operates whenthere are free manipulated variables and no controlled variables are predicted to cross limits. Thisfeature can drive the production process to more economically attractive operating points. If a

controlled-variables oscillation is reaching operator limits, the controller must leave the optimizingmode and return to enforcing the limits of the variables. This is inefcient and could be the cause

of some cycling itself (gure 2).

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Figure 2. CV cycle relevance detects the severe cycle.

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The period of the oscillation should also be considered. Long-period oscillation is less of aconcern, and could be just due to the controller making adjustments for unmeasureddisturbances. Another possible long-period oscillation is the multivariable controller responding to

day-to-night temperature cycles. In this situation that cycle could be economically favorable;perhaps the operation runs at a cooling or heating constraint most of the time. The cycle isobserved as the multivariable controller takes advantage of the temperature change. It can reduceenergy consumption or, more likely, increase production to take advantage of the atmospherictemperature changes. A common impairment to a multivariable controller that can cause a cycle is

malfunctioning valves. A regulatory layer controller or valve problem can be seen as an

oscillation period that is considerably smaller than the control horizon time. These cycles wouldalso be observable at the individual loop level. Because a multivariable controller processesmultiple inputs and outputs, the effects of a hardware-induced cycle can be magnied. It is a good

practice to monitor regulatory layer control loop performance to quickly sort out the origin of aregulatory layer problem. It is possible that the problem is occurring on a regulatory layercontroller that is not part of the multivariable control scheme (gure 3).

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Figure 1. A CV with a 22 minute cycle that was not detected and corrected for 12 hours

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Figure 3. Regulatory layer control valve malfunction affecting MPC MV____________________________________________________________________________

ConclusionThe metrics discussed in this article provide some key insights into the health of a multivariablecontrol application. Use the high-level metrics to identify impairment, and the detail metrics to sortthe root cause of the impairment. The sooner issues are discovered and corrected, the more likelyit is that the benets obtained will be sustained. Knowing the economic penalty for a particular

problem allows companies to prioritize and allocate resources.

About the AuthorSteven Obermann is a senior product manager with Metso ExperTune; he has worked in theprocess automation eld for more than 30 years. Obermann has extensive experience in the

rening and petrochemicals sector, having been employed by Texaco, WR Grace, UOP,

Honeywell, and Texas Petrochemicals. His expertise includes process modeling, advance control,optimization, software development, process and control system performance evaluation/bench-marking, project nancial analysis, and management. Obermann has a B.S. in chemical

engineering from Lafayette College in PA. He has been a member of AIChE since 1981.

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