Performance Assessment of Plant-Wide Control Systems

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Performance Assessment of Plant-Wide Control Systems

Document by:Bharadwaj

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Abstract: This paper addresses performance assessment of plant-wide control (PWC)

systems, which is one of the important areas of PWC of industrial processes but has

received very little attention in the past. Some of the performance measures in the literature

are the steady-state disturbance sensitivity and the capacity-based economic approach.

However, there are some limitations in the measures that have been proposed for

performance assessment, from the plant-wide perspective. In this study, several measures

based on plant dynamics are described and discussed for evaluating the performance of

different PWC structures. These include overall process settling time based on absolute

accumulation in the system, dynamic disturbance sensitivity, net variation from the nominal

operating profit and deviation from the production target. These measures are then applied

to two alternative control structures for a styrene monomer plant, in order to test their

applicability. The results indicate that some of the presented measures are indeed effective

for evaluating and comparing PWC structures.

Keywords: Plant-wide control, Performance assessment, Settling time, Operating profit,

Dynamic disturbance sensitivity, Deviation from the production target.

Introduction

PWC design is essential because of complex, integrated nature of many chemical plants.

The development of a PWC system does not stop with the generation of the control

structures. The dynamic performance of the alternative control structures generated must be

evaluated in order to make the final control system selection. Thus, performance assessment

of PWC systems is important but has not received much attention in the past, especially in

the context of dynamic simulations.

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The presence of numerous combinations of controlled and manipulated variables in a

process leads to many alternative control structures. In the preliminary steps of the control

system development, steady-state and dynamic controllability measures such as relative gain

array (RGA), condition number (CN), Neiderlinski Index (NI), singular value

decomposition (SVD), etc. can be used for initial control structure screening. However, a

few alternative control structures may still remain in the end, and more rigorous analysis is

needed for the final selection to be made. Also, there is a possibility that measures like RGA

and NI may fail, and result in poor closed loop performance, as has been proven in several

case studies [1, 2]. These issues have led to the proposition of other performance measures

that give more consistent results even for highly complex processes.

Yi and Luyben [3] proposed a measure named steady-state disturbance sensitivity to

screen alternative control structures. Control structures that require a large change inmanipulated variables to handle the disturbances are not recommended, as they are more

prone to hit constraints and valve saturation limits. This measure can give us desirable

results under normal circumstances, but the decision would be difficult to make in cases

where the manipulated variable changes more for some disturbances and less for some other

disturbances in one control structure as opposed to the other control structures. Also, the

steady-state disturbance sensitivity does not consider the changes during the transient phase.

Elliott and Luyben [4, 5] and Elliott et al. [6] devised a generic methodology called the

capacity-based economic approach to compare and screen preliminary plant designs by

quantifying both steady-state economics and dynamic controllability. They basically

proposed a measure based on product quality regulation to measure the dynamic

performance of alternative control structures. Specifically, they calculate the loss in plant

capacity due to off-spec production. As with the previous measure, this approach is useful

under some situations. However, it cannot be always applied as the off-spec product is

assumed to be disposed, whereas the normal practice in industry is to recycle the off-spec

product in order to avoid yield losses and additional cost of disposal. Also, product quality

though important cannot be the only measure for evaluating the control system performance.

The dynamic performance of all control loops in the whole plant has to be considered too.

Keeping the above measures and limitations in mind, a new dynamic performance index

called dynamic disturbance sensitivity (DDS) has been recently developed by Konda and

Rangaiah [7]. DDS is equal to the sum of absolute accumulation of each and every

component in the process since the onset of the disturbance(s). Konda and Rangaiah [7]

have applied DDS to three different PWC structures of the toluene hydrodealkylation

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(HDA) process and proven its effectiveness for PWC performance assessment and

comparison. DDS measure offers several advantages over the other methods discussed

above. However, one major drawback of it and many other measures is that they do not

include the economic quantification of the dynamic performance.

Hence, a new economic measure based on deviation from the production target (DPT) of

the main product during the transient period is proposed in this study. In addition, two more

performance measures are discussed. These are the net variation in the plant operating profit

and the process settling time based on overall absolute component accumulation. The basic

idea behind these measures and their development are discussed, together with the

procedure for their computation. These measures are then applied to two different control

structures of the styrene monomer plant in order to test their applicability and usefulness.

The rest of the paper is organized as follows: the next section discusses the various performance measures, namely, the process settling time based on overall absolute

component accumulation, DDS, the net variation in the plant operating profit and DPT. The

subsequent section discusses the application of these measures to the styrene plant together

with an analysis of the results. The conclusions are finally presented in the last section.

Performance Measures for PWC Systems

A few performance measures based on plant dynamics are presented in this section. Not

much has been said or discussed on what constitutes a good performance measure. A

performance measure must be comprehensive (to include transients and steady-state

performance), consistent and robust (i.e., less affected by controller fine-tuning), able to

differentiate control structures, simple (to define and compute), and also give some

indication of the economics and control effort of the control system. A good measure should

meet most or all of these features.

Process Settling Time Based on Overall Absolute Component Accumulation

Settling time is defined as the time required for the process output to reach and remain

within certain (5% or 1%) of the final steady-state value of the process variable [8].

While this definition pertains to a single control loop, the question in a plant-wide context is

how to define the settling time of a highly integrated chemical process plant with many

controlled variables and controllers. We propose to calculate settling time based on transient

profile of absolute accumulation of all components in the plant, which is defined as follows:

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+=n

nConsumptioGenerationOutflowInflowonaccumulatiAbsolute

1

(1)

where n is the total number of components in the system. The inflow and outflow refers to

the component flows in the input and output streams of the plant at any time. The settlingtime thus calculated indicates the time taken by the PWC system to bring the overall process

to the steady state after the onset of the disturbance(s).

Dynamic Disturbance Sensitivity (DDS)

DDS is a new dynamic performance index developed by Konda and Rangaiah [7]. The basic

idea is to make effective use of rigorous process simulators in the performance assessment

of PWC systems. DDS makes use of the strong correlation between the overall control

system performance and the sum of the individual component accumulations. When a

process is affected by a disturbance, all the process variables go though different transients

and ultimately reach steady state only when the overall accumulation of all the components

in the plant becomes negligible. The time integral of sum of absolute accumulation of all

components in the plant is a measure of the PWC system performance. Accordingly, DDS is

defined as

( ) dticomponentofonaccumulatiabsoluteDDSst

t ntoi = =

=

0 1

(2)

where ts is the time taken for the process to reach steady state. Obviously, a smaller value of

DDS indicates better control.

Net Variation in the Plant Operating Profit

A profit function has been used in PWC methodologies for steady-state optimization. An

example is the self-optimizing control procedure of Skogestad [9]. We propose to compute

the operating profit during the transient state in the presence of disturbances. As it is

possible that the operating profit may settle at a different value due to changes in the

production rate, we propose using profit per unit production rate of the main product. This

goes back to almost the same value at the final steady state conditions (see Figure 1). The

net area gives an indication of the net variation in the plant operating profit. A positive

number indicates an overall increase in the plant operating profit whereas a negative number

indicates otherwise. A control system can be taken to be performing well if the computed

area is either equal to or greater than zero.

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Time

US$/kgP

roduct

Steady-State

Profit

Positive Area

Negative Area

Fig. 1. Transient profile of profit per unit production rate due to a disturbance

Deviation from the Production Target (DPT)

There could be one possible drawback with the computation of the net variation in plant

operating profit. It is possible to obtain a higher value of the computed area for an inferior

control structure primarily due to the large magnitude of the initial production rate transient.

This issue is discussed in detail later in the next section. Hence, to overcome this

shortcoming, we propose an indirect economic measure based on the production rate. The

idea is to compute the DPT (of the main product) during the transient state by computing the

net area as shown in Figure 2. DPT is defined as

( ) dtrateproductionettrateproductionactualDPTst

t

=

=0

arg (3)

When the plant management wants to increase (decrease) the production rate, the new

production target should be achieved at the earliest and any deviation from it is undesirable.

So, total deviation from the production rate during the transient can be used as a

performance measure of the control system. This can be calculated by the area under the

transient in Figure 2 for a production rate change. On the other hand, when the plant is

subjected to other unexpected disturbances, the computation of area is done based on the

original production rate. The effectiveness of this measure in indicating relative control

system performance is illustrated in the next section.

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Time

ProductionRate

Over production

Production ra

Initial production rate

Under Production

Fig. 2. Production rate transient in the presence of disturbance(s)

Application of the Performance Measures to the Styrene Monomer Plant

Process Description and Simulation

In the styrene process (Figure 3), fresh ethyl benzene (EB) and a part of the low-pressure

steam (LPS) are mixed and then pre-heated in a feed-effluent heat exchanger (FEHE) using

the reactor effluent stream. The remaining LPS is superheated in a furnace to 700-850C,

and then mixed with the pre-heated mixture to attain a temperature of around 650C. It is

then fed to two adiabatic plug-flow reactors (PFRs), in series with a heater in between, for

the production of styrene. The six main reactions that occur in the reactors are as follows:

22563256HCHCHHCCHCHHC + (4)

42663256HCHCCHCHHC + (5)

435623256CHCHHCHCHCHHC ++ (6)

2422 422 HCOHCOH ++ (7)

242 3HCOCHOH ++ (8)

222 HCOCOOH ++ (9)

The reactor effluent is cooled in the FEHE and then in a cooler before being sent to the

three-phase separator, where the light gases are removed as the light products and water is

removed as the heavy product. The intermediate organic layer is sent to two distillation

columns for styrene separation from the other components. In the first column (i.e., product

column), operating under vacuum to prevent styrene polymerization, styrene is removed as

the bottom product, and the top product is sent to a second column (i.e., recycle column) to

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separate un-reacted EB from the by-products, toluene and benzene. The un-reacted EB is

then recycled back.

For simulating the styrene plant in HYSYS, Peng-Robinson equation of state is chosen as

it is very reliable for predicting the properties of hydrocarbon components over a wide range

of conditions and appropriate for the components in the styrene process. The steady-state

model of the styrene process is developed and optimized in HYSYS. The optimal

conversion is 66.6%. The distillation columns are modeled by rigorous tray-by-tray

calculations. Preliminary estimates of the number of trays and feed tray location for each

column in the process are obtained by using the shortcut column in HYSYS, and then

optimized using the rigorous calculations. The final steady-state flowsheet developed is

shown in Figure 3.

Dynamic Simulation of the Selected Control Structures

Four different control structures have been recently developed for the styrene monomer

plant [10]. We consider two of the control structures here; these are summarized in Table 1.

HS is the control structure developed using the heuristics procedure of Luyben et al. [11].

One of the characteristic features of this procedure is to control a flow somewhere in the

recycle loop supposedly to overcome the snowball effect. IF is the control structure

developed using the integrated framework of simulation and heuristics [12]. One of the main

features of this procedure is the detailed analysis of the effects of recycle in order to

overcome its negative impact on control system performance.

There are several main differences between the two control structures in Table 1. Firstly,

throughput manipulation is achieved by changing EB feed flow in IF, while it is achieved by

changing total EB flow (feed plus recycle) in HS. Secondly, the recycle flow is explicitly

fixed in HS; this is achieved by controlling the total feed flow. Thirdly, IF utilizes the

conversion controller as a result of the detailed analysis of the effects of recycle. Finally, the

number of control loops is different: HS has 20 feedback control loops, while IF has 21

control loops, 2 of which form a cascade loop. The two control structures are implemented

in HYSYS dynamic mode; the controller tuning parameters are also given in Table 1.

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Fig. 3. Steady-state HYSYS flowsheet of the styrene monomer process.

Results and Discussion

Both the control systems are analyzed for their relative performance for production rate and

feed composition disturbances. The dynamic performance measures discussed in the

previous section are employed to analyze their performance.

Overall Process Settling Time

Settling times based on overall absolute component accumulation are computed for both the

control systems and presented in Table 2. The criterion for computing the settling time is

that the overall absolute component accumulation should be below 1 kmol/h (= 0.84% of the

styrene production rate of 120 kmol/h). The results in Table 2 show that IF performs better

in terms of the settling times, for the disturbances studied. This means that this structure is

able to attenuate the effect of disturbances quickly with smaller settling time for the

disturbances considered. The overall absolute component accumulation is a good basis for

computing settling time as it takes into account the entire plant performance during the

transient state and not just individual process variables or control loops.

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Table 1. HS and IF Control Structures for Styrene Plant

Controlled Variable

(See Figure 3 for

Abbreviations)

Manipulated Variable with Controller Parameters:

Kc (%/%), Ti (min) in Brackets

HS IF

Reaction Section

Total EB Flow EB Feed Flow (0.5, 0.3) -EB Feed Flow - EB Feed Flow (0.5, 0.3)

PFR1 Inlet Steam/EB Ratio Steam Feed Flow (0.36, 0.035)

LP1 Flow LP1 Flow (0.5, 0.3)

EB Conversion - PFR1 Inlet T SP (0.1, 0.5)

PFR1 Inlet Temperature Furnace Duty (0.11, 0.088)

PFR2 Inlet Temperature Intermediate Heater Duty (0.54, 0.087)

Phase Sep Temperature Cooling Water Flow (0.13, 0.14)

Phase Sep Pressure Lights Flow (2, 10)

Phase Sep Liquid % Level Organic Flow (18.8, 0.45)

Phase Sep Aqueous %Level Water Flow (1.31, 0.12)

Product Column

Condenser Pressure Condenser Duty (2, 10)

Condenser Level Distillate Flow (0.8) Distillate Flow (2)

Reboiler Level Bottoms Flow (0.5) Bottoms Flow (1.5)

Top Styrene Composition - Reflux Flow (0.5, 27.3)

Reflux Flow Reflux Flow (0.5, 0.3) -

Bottoms EB Composition Reboiler Duty (0.12, 108) Reboiler Duty (0.23, 54)

Vent Flow Compressor Duty (0.5, 0.3)

Recycle Column

Condenser Pressure Condenser Duty (1.5, 30) Condenser Duty (2, 20)

Condenser Level Reflux Flow (1.2) Reflux Flow (2)

Reboiler Level Bottoms Flow (2)

Top EB Composition Distillate Flow (0.43, 73.5)

Bottoms Toluene Composition Reboiler Duty (6.54, 1.05)

Table 2. Process Settling Times for HS and IF Control Structures based on Overall

Absolute Accumulation Profile

No. Disturbance Magnitude

Settling Time (minutes) for

Overall Absolute Accumulation

HS IF

d1

Production Rate

-5% 710 345

d2 +5% 700 335

d3 -20% 865 455

d4 Feed Composition -2% 595 245

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Dynamic Disturbance Sensitivity (DDS)

Since the computation of DDS is also based on overall component accumulation as

discussed earlier, it is imperative that the results based on both DDS and settling time based

on accumulation be compared. Accordingly, DDS values are computed and presented in

Table 3. Again, IF shows better performance than HS in terms of DDS. However, one major

difference between settling time and DDS is the ability of the latter to track the transient

behavior of the process variables. On the other hand, settling time ignores the magnitude of

the absolute component accumulation during the transient state, and hence is not a

comprehensive measure compared to DDS.

Table 3. DDS Values for HS and IF Control Structures

No. Disturbance Magnitude DDS (kmol)HS IF

d1

Production Rate

-5% 43 19

d2 +5% 44 18

d3 -20% 177 74

d4 Feed Composition -2% 21 11

Net Variation in the Plant Operating Profit

The data for the profit function per unit production rate is collected and the net area

indicated in Figure 1 is computed for both the control structures. This area that gives an

indication of the net variation in the plant operating profit, is given in Table 4. For easier

understanding, the net variation in profit per tonne of styrene is computed for the duration

for which the simulation is run in all cases (2000 minutes, i.e., approximately 1.4 days) by

the following equation:

tonne

kg

hrstyrenekg

hrVariationNet

styrenetonneVariationNet

1000

min2000

1min60$.$

=

(10)

These values are also given in Table 4. A positive value indicates profit increase and

vice-versa, and so a profit increase indicates better performance. As shown in Table 4, HS

shows better performance for d1 and d3, even though the other performance measures

applied so far indicate otherwise. This can be attributed to the greater production of styrene

during the transient state (as a result of larger fluctuations in the process variables) which is

manifested in higher profit. Actually, when the objective of the plant operator is to decrease

styrene production in the case of d1 and d3, a higher amount of styrene produced during the

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transient state is undesirable. The reason for this is that any excess amount of styrene

produced cannot be sold easily given the lower demand. Thus, there is a major drawback

with this economic measure as it does not take into account the over-produced amount of

styrene during the transient state. Hence, as discussed in the previous section, an alternative

economic measure (DPT) is evaluated next.

Table 4. Net Variation in the Plant Operating Profit with Units of (a) $/(kg of

Styrene/hr) and (b) $/(tonne of Styrene), for HS and IF Control Structures

No. Disturbance MagnitudeNet Variation ($/kg/hr) Net Variation ($/tonne)

HS IF HS IF

d1

Production Rate

-5% 0.20 0.13 5.9 4.0

d2 +5% -0.21 -0.12 -6.2 -3.7

d3 -20% 0.76 0.50 22.7 15.1d4 Feed Composition -2% -0.013 0.00 -0.38 0.07

Note: In this table, the largest value of the net variation for each disturbance is shown with grey background.

Deviation from the Production Target (DPT) of Styrene

The DPT of styrene over the duration of the total simulation time (2000 min) is computed.

The results presented in Table 5 give a clear picture. For d1 to d3, the target production rate

in equation 3 is the final production rate at the new steady-state. For d4, the target

production rate in equation 3 is the original production rate. A positive value of DPTindicates over production, while a negative value indicates under production. Since both

over and under production is undesirable, smaller (absolute) deviation from the desired

production rate target indicates better performance. In general, IF shows better performance

for all disturbances except d4. This means that a smaller amount of styrene over/under

production is achieved with this control system. This translates into a lower loss due to

unwanted amount of product being produced. Interestingly, IF shows poorer performance

for d4. This could be due to the fixing of EB feed flow in IF, whereas it is allowed to vary in

HS. For d4, this results in a 2% decrease in the fresh EB flow in IF as opposed to 0.75%

decrease in the case of HS. The greater decrease in the fresh EB flow is manifested as a

larger DPT as the styrene production rate is directly proportional to the fresh EB flow rate.

General Assessment of the Performance Measures

The performance measures presented in the previous section have been evaluated on two

different control structures for the styrene plant in this section. In general, control structure

IF performs better in terms of most of the measures except for the net variation in the plant

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operating profit, where a clear picture does not emerge from the results. However, as

discussed earlier, this measure does not indicate the superior performance of a control

structure. Of all the measures presented, we recommend DDS (as it gives an indication of

the ability of the control system in handling disturbances dynamically) and DPT (as it gives

an indication of the economic performance of the control system).

Table 5. DPT of Styrene for HS and IF Control Structures

No. Disturbance MagnitudeDPT of Styrene (kg)

HS IF

d1

Production Rate

-5% 2329 1558

d2 +5% -2275 -1376

d3 -20% 8844 5656

d4 Feed Composition -2% -2558 -5947

Note: In this table, the smallest DPT of styrene for each disturbance is shown with grey background.

A typical plant with a control system has many process and operating variables that have

to be monitored, and it can be quite time-consuming and difficult to analyze and compare

the numerous profiles of the different alternative control systems. Besides, such qualitative

analysis is subjective. Hence, quantitative measures based on process dynamics such as

presented here enable effective and easy analysis with minimal computational effort. All the

calculations presented can be easily automated and done using a spreadsheet.

Conclusions

Several performance measures based on plant dynamics for assessing PWC systems have

been presented in this work. The main aim of this is to present easier and more reliable

quantitative tools for assessing different PWC structures. The feasibility of using these

measures for performance assessment of PWC systems has been illustrated on two

alternative control structures for the styrene plant. In particular, DDS and DPT are

recommended in order to get an overall picture of PWC system performance covering

various aspects.

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Performance Assessment of Plant-Wide Control Systems