Pergamon

PII:S0967-0661(96)00137-2

Control Eng. Practice, Vol. 4, No. 9, pp. 1297-1303, 1996 1996 Elsevier Science Ltd

Printed in Great Britain 0967-0661/96 $15.00 + 0.00

PLANT-WIDE FEEDBACK CONTROL PERFORMANCE ASSESSMENT USING AN EXPERT-SYSTEM FRAMEWORK

T.J. Harris*, C.T. Seppala*, P.J. Jofriet*** and B.W. Surgenor**

*Department of Chemical Engineering, Queen's University, Kingston, Ontario, Canada, K7L 3N6 (harrist@chee.queensu.ca) **Department of Mechanical Engineering, Queen's University, Kingston, Ontario, Canada, K7L 3N6

***Donohue QUNO Inc., Allanburg Road, Thorold, Ontario, Canada, L2V 3Z5

(Received December 1995; in final form May 1996)

Abs t r ac t . There are many applications where multivariate control schemes are jus- tified from an economic and quality improvement standpoint. Nevertheless, single- input single-output (SISO) and multi-input single-output (MISO) controllers remain the most commonly used controllers in process applications. This paper reviews SISO control performance assessment and details the development of an expert system that quantifies control loop performance on an on-going basis. The expert system schedules each of a newsprint mill's control loops for analysis, directs the sampling of data, ver- ifies the validity of the data, and quantifies the loop's performance using a normalized performance index.

Keywords . Performance analysis, Performance monitoring, Expert systems, Time series analysis, Feedback control

1. INTRODUCTION

Although there are an enormous number of meth- ods for designing and implementing control loops, comparatively few methods exist to assess the per- formance of these loops. When a poorly perform- ing control loop is identified, it is necessary to di- agnose the underlying cause of this poor behav- ior. For example, poor performance could be due to improper tuning, improper controller structure, changing process dynamics, or an excursion in the process disturbance. The emerging area of process assessment provides a means of diagnosing control loop performance using time series and digital sig- nal processing techniques. Expert systems provide an ideal environment for the automation of plant- wide performance assessment.

Harris (1989) showed that a lower bound on the closed-loop process variable variance could be ob- tained by analyzing routine closed-loop operat- ing data. Stanfelj, et al. (1993) have developed a hierarchical technique for the analysis of var- ious control schemes, including a class of feed- forward and feedback control schemes. The re- sults of Harris (1989) and Stanfelj et al. (1993) have been extended by Desborough and Harris (1993). They have developed means for assessing the performance of linear SISO and MISO con- trol schemes. These performance assessment tech- niques have been demonstrated in the petroleum, cement, and fibre processing industries. Potential paper-mill applications were discussed by Perrier and Roche (1992). Kozub and Garcia (1993) out- lined the requirements for large-scale industrial applications of performance monitoring. They sug- gested that artificial intelligence technology could play an important role in reducing the manpower requirements for performance assessment. This pa-

1297

1298 T.J. Harris et al.

per describes a large-scale application of SISO per- formance-assessment methods in an expert system which remotely monitors control performance in a pulp and paper mill.

2. MINIMUM VARIANCE CONTROL AS A PERFORMANCE BENCHMARK

The performance of an existing control loop is often measured against a benchmark. There are many different measures of control performance, such as offset from setpoint, overshoot, rise-time and variance. For regulatory control, the latter is an important measure. The performance of a control loop might be deemed unacceptable if the variance of the controlled variable exceeds some critical value. This criterion, however, fails to rec- ognize the difference between acceptable perfor- mance and good control.

When the controller is already giving minimum variance performance, it is not possible to reduce the variance by a simple re-tuning of the con- troller or by choosing a more sophisticated linear feedback control algorithm. Although the result- ing variability may be unacceptable from a pro- duction or sales perspective, the performance of the control loop from a control standpoint is good. In these cases, reductions in variability are only achieved by modifying the system.

The design of minimum variance feedback-only controllers is well established (/~strSm, 1970; Box and Jenkins, 1976). The adoption of minimum variance control as a benchmark does not imply that it should be the goal towards which the ex- isting control should be driven, or that it is al- ways practical, desirable, or even possible to im- plement. Nevertheless, the performance bound set by minimum variance control is exceeded by all other controllers; hence, it serves as an appropri- ate benchmark against which the performance of other controllers may be compared.

/~str5m (1970) and Box and Jenkins (1976) de- scribe a simple autocorrelation test for minimum variance control. This test has been shown to be a valuable tool for process analysis (Bialkowski, 1992; Smith, 1992).

Yt is the measured process output, g is the mean of Yt, and ut is the deviation of the manipulated vari- able from a reference value required to keep the process at its mean value, w ( B ) and 6(B) are poly- nomials in the backward shift operator B where BJYt =- Y t - j . b is the number of whole periods of delay in the process. The unmeasured disturbance Dt represents the combined effect of all unmea- sured disturbances. Often, Dt can be represented by an autoregressive integrated moving average (ARIMA) time-series model of the form:

O(B) D t - ¢(B)Vdat, (2)

where at is a sequence of zero mean independently and identically distributed random variates. O(B)

and ¢(B) are stable polynomials in B, and V is an abbreviation for 1 - B.

3.1 M i n i m u m variance control

Let the transfer function of the linear time-invariant controller being used to regulate Yt about its set- point Ysp be Gc(B) . Then ut is given by

u t = - Y s p ) . ( 3 )

Under minimum variance control, the process out- put is the error in forecasting the disturbance. It can be shown (Harris, 1989) that the closed-loop system can be described in terms of the unmea- sured disturbance driving force alone:

yt - #y = ~ ( B ) a t , (4)

where ~" (B) is the closed-loop transfer function between yt - #y and the driving force for the un- measured disturbance. This transfer function can be expanded in a Taylor series in B:

@a(B) = 1 + ~ B + @~B 2 + . . . (5)

Yt is then given by

Yt : e t W Y t , (6)

3. PROCESS DESCRIPTION

Many industrial processes can be adequately mod- eled at a nominal operating point as the sum of a series of disturbances and a linear transfer func- tion:

w ( B ) B b Yt - # - 5(B----~ ut + Dr. (1)

where et is composed of the first b terms in the series expansion of ~a(B) and ~t is composed of the remaining terms, et and ~t are statistically independent, and can be interpreted as the b-step ahead forecast error and forecast, respectively.

When a minimum variance controller is imple- mented, the b-step ahead forecast is set to zero (Harris, 1989; /~strSm, 1970), hence the second term on the right-hand side of Eq. 6 vanishes.

Plant-Wide Feedback Control Performance Assessment 1299

3.2 The normalized performance index

In the more general case where the controller is not minimum variance,

2 2 0.2 % = 0.m~ + y, (7)

2 is the total variance of the deviations where cry from setpoint, amy2 is the process variance under minimum variance control, and a~ is the variance

Yt inflation due to non-optimal control.

Desborough and Harris (1993) introduced the nor- malized performance index r/(b) as a means of assessing the current controller's departure from minimum variance control:

tr~ 2 y, + #y fl(b) - ~ + ,~ (8)

sion. This may result in a loss of information use- ful to the assessment of controller performance. The spectrum provides a means of characteriz- ing the components of the process variance by frequency. For feedback-only control, Desborough and Harris (1993) provide a spectral interpreta- tion of the normalized performance index, which makes it possible to determine the frequencies in which the present control differs from minimum variance control. It is also straightforward to de- compose the spectrum of the process output into components attributable to the disturbances which affect it. Bialkowski (1992), Smith (1992), Pryor (1982), DeVries and Wu (1978), and Ohtsu and Kitagawa (1984) discuss the applications of spec- tral analysis in the diagnosis of process-control performance.

r/(b) is bounded by [0,1], where a value of 0 in- dicates minimum variance control and a value of 1 indicates essentially no control. Extensions of this approach to multivariate systems are given in

(Harris, et al., 1996).

3.3 Estimation of rl(b)

Desborough and Harris (1992) show that it is pos- sible to estimate r/(b) from a representative sample of closed-loop operating data by fitting the follow- ing lagged regression:

m

- , y = + k(Y -b+k+l - , y ) , ( 9 )

k = l

where m is the order of the autoregression and ak is the k th regression coefficient. The residual vari- ance provides an estimate of the minimum vari- ance achievable. Furthermore, it can be shown that ~(b) is the adjusted R 2 for the regression in Eq. 9. Note that no perturbation of the process is required in order to assess the performance. The normalized performance index can also be inter- preted directly in terms of the closed-loop impulse response weights (Desborough and Harris, 1993).

An expression for the variance of the estimate of 7/(b) is given in (Desborough and Harris, 1993). The variance is a function of the sample length, u(b), and the degree of autocorrelation. It is useful for establishing approximate confidence limits for r/(b), as well as for selecting an appropriate sample length.

3.4 Spectral Interpretation

The normalized performance index rl(b) can be regarded as an extreme form of data compres-

4. CONTROL PERFORMANCE ANALYSIS IN AN EXPERT SYSTEM FRAMEWORK

In this section, a large-scale industrial application of control performance assessment techniques in QUNO's Thorold Newsprint Mill will be briefly discussed. The performance analysis techniques discussed above have been incorporated into an expert system which has been integrated into the mill's process-control and information system.

A single control loop, consisting of an actuator, sensor and controller, must be well maintained and properly tuned to properly fill its role in deter- mining the overall quality of the end product. The actuator must be properly sized, and must not exhibit excessive hysteresis or stick-slip response. Sensors must provide accurate signals, and con- trollers must be tuned to provide fast stable feed- back control. Over time, as conditions change and parts wear, the performance of a control loop will degrade. By quantifying the performance of the mill's control loops and comparing the results to historical data, mill engineers will know when a particular loop's performance has deteriorated be- yond acceptable limits.

An expert system (named QCLiP for Queen's- QUNO Control Loop Performance analysis expert system) has been implemented which is capable of monitoring and evaluating controller performance in the mill (Jofriet, et al., 1995). The expert system operates in the background: collecting sets of data from the plant, evaluating performance on the ba- sis of the previously outlined performance index, archiving relevant performance data, and report- ing problems by exception. Through the expert system's graphical user interface, real-time plant data and historical data for any control loop a.re available at any time, along with a host of perfor- mance-assessment tools.

1300 T.J. Harris et al.

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Fig. 1. Hardware schematic.

Pnw~ Sp~k~ Pmiodogl~ SmlM~alM PeCoOk~ Compo~ Ba~Nn~ Fowm Spec4runa Ba~ Pedodogrlm BleMI~ Pm~,o¢~ Compon~t~

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4.1 System hardware and software

The expert system is implemented in Gensym's G2, an advanced development and deployment tool for intelligent real-time systems. G2 has read-write connectivity to plant distributed control systems (DCS) through Gensym's GSI bridge products, al- lows remote procedure calls to C subroutines, and facilitates the creation of a dynamic graphical user interface. The mill's hardware (see Fig. 1) consists of a Fisher-Rosemount DCS, linked through a net- work interface unit to a DECnet data highway connecting various supervisory VAX-stations and data archiving facilities. The expert system itself resides on a VAX-station. Fisher's computer high- way interface package (CHIP) allows G2 to access data at relatively high speeds, with a maximum sampling rate of once per second. Ten data points can be read simultaneously at this maximum fre- quency without excessively burdening the system.

4.2 Control performance analysis toolbox

The requirement for an extensive toolbox of ana- lytical and/or statistical techniques was fulfilled using remote procedures. The expert system is linked to an external C program that contains functions that perform all of the statistical and time series analysis calculations required by the knowledge base. A summary of the major com- putational algorithms used to evaluate a control loop's performance is provided below. Note that any of these techniques may be also be applied to historical data sets.

The sample autocorrelation function. The sample autocorrelations of the deviations from setpoint are routinely estimated for every incoming data set. The autocorrelation function is useful for vi- sualizing the effectiveness of control, and also as a starting point for other computations.

Estimation of the performance index. QCLiP esti- mates the performance index ~/(b) for every valid data set retrieved from the mill.

Spectral density estimates. The smoothed sample spectrum presents a useful interpretation of the

Fig. 2. Sample cycling information workspace.

variance or energy distribution of a signal as a function of frequency. QUNO's engineering staff are most familiar with the spectrum as a tool for diagnosis. A power spectrum workspace (see Fig. 2), complete with peak identification algorithms and sliders to control lag window size, has been included in the expert system.

A portmanteau test for minimum variance control. The sample autocorrelation function provides the user with a visual test of the effectiveness of con- trol. Unfortunately, visual tests do not lend them- selves very well to rule-based interpretation. In- stead, a modified Box-Pierce statistic (Desborough and Harris, 1993) is used to test whether all of the autocorrelations beyond the deadtime are zero. This portmanteau test is useful in that it pro- vides a test for minimum variance control with- out the need for visual interpretation. In this way, the Box-Pierce test formalizes and automates the visual pass/fail test for minimum variance control.

The periodogram and Fisher's Test for periodic components. The periodogram is computed for Yt using a fast Fourier transform (FFT) algorithm. The periodogram frequency and ordinate vectors are used in subsequent tests for periodic compo- nents. One of the areas where it is hoped QCLiP will prove useful is in the detection of unexpected or hidden cycles. Since the periodogram ordinates are independent and identically distributed chi- squared random variables, groups of periodogram ordinates can be tested against the F-distribution (Wei, 1990). A ratio of each ordinate's variance to the total variance is computed and tested against the F-distribution. Thus a subset of statistically significant (frequency, power) ordered pairs are derived from the periodogram. This screened sub- set of periodogram ordinates is then passed to an algorithm (Fisher's Test) which tests each pair in- dividually to ascertain whether or not it is repre- sentative of a possible periodic component in the original data (see Fig. 2).

Plant-Wide Feedback Control Performance Assessment 1301

4.3 Interpretation hierarchy

For reasons relating to computational speed, all of the toolbox calculations described in the pre- vious section are carried out using remote proce- dure calls. However, the scheduling, decision mak- ing, and reporting processes are left to G2. Using rules, procedures and G2 built-in displays, the ex- pert system can interpret the data and present it to the user in a concise and organized fashion.

The analysis for each control loop follows a hier- archical process, eventually leading to a series of alarms or messages indicating the performance of a particular control loop. When the system sched- uler determines that a control loop should be up- dated (or the performance should be examined), a batch of data is collected for that particular con- trol loop.

In the next stage of the hierarchy, the validity of the collected data is confirmed by G2. For exam- ple, it is necessary to ensure that the plant or pro- cess continued to operate throughout the entirety of the data collection procedure. Confirmation is also necessary to ensure that a data set is com- plete (i.e., no missing datapoints), and that sam- ples have been taken at equispaced intervals.

Given a valid data set, a detailed statistical anal- ysis of the data is performed. The sample auto- correlation function, the smoothed sample spec- t rum, the minimum variance spectrum, the peri- odogram, and the performance index are calcu- lated for the control loop. The results of these calculations can be displayed for any loop at any time, allowing the user easy access to control per- formance diagnostics.

Fisher's test and the Box-Pierce test are carried out to further examine the data with the inten- tion of providing not only visualization of data, but also interpretation. Plotting the autocorrela- tion function or the sample spectrum provides a visual insight into the characteristics of a particu- lar da ta set. Fisher's test and the Box-Pierce test are required to furnish the user with a series of succinct alarms or messages to aid in the assess- ment of a loop's performance.

Operator alarms and messages are also generated by examining the performance index and the vari- ance of the data set as they change with time. These two variables are charted on a standard control chart (Mason, et al., 1989), used in combi- nation with the Western Electric rules. Each time the performance of a control loop is updated (once a day, once a week, etc.) the performance index and variance are stored (see Fig. 3). The con- trol chart is useful in identifying rapid short-term changes or longer-term disturbances.

[ ~ I ~ J M I mmll la

:: P.-? J Gonmml O h ~ o~ P ~ o ~ l

oo {poor p*~o,~el --> I o ( r e d p . ~ o ~ . )

Fig. 3. Control loop performance workspace for loop 33-211.

4.4 Experiential knowledge

summary

Plant data is almost always very noisy and highly correlated. Consequently, process knowledge and experience are vital for creating meaningful alarms. For instance, reporting that a control loop is cy- cling to a user could elicit the response that the loop always cycles. It is necessary to include in the expert system a method of retaining this process knowledge or expertise. If too many alarms are re- ported the effectiveness of the system is reduced.

Baseline data plays an important role in repre- senting user experience, and occasionally the user is required to select a set of data that represents the typical operation of a control loop. When the performance of a control loop is examined, the re- sults are compared to the results obtained for this baseline data set. In some instances it is accepted that a control loop may have a certain amount of cycling at a given frequency. If the user stores a typical baseline data set with this accepted cyclic component in it, then the expert system will not alert the user unless there is a change from the baseline case.

Knowledge of the overall variability of a process is also important to the user. For instance, if a control loop is cycling, but the total variance con- tribution of the cycle is only 2 % of the process variance, then perhaps the cycling alarm should not be reported. An expert system is the ideal en- vironment within which to capture this type of knowledge. By incorporating past experience and rules of thumb, QCLiP makes the results of the statistical analyses more meaningful to the user.

4.5 User interface

Process knowledge or experience is also required in the design of a user interface. In order to pro- vide the user with a meaningful presentation of its expertise, QCLiP is subdivided into a series of schematics that represent particular mill and

1302 T.J. Harris et al.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Fig. 4. Sample process area workspace.

! o ~ o ~ . ; k '.

P*~. , s p . . . . m . ~

P ~ G ~ s V i d ~ l o U l s ~ g r l m

S a ~ l . t . n 0 t ~ , i o ~ o o I . , ~ 0 ~ , ,~d*y of P . ~ ° , m s A ~ . . O.47O. smmpit l a r v a l , t s~onda C*I,~II~I. ~ l ~ s (2 ~cond.)

Fig. 5. Sample time series analysis workspace.

process areas of the QUNO operation (see Fig. 4). Through this hierarchy of schematics, the user can intuitively access the performance informa- tion associated with each control loop. Through the use of icons and color, the user can quickly use this interface to determine whether a loop is in alarm, what type of loop it is, what mode the loop is running in (i.e., automatic, manual, etc.) and the performance of the loop during the cur- rent month. The performance information is sum- marized by the small graph located below each control-loop icon in the system schematic views.

Selecting a control loop provides the user with a list of options to expand on the information pre- sented on the schematic. The user can display de- tailed performance information, current time se- ries analysis results (see Fig. 5), or the most recent textual summary of the interpretation resulting from the analysis of the gathered data set.

The interface is often the key to user acceptance, and therefore must be intuitive and easy to use. The interface is required to provide the user with a summary of problem areas that may exist in the mill, as well as a detailed presentation of the data collected and the analysis done.

5. CONCLUSIONS

An expert system for control-loop performance analysis has been installed at QUNO's Thorold Mill. The control loops for the thick stock system and the dry end of one paper machine are being

used to test the system. The performance-assess- ment techniques outlined in this paper are contin- uously being applied to these loops, and histori- cal performance data is accumulating. Initial re- sults indicate that the performance index is useful for indicating short-term changes in control-loop performance. Long-term results will follow, once QCLiP has spent more time on-line.

An additional benefit that has been realized from this project stems from the increased availability of process information. The QCLiP expert system has proved itself as a superior interface for users to acquire, examine and store process data. Mak- ing data and summary statistics available to plant personnel increases their awareness of the perfor- mance of individual control loops.

Acknowledgements

NSERC is acknowledged for their support in the form of a Cooperative Research and Development Grant. Also, the assistance of Mike Harvey, Senior Control Systems Engineer, QUNO Inc., is greatly appreciated.

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Stanfelj, N., T.E. Marlin and J.F. MacGregor (1993). Monitoring and diagnosing process control performance: The single-loop case. Ind. Eng. Chem. Res. 32, 301-314.

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