Challenging control problems and emerging technologies in enterprise optimization

Control Engineering Practice 11 (2003) 847–858

Challenging control problems and emerging technologies in enterprise optimization Joseph Z. Lu* APC Research and Development, Honeywell Hi-Spec Solutions, 16404 N. Black Canyon, Highway, Phoenix, AZ 85308, USA Accepted 16 January 2003

Abstract As the scale of control systems increases from individual model predictive control (MPC) applications to integrated control systems for enterprise optimization, two challenges arise. First, the classic MPC regulatory control formulation is not always sufficient—the multivariable controller needs to be more than a regulator. Second, dynamic coordination among MPC controllers is a key to tight integration between advanced process control and plantwide optimization. The first half of this paper discusses the common control needs in the process industries and proposes a range control solution. The balance of the paper discusses the needs and complexity of the dynamic coordination problem, and proposes a three-tier integration method. Because enterprise optimization is a relatively new endeavor, this paper focuses on problems and issues, as well as solutions. The problems and proposed solutions are intended to stimulate discussion and attract more research interest. r 2003 Published by Elsevier Science Ltd. Keywords: Enterprise optimization; Range control; Model predictive control; Cooperative control system; Plantwide optimization

1. Overview 1.1. Wide use of MPC Model predictive control (MPC) has become a standard multivariable control solution in the continuous process industries, and it is becoming increasingly popular in the semi-batch and batch industries as well. More than 90% of industrial implementations of multivariable control solutions employ some form of MPC (Qin & Badgwell, 1996). MPC’s wide use establishes a solid foundation for large-scale optimization. The result is an increased industry focus on the automated optimization of an enterprise—a plant, a multifacility business, or perhaps even a cross-corporate industry sector. 1.2. Two-tier RTO solutions For a single-facility plant or portion thereof, a twotier solution as described in Table 1 has been proposed

*Tel.: +1-6023134912; fax: +1-6023133012. E-mail address: [email protected] (J.Z. Lu). 0967-0661/03/$ - see front matter r 2003 Published by Elsevier Science Ltd. doi:10.1016/S0967-0661(03)00006-6

by many academic and industrial researchers (Prett & Garcia, 1988; Marlin & Hrymak, 1996). This wellknown approach is referred to as steady-state real-time optimization (RTO). Integrated design: From a system design viewpoint, the two layers can be integrated. One way to integrate is to codesign the two layers. As a minimum, the design of one layer should take the other layer into account. The final goal of codesigning is tighter integration, stronger dynamic coordination, more flexibility, and higher user acceptability. Preferred flexibility: In a well-integrated system, the operator of an MPC controller should have an option regarding participation in the plantwide optimization. This decision is made locally, based primarily on the current conditions in the unit. When some MPC controllers do not participate, the optimizer should treat the non-participants as if in a feedforward mode, and then re-optimize the entire plant based on the participants. Cross-functionality: This integration commonly overlaps with multiple functional groups in a plant. Therefore, it is referred to as cross-functional integration (Lu, 1998; Kulhav!y, Lu, & Samad, 2001) throughout this paper.

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

848 Table 1 Two-tier solution for a single-facility plant

Regulatory Control

Tier

Composed of

Serves as

Top Bottom

Steady-state optimizer Layer of MPC controllers

Global decision-maker Implementation arms

• App. X

Regulatory/ Constraint Control

Servo Control

2. Three facets of control Under cross-functional integration, a control system is used to: * * * * *

maintain the stable operation of a process, reduce variability in the product specification, protect the physical and operational constraints, maintain a maximum operating efficiency, and sometimes maneuver the process from one operating point to another.

Three common elements comprise the objective of the control system, as listed in Table 2. Control emphasis: The emphasis on each element varies from application to application. Even within the same application, the emphasis often varies from time to time for different operations. Triangle coordinates (see Fig. 1) can be used to describe the control emphasis. For the purpose of discussion, each vertex of the triangle defines a ‘‘pure’’ form of control, or a facet. Each side then represents a combination of two facets. Furthermore, any point within the triangle represents a combination of three facets with different relative emphases. For two applications far apart in the triangle, a control strategy that works well for one application may not work well for the other. The same can be said when a process has quite different objectives under different operations. It is desirable to have a control design method that will unify all three control objectives in a single MPC framework. However, before the unified control problem and proposed formulation can be thoroughly discussed and presented, it is necessary to describe each ‘‘pure’’ control in detail to help clarify the problem. Table 2 Elements of the control objective No.

Element

Purpose

1

Regulatory control

2

Constraint handling

3

Maneuvering control

Reducing variability of a set of variables Preventing another set of variables from violating their bounds Moving the operating point from A to B (e.g., for better profitability)

• App. Y Constraint Control

Maneuvering Control Transition Control

Fig. 1. Using triangle coordinates to describe control emphasis.

2.1. Regulatory control A wealth of theories and design methods exists on regulatory control. In fact, the majority of MPC is developed in the context of regulatory control. Due to the size constraints of this paper, interested readers are referred to Prett and Garcia (1988), Prett and Morari (1987), Ricker (1990), Muske and Rawlings (1993), Morari and Ricker (1995), and Camacho and Bordons (1999). Control objective: In regulatory control, the common objectives are to reduce the controlled variable (CV) variance around the setpoint, to track setpoint changes, and to reject disturbances. Error penalty: It is important to note that the performance measure for regulatory control is doublesided. This means that the criterion cannot distinguish the error on one side of the reference point (or trajectory1) from that on the other side. All quadratic error performance indices, as well as absolute-error indices, fall into this category. Two common error examples are the integral (or summation) of the square error (ISE or SSE) and the integral (or summation) of the absolute value of the error (IAE or SAE). Neither the square error nor the absolute error distinguishes the error from either side. Fig. 2 depicts the shape of the error penalty for both cases, which is quite different from that of constraint control.

2.2. Constraint control Unlike regulatory control, constraint control requires control action only when the CV is, or will be, outside of 1 A reference trajectory is composed of many reference points temporally arranged.

4

4

3.5

3.5 Performance Measure

Performance Measure

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

3 2.5 2 1.5

849

ss

3 2.5 2 1.5 1 0.5

1

0 ss -2 -1 0 0 2 1 Negative error is below the low bound; positive error is above the high bound.

0.5 0 -2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Fig. 3. Error penalty in constraint control.

Negative error is on one side of the reference point; positive error is on the other side. Fig. 2. Error penalty in regulatory control.

its constraint. The need for constraint control stems from the fact that many control specifications are naturally one-sided. The typical examples are listed in Table 3. In constraint control, it is common for a CV to have both high and low constraints. A single high or low bound can be viewed conceptually as the special case of having both bounds, but with one of the limits set to infinite. This paper assumes that both high and low bounds exist for each constraint CV. Control objective: In constraint control, the objective is to prevent a CV from going outside of its limits. When a CV and its future predicted values are within the limits, little control is required. The penalty function for the CV to go outside the constraints should look like a bathtub (see Fig. 3). Note that regulatory control can be conceptually viewed as a special case of constraint control, where the high and low constraints are set equally. In the process industries, constraint control is typically treated as regulatory control. This practice has some significant drawbacks. For example, overcontrolling a CV that is well within its constraint can

cause unnecessary, and sometimes excessive, wear and tear on the control valve. Furthermore, the practice can make a controller less cooperative with other controllers, i.e., less likely to absorb conflicts with its neighboring units. In a plant with high material and energy integrations, overcontrolling can make a plantwide control problem formidable. These formidable conflicts (under regulatory control) and other related structural issues have been recognized and discussed by many authors (e.g., Ng & Stephanopoulos, 1998; Skogestad & Truls, 1998; Luyben, Tyreus, & Luyben, 1999). Note also that the number of CVs in a unit can be greater than the number of manipulated variables (MVs) (Sheehan & Reid, 1997; Smith, 1993). This is usually the case in constraint-dominant processes. Regulatory control for all CVs is not feasible. One of the heuristic solutions is to use a steady-state optimizer to select which CVs are controlled. The drawback of this approach is that the decision is based solely on steady state, and the heuristic will fail for processes where there are more integrating CVs than MVs (see the example in the next section). 2.3. Maneuvering control

Table 3 Typical control requirements Limit types

Examples

Operational Specification













The need for maneuvering control typically arises in conjunction with a larger scheme, which is related to: *

Safety

Surge Capacity Inventory

Flooding in a distillation column Reid vapor pressure of gasoline Impurity content in product Operating pressure in a vessel Temperature limit due to metallurgical property Explosive components in a processing unit Gasoline rundown temperature Level in a surge tank Pressure in a storage sphere Level in a pool tank

* *

production change, process coordination, or plantwide optimization.

Control objective: A common maneuvering control objective is to move a process from its current operating point to a new one. In some applications, a desired maneuvering trajectory is known a priori. In those cases, the maneuvering control is a form of servo control.

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

850

In other cases, only a destination, along with certain constraints, is known (but not the exact path). Those cases are often referred to as ‘‘transition control’’. Common examples of transition control include: * * *

grade changes, crude switches, and feed changes.

In the process industries, maneuvering control usually coexists with constraint control, and sometimes also with regulatory control. The performance requirement varies from application to application. Some applications call for a faster transition, while others focus on a smooth path for the overall transition (no overshoot, for example). Between transitions, many applications require the controller to operate in a specified operating zone with different control performance criteria (Lu, 1998). Application-wide economic optimization, or unit optimization as it is commonly referred to in industry, is also a form of maneuvering control. The objective of a unit optimizer is to move the process from the current operating point to the most profitable operating point without violating any operating constraints. Traditionally, maneuvering control is treated as a form of regulatory control, typically through a cascade control structure. The optimizer or the production scheduler ‘‘dials in’’ the setpoint, and it is up to the downstream controller to accomplish the maneuvering, often with regulatory control criteria. 2.4. Constraint and maneuvering control example Solvent dewaxing is a key unit for lubricant and wax production in refineries. In this unit, the following operations take place: 1. In multiple stages, waxy lubricant feed is diluted at approximately a 2-to-5 volume ratio with methyl ethyl ketone (MEK) and toluene to reduce the viscosity of the feed. 2. In the same multiple stages, the feed is also chilled to a temperature between 18 C and 26 C; and the wax crystallizes. 3. This wax slurry is then filtered to remove the wax.

4. The solvent is recovered from the filtrate by distillation. Facts to consider: In this unit, the solvent acts as an enabler in the production by modifying the crystal-wax solubility in the lubricant and by reducing the viscosity of the slurry. It moves along with the products through many processes, but it is almost 100% (less the loss) recovered. The solvent flow rate is rather significant, and it is about 3–4 times that of the feedstock. Therefore, the solvent inventory balance in the unit becomes an interesting and essential control problem in the entire production. Many tanks and vessels hold the solvent in various stages of the production. Only a few selected flows can be used for balancing the solvent inventory (the other flows are designated for production). Since the solvent is almost 100% recycled, it is not plausible to add new solvent to the system just for maintaining the level in any vessel. The solvent has to be appropriately distributed among various vessels for the overall production to run smoothly. Major challenges: There are two major disturbances to the inventory balance. One is grade change, a form of maneuvering control as discussed previously. The other is filter wash. Filters need to be taken off-line and washed with hot solvent when small wax (and some ice) crystals clog the filter cloth. During the wash, the filtrate flow of the filter reduces to zero, and the wash-off solvent goes into the ‘‘slop’’ solvent tank. Without a good multiinput, multioutput (MIMO) constraint control system to balance the inventory, disturbances can cause some of the vessels to overflow while others to run dry, interrupting the production. Inventory levels in multiple vessels need to be consolidated and appropriately distributed. Therefore, a multivariable control strategy is needed. Real-world application: Hall and Verne (1995) reported such an MIMO application, in which there are six tank levels (the controlled variables) and five flows (the manipulated variables). The dynamics are summarized in Table 4. The operating limits are shown in Tables 5 and 6 With six integrating CVs and only five MVs, applying regulatory control would make the system infeasible. Steady-state selection heuristics or partial control (Arbel

Table 4 MIMO constraint control system model dynamics

Primary filtrate level Repulp filtrate level Dry solvent drum level Moist solvent drum level Slop solvent tank level Slack wax tank level

Primary filtrate flow

Repulp kickback flow

0:00142 1s

0:00142 1s 0:00139 1s

0:0016 1s e5s 0:00162 1s e5s

Slop solvent flow

Slack wax flow

Fifth dilution flow ratio 1:13 1s e10s 1:11 1s

0:00216 1s 0:00123 1s

0:00108 1s e5s 0:0001 1s

0:173 1s

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858 Table 5 CV operating limits

851

3. Implement the first move and discard the rest. 4. Wait one sample time and repeat from step 1.

CV names

Operating limits (%)

Primary filtrate level Repulp kickback level Dry solvent drum level Moist solvent drum level Slop solvent tank level Slack wax tank level

720 715 70 715 720 720

In the open-loop control step 2, a slack variable, y; is introduced to form the aforementioned bathtub-shaped error-penalty function: min jjWðAx  yÞjj2 þ xT Lx

ð1Þ

x;y

y lopypy hi;

Table 6 MV operating limits

x lopxpx hi;

MV names

Operating limits

Primary filtrate flow Repulp filtrate flow Slop solvent flow Slack wax flow Fifth dilution ratio

7500 KL=D 100–300 KL=D 7150 KL=D 7200 KL=D 720 Vol%

mv lopSxpmv hi; 2 1 6 6^ & 6 61 ? 1 6 6 6 1 6 6 ^ 6 S¼6 6 1 6 6 6 6 6 6 6 4 0

et al., 1995) do not work well, since all CVs can violate constraints under disturbances. In the following discussions, a range control solution for a wider class of control problems, including this inventory constraint control problem, is proposed. 3. Model predictive range control

0

& ?

1 & 1 ^ & 1 ?

A model predictive range control (MPRC) is proposed in this section. This formulation unifies regulatory control and constraint control. In fact, regulatory control is treated as a special case of constraint control, where the high and low bounds happen to be equal. MPC scheme: Range control employs the MPC fourstep recursive scheme. The four steps are: 1. Predict the future response. 2. Compute an open-loop optimal control solution.

cv_hi: high beginning allows some overshoot The funnel end is set to the setpoint Optimal Response, y* Unforced Prediction

PV

cv_lo: low beginning allows inverse response MV Assumed Values

Past

7 7 7 7 7 7 7 7 7 7 7; 7 7 7 7 7 7 7 7 5

1

where A is the dynamic (step-response) matrix of the model, W is a diagonal weighting matrix, S is an accumulating-sum matrix, y hi and y lo are high and low y bounds, x hi and x lo are high and low MV slope bounds, mv hi and mv lo are high and low MV bounds, and xT Lx is the move-penalty term (L is semi-positive definite). This term is optional, depending on the funnel design and user preference. Funnel design: y lo and y hi for each CV can be specified in a funnel shape. For a regulatory CV, the funnel tail end narrows down to a single line at the value of the setpoint as shown in Fig. 4. For a constraint CV, the funnel tail end opens to the high and low CV limits.

3.1. Formulation

Known Values

3

Present

Future Minimum Effort Move, x*

Fig. 4. MPRC with a funnel design.

852

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

In either case, the funnel opening is wider than the tail end to allow some dynamic interaction. With a proper funnel design, the move-penalty term can be removed. As a result, the number of tuning knobs is reduced, and the control performance can be specified directly on a per-CV basis. Other geometric shapes, such as pipe or stairway, can be used if special control needs warrant them. For most applications in the process industries, a funnel provides a simple tuning parameterization, and yet it is versatile enough for various application needs. If a reference trajectory, y ref; is preferred, both y lo and y hi can be set to y ref: In this case, a move-penalty term xT Lx can be added to ensure the system stability, and formulation (1) of MPRC reverts to a classic regulatory formulation of MPC. Therefore, MPRC (1) is a generalization of a regulatory formulation of MPC. The bathtub-shaped error-penalty function is used to replace the parabolashaped one in regulatory control. Both regulatory control and constraint control are unified into range control. Following the same range control method, one can also generalize other forms of MPC. 3.2. Solution structure and analysis When y is not fully specified by y ref; both x and y need to be solved in (1). Moreover, there may exist an infinite number of solutions ðx; yÞ to (1). Further specification is needed to narrow the solution. If the application does not provide a preference, a minimum effort (in x) solution is commonly selected. A simple form of the minimum effort solution is the minimum 2-norm (of weighted x) solution. It can be conveniently computed by applying singular value decomposition (SVD) to the active rows of A: As a result, the solution, ðxn ; yn Þ; carries some physical meaning. xn is the minimum (2-norm) effort move, and yn is the minimum-effort (or optimal) response trajectory as depicted in Fig. 4. Furthermore, the minimum effort (2-norm) solution brings added, and sometimes significant, robustness to the closed-loop system. The added robustness comes from a unique source that has not been fully explored to date. It is gained from the slackness between the CV funnel bounds, rather than from knowledge of the model uncertainty. Note that all of the funnel ends for constraint CVs are open. For regulatory CVs, one can analyze MPRC from a frequency perspective. First, the equality bounds at the funnel end always require MPRC (1) to pseudo-invert the low-frequency dynamics. After that, MPRC (1) may invert additional high-frequency dynamics, but only as much as needed to meet the control performance. As an extreme, all inequality bounds can be non-active, and thus no additional dynamics are inverted. For constraint

CVs, a similar statement can be made with some care. This feature is attractive for many industrial applications where the model uncertainty in high frequency is known to be much greater than that in low frequency. 3.3. Augmented MPRC for maneuvering control MPRC (1) can be augmented to provide maneuvering control. This is particularly suitable when the final destination is known, but the exact path is not specified:

0 102 3 2 31

2

W

A y



B CB6 7 6 7C

min

@ Wp A@4 Ap 5x  4 yp 5A

x;y





W0 S1 xss þ xT Lx

ð2Þ

y lopypy hi; yp lopyp pyp hi; x lopxpx hi; mv lopSxpmv hi; 2 1 6 6^ & 6 61 ? 1 6 6 6 1 6 6 ^ & 6 S¼6 6 1 ? 1 6 6 & 6 6 6 6 6 4 0 2 1 ? 1 6 1 ? 1 6 S1 ¼ 6 4 &

0

1 ^ 1

3 7 7 7 7 7 7 7 7 7 7 7; 7 7 7 7 7 7 7 7 5

& ? 1 3

7 7 7: 5 1 ?

1

In the second and third block-rows, Ap and yp are for specifying shaping constraints for the maneuvering control, S1 is a summation matrix, one row per each MV, xss is the destination location for the maneuvering, and W; Wp and W0 are diagonal weighting matrices. The relative value of W0 determines the relative speed of maneuvering control. Note that the mathematical structure of augmented MPRC (2) is identical to that of MPRC (1), except that the number of rows in the system is increased. A solver for (1) can also solve (2). Likewise, the solutions to both (1) and (2) share the same mathematical properties. For instance, they both may have an infinite number of solutions, and a minimum effort (in x) solution can then be defined and solved.

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

853

Controlled Variables

15 10

4

5

3

5

0

6

2

-5 -10 -15

1 0

100

200

300

400

500

600

700

800

900

1000

Manipulated Variables 100% 2 50 1

Time[Min]

5

3

0 4

-50 -100%

5 0

100

200

300

400

500

600

700

800

900

1000

Min Fig. 5. Solvent-level control under a filter wash and a grade change.

Maneuvering control may be new to many readers. The destination location can come from different sources in different applications. To illustrate its wide applicability, two different sources are discussed for two common applications. If the destination, xss ; comes from a local economic optimizer, a unit optimization is implemented as a form of maneuvering control. In this case, all three common tasks of advanced process control (APC), namely, regulatory control, constraint control, and local economic optimization, are unified in a single range control formulation. The balances among the three tasks can be conveniently adjusted, and the relative speed of each control task can be specified explicitly. Honeywell’s Profit Controller (a.k.a. RMPCT2) employs such a formulation, and it has been successfully implemented in more than 1000 applications to date in various process industries. If xss comes from a production scheduler, or from a plantwide or local economic optimizer with a changed objective function, transition control is thus implemented as a form of maneuvering control. In this case, MPRC (2) finds a set of minimum effort transition moves within the allowable transition constraints.

inventory control problem. Hall and Verne (1995) reported the actual implementation and the resulting benefits. To further illustrate the property and performance of range control, two simulation results are discussed here. In Fig. 5, a filter wash and a grade change are simulated. A prolonged filter wash begins at time zero and ends at time 40. During the wash, one of the three filters is taken offline, and the total filtrate reduces by a third, causing a severe inventory imbalance. The control objective is to gradually recover from that without upsetting the production. The grade change from heavy to light oil occurs at time 400. The overall dilution ratio in the unit is reduced by 20%. The total amount of solvent holdup in the primary filter section is significantly reduced, and the overall inventory needs to be re-balanced. Fig. 5 depicts both simulations in a single run. All of the CVs are levels and are measured in percent. All of the MVs are re-scaled with their high–low limit ranges so that the moves fill up the plot span. As shown in Fig. 5, all six integrating CVs are controlled with five flows (sometimes four when MV 2 or MV 5 is saturated to its limit).

4. Simulation results for solvent inventory control problem

5. Cross-functional integration

Formulation (2) of MPRC and its solution have been successfully applied to the aforementioned solvent 2

RMPCT (Robust Multivariable Predictive Control Technology) is a Honeywell MPC product.

5.1. MPC coordination and enterprise optimization With MPRC (2), each MPC controller can provide regulatory and constraint control. With its maneuvering control capability, it can also provide local optimization.

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

854

Supply & Distribution

Material & Equipment Plan

Production Goals

Demand Forecast

Orders Business Planning Production Planning

Raw Material Allocation

Inventory Management

Consumer

Schedule & Optimization

Production Schedule

Control Measurement

On-Market Product Product Blending

Plant Optimized Production Fig. 6. A refinery example of enterprise optimization.

However, from a plantwide optimization perspective, each MPRC (or any MPC) controller without a global coordination can reach only its local optimum at best. In a complex plant, the composition of local optima can be significantly less than the potential global optimum. For example, the estimated latent global benefit for a typical refinery is 2–10 times more than what MPC by itself can capture (Bodington, 1995). Conceptually, one could extend the envelope of MPRC (2) to encompass an entire plant for both plantwide control and optimization. However, such a solution is often undesirable and difficult to implement, particularly for large plants. A common reason is its poor operability and flexibility. When the envelope of a system exceeds far beyond what an operator can possibly monitor during normal operation and during disruptive upset, a flexible, decentralized solution can be much more operable than an all-or-nothing centralized one. Lu (1998) discussed the need for building such a flexible, decentralized system in the context of nonlinear control systems. Fig. 6 summarizes such a layered enterprise optimization scheme. Each layer is built at an appropriate level of abstraction and over a suitable time horizon. The decentralized, lower layers capture the detailed information of local process units over a shorter time horizon, whereas the more centralized, higher layers capture the business essence of a plant over a longer horizon. Solutions supporting this entire integrated system are not complete, and unsolved or partially solved problems still exist. One challenge is how to integrate aspects such as measurements, control, optimization, scheduling, planning, forecasting, and business decision-making into a user-friendly layered system. As an initial attempt, some prototypes and emerging technologies have been developed (e.g.,

Watano et al., 1993; Bain et al., 1993; Kulhav!y et al., 2001; Samad & Weyrauch, 2000). Another challenge is how to solve a large-scale, mixed-integer control and optimization problem. The recent development in hybrid systems (e.g., Morari, 2001) seems very promising. This current paper, however, focuses on a specific, different challenge in the middle layers, namely the cross-functional integration for the continuous processes in a plant. 5.2. New plantwide control and optimization integration approach Traditionally, the optimization layer in many steadystate RTO approaches is executed at a much slower rate than the execution rate of its downstream MPC controllers. The limiting factor has been the requirement of detecting and waiting for a steady state. In a large plant, that could take a number of hours, and in some instances, even a few days. If a large gap exists between the two execution rates, it is difficult to integrate the two layers tightly or dynamically. One way to solve this problem is to extend the feedback control to the optimization layer. To accomplish this, a gain-only MPC3 scheme is proposed to establish the basis for optimization. At each execution, the constraints for optimization are predicted out to a future point, utilizing dynamic models. The predictions, available in each MPC controller, can be used as a starting point. The future point is referred to as the optimization point, and the distance between it and the origin (time zero) is referred 3

Gain-only MPC uses the same four-step scheme described in Section 3.1, except that in step 2, only the gain is used to resolve the steady-state error.

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

to as the optimization horizon. The optimization point can be a user-specified parameter, commonly selected as the nearest point after all the dynamics settle out. The plantwide optimization is performed at the optimization point, as opposed to at the origin as in steady-state RTO. In this proposed approach, the optimizer works like a gain-only predictive controller. The global economic optimization is thus defined in a future feasible space, bounded by the predicted constraints. The optimization can be executed in synchronization with its downstream MPC controllers, eliminating the need for detecting and waiting for a steady state. Many existing optimization methods in steady-state RTO can be retrofitted into this scheme, as long as some care is given in keeping the consistency between the firstprinciple non-linear model and the MPC linear models. Alternatively, one could reuse the controller model for optimization, particularly if the actual gain relationship is linear or near linear. Conceptually, one could also use a hybrid of first-principle and experimental models to strike a balance between the non-linearity and the simplicity. In the case of reusing the MPC controller models, some additional structure is required for describing the dynamic interactions among the MPC controllers. Those interactions are generally sparse, but they are important to ensure a completeness of the plantwide dynamic system. 5.3. A three-tier integration method A three-tier approach is proposed to integrate and coordinate MPC controllers. The top tier is for plantwide optimization based on the future constraints. The bottom tier is a layer of the MPRC controllers. The middle tier is a coordination ‘‘collar’’ for preventing each controller from receiving a locally infeasible maneuvering command. Formulation: The steps for integrating and coordinating MPC controllers are: Step 1: Perform plantwide optimization based on the predicted future constraints: min f ðug Þ ug

ð3Þ

cv lopGug pcv hi; mv lopug pmv hi; gðug Þpc: Step 2: For each of the MPC controllers, find a closest locally feasible point to the global optimum: X ðiÞ 2 min ðxðiÞ ð4Þ ss  ug Þ xðiÞ ss

855

ðiÞ cv loðiÞ pG ðiÞ xðiÞ ss pcv hi ; ðiÞ mv loðiÞ pxðiÞ ss pmv hi :

Step 3: Pass the solution of step 2 to the corresponding ith controller; use MPRC (2) to accomplish the global coordination and optimization:

0 102 3 2 31

2

W

y A



B CB6 7 6 y 7C

Wp min

@ A@4 Ap 5x  4 p 5A

x;y





W0 S1 xðiÞ ss

þ xT Lx

ð5Þ

y lopypy hi; yp lopyp pyp hi; x lopxpx hi; mv loðiÞ pSxpmv 2 1 6 6^ & 6 61 ? 1 6 6 6 6 6 6 S¼6 6 6 6 6 6 6 6 6 4 0 2 1 ? 1 6 6 S1 ¼ 6 4

hiðiÞ ; 0

1 ^

&

1

?

1 &

1

1 ^

&

1

?

3 7 7 7 7 7 7 7 7 7 7 7; 7 7 7 7 7 7 7 7 5

1 3 7 7 7: 5

? 1 & 1 ?

1

In step 1, the first two sets of constraints, cv lopGug pcv hi and mv lopug pmv hi; represent the composition of all the constraints that are transferred from each of the MPC controllers. G in the first set of constraints is the global gain matrix. With this constraint transfer, the optimizer will honor the same set of constraints within which the MPRC controllers try to control. Additional linear or non-linear constraints can be included in the third constraint set. In step 2, the two sets of constraints, ðiÞ ðiÞ ðiÞ ðiÞ cv loðiÞ pG ðiÞ xðiÞ ss pcv hi and mv lo pxss pmv hi ; represent the constraints corresponding to those in the ith controller at the end of its prediction horizon. Matrix G ðiÞ is the model gain for the ith controller, which also equals the ith diagonal block in matrix G: Step 2 is a coordination collar, through which one can protect the MPC controller from receiving a locally infeasible maneuvering destination. It is important to

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

app1

app1 15

1.5 CV1.1

10

1

cv 2

To further explain how the overall integrated system works, an illustrative two-unit control-optimization application is presented here. These two units are connected via other processes and intermediate storage tanks. To simplify matters, unessential parts of each application are taken out, and only the two relevant CVs and two relevant MVs of each unit remain. The simplified overall system dynamics are shown in Fig. 7. Both units have two CVs, two MVs, and one DV. They are connected by long delayed (mostly transport delay) bridge models. Neither controller has any knowledge of the other controller or the inter-application dynamics—the bridge models. Global coordination is therefore essential in resolving any interaction between the two units. The two MVs in the first unit are the product draws, which are further processed before being sent to the

0

0

100

200

0

300

app1

0.5

0

100

200

300

app1

4 Xss 1.2

0

3

-0.5

MV 1.1

-1 -1.5

MV 1.2 2 1

Xss 1.1 0

100

200

0

300

0

100

200

300

Fig. 8. Simulation results, first unit.

app2

app2 10

0.05 cv 2

cv 1

0.1

CV 2.1 0

-0.05 0

100

200

100

200

300

app2

2 1.5 mv 2

mv 1

CV 2.2

MV 2.1

0 -0.5

0

100

200

300

Xss 2.2

1

0.5

Xss 2.1 -1

5

0 0

300

app2

0.5

Fig. 7. Overall integrated system dynamics example.

CV 1.2

5

0.5

mv 2

5.4. An example

second unit as feed. The first MV in the second unit is a recycle stream that is sent back immediately. The first CV of each unit is a quality variable, which is controlled to a setpoint. The second CV of each unit is an operating constraint, which is controlled within its high and low bounds of 710: The high and low bounds for both MVs in each unit are 710: The first CV in each unit is also affected by the MVs in the other unit. These two CVs are selected to be regulated for the testing of the overall integrated system. An ability to resolve the dynamic interactions between these two units indicates the system’s capability for dynamic coordination. To this end, the setpoint of CV1 in Application 1 is raised from 0 to 1 at time 0. At the same time, the global optimizer starts to maximize CV2 in each unit. To achieve the setpoint change and the plantwide optimization, the system must potentially move the MVs over a large span while keeping the interacting CVs on their setpoints or within their bounds. Figs. 8 and 9 show the simulation results. The coordination capability of the system is best illustrated in the second application. In the first 60–120 min of the simulation, the global solution was not locally feasible

cv 1

note that a globally feasible solution may not be feasible to a local controller. Note that, in steps 1 and 2, different prediction horizons and different scopes (hence different G and G ðiÞ ) are used. In a plant, a local infeasibility in a process can often occur if it is connected to its upstream unit via an intermediate storage tank or other processing units. Refer to the example in Section 5.4 for more details. The coordination collar (4) provides a way to protect the ‘‘local interest’’, and, in fact, favors the local interest the most. If one prefers to balance the local and global interests, one could construct an objective function that would trade off the local interest for the global considerations, or even skip the collar completely. Note that the local and global interests always converge at the end of the optimization horizon, and that the conflict arises only in transient. In step 3, (5) is essentially the same as MPRC (2), which has been discussed. Note that not all forms of MPC can serve in step 3. Constraint consistency from steps 1–3 is essential to a successful integration.

mv 1

856

0

0

MV2. 2

100

200

Fig. 9. Simulation results, second unit.

300

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

to the second unit. The coordination collar modified the solution to the extent that even the direction of MV1 was altered. In Fig. 9, one can see that the global solution for the second unit was approximately [0.12, 1.85], whereas the coordinated maneuvering destination was ½0:73; 1:45 : The local infeasibility sustained until the material that the global optimizer had foreseen coming passed the bridge dynamics and arrived at the second unit. The results in Figs. 8 and 9 illustrate that the proposed three-tier cross-functional integration provides a strong dynamic coordination. Its overall dynamic decoupling capability appears reasonably close to that of a single MPRC controller for the combined system (the two units and the bridge model), assuming that the performance tunings on both cases are comparable. The field implementation feedback has been very positive, particularly to the feature that the flexibility of a decentralized control solution is gained without sacrificing much of the overall dynamic decoupling capability. 5.5. Field implementation results This new integration approach of optimization and MPRC control has been successfully commercialized. The technology has been deployed in both refineries and ethylene plants. The initial projects in cross-functional integration are yielding exciting results. A cross-functional RMPCT integration is discussed by Verne and Escarcega (1998); they report significant benefits. To date, the technology has been successfully implemented on many other units or multiunits (e.g., Wijck & Bassett, 1999) in a number of refineries worldwide. In addition, Nath and Alzein (1999) report an application of this technology to an entire ethylene facility at Petromont’s Varennes olefins plant. With the tight integration of plantwide control and optimization, the optimizer dynamically coordinates ten RMPCT controllers, covering the entire plant except for the debutanizer. The optimizer executes every minute, whereas a comparable RTO solution in a similar plant runs every 2–4 h: When a disturbance enters the plant and drives it away from the optimum, the optimizer compensates for it and finds the new optimum in just 1 min: The acceptance test for the project demonstrated a sustained increase of over 10% in average production. The production level surpassed the previous all-time record for the plant by over 3.7% and was well above the guaranteed 2.7% increase. In 2001, as of the writing of this paper, three more olefins-plant projects have been completed (e.g., Nath & Alzein, 2001). Seven more olefins-plant projects are in progress, with the largest implementation to date coordinating as many as 40 RMPCT controllers. The total number of CVs and additional constraints well

857

exceeds the 1000 mark, and the global optimizer is scheduled to run every 2 min: On the refinery side, over a dozen projects are in progress, with the largest implementation covering the entire continuous production of a small refinery. 6. Conclusion In the advancement toward enterprise optimization, new challenges are encountered. Two of them are discussed in this paper. The first challenge is how to extend regulatory control to satisfy other control needs. In the process industries, the other common needs are constraint control and maneuvering control. A model predictive range control (MPRC) formulation is proposed to unify all three types of control. Two applications of MPRC, transition control and economic optimization, are discussed. An example of six integrating CVs with only five flow MVs is given to illustrate the need for and the capability of range control. The second challenge is how to design a layered, decentralized control system for a tight integration of plantwide control and optimization. The difficulty is twofold. A tight integration of the plantwide control and optimization is the first challenge. A flexible balance between the user-preferred decentralized control solution and the capability of resolving interactions among the controllers is the other. A three-tier integration method is proposed, and an example is given to demonstrate its capability of unifying the plantwide control and the plantwide optimization. The field implementation of the solution has been very successful. In the search for a path to the completion of an enterprise optimization system, many problems are encountered. While some of them are now well analyzed and understood, others are not. Enterprise optimization is a very complex and multifaceted problem. In addition to studying and analyzing the problem, one can often understand the problem better by trying to find and analyze a solution. In this light, the proposed solutions, along with the discussion of the problems, are intended to explore further the design methods for enterprise optimization, stimulate more discussion, and attract more research interest.

References Arbel, A., et al. (1995). Dynamics and control of fluidized catalytic crackers. 1. Modeling of the current generation of FCC’s. Industrial and Engineering Chemistry Research, 34, 1228. Bain, M. L., et al. (1993). Gasoline blending with an integrated on-line optimization, scheduling, and control system. Proceedings of the national petroleum refiners association computer conference, New Orleans, Louisiana, November 15. Bodington, E. (1995). Planning, scheduling, and control integration in the process industries. New York: McGraw-Hill.

858

J.Z. Lu / Control Engineering Practice 11 (2003) 847–858

Camacho, E. F., & Bordons, C. (1999). Model predictive control. London: Springer. Hall, J., & Verne, T. (1995). Advanced controls improve operation of lubes plant dewaxing unit. Oil and Gas Journal, 24, 25–28. Kulhav!y, R., Lu, J., & Samad, T. (2001). Emerging technologies for enterprise optimization in the process industries. In J., Rawlings, B., Ogunnaike (Eds.), Chemical process control IV, p. 411. Lu, J. (1998). Multi-zone control under enterprise optimization: Needs, challenges and requirements. Proceedings of the international symposium on nonlinear MPC, Ascona, Switzerland, June. Luyben, W., Tyreus, B., & Luyben, K. (1999). Plantwide process control. New York: McGraw-Hill. Marlin, T., & Hrymak, A.N. (1996). Real-time operations optimization of continuous processes. Chemical process control-V conference, Tahoe City, Nevada, January 7–12. Morari, M. (2001). Hybrid system analysis and control via mixed integer optimization. In J., Rawlings, B., Ogunnaike (Eds.), Chemical process control IV. Morari, M., & Ricker, L. (1995). Model predictive control toolbox user’s guide. Natick, MA: The MathWorks. Muske, K., & Rawlings, J. (1993). Model predictive control with linear models. A.I.Ch.E. Journal, 39(2), 262–287. Nath, R., & Alzein, Z. (1999). On-line dynamic optimization of an ethylene plant using Profits Optimizer. In NPRA Computer conference, Kansas City, Missouri, November. Nath, R., & Alzein, Z. (2001). Dynamic real-time optimization and process control of twin olefins plants at DEA Wesseling Refinery. In Proceedings of the 13th annual ethylene producers conference, Houston, TX. Ng, C., & Stephanopoulos, G. (1998). Plant-wide control structure and strategies. In C., Georgakis (Ed.), Proceedings of the fifth IFAC

symposium on dynamics and control of process systems (pp. 1–16). IFAC. Prett, D., & Garcia, C. (1988). Fundamental process control (pp. 1–25). Stonelam, MA: Butterworth Publisher. Prett, D., & Morari, M. (1987). Shell process control workshop (pp. 351–360). Stonelam, MA: Butterworth Publisher. Qin, S. J., & Badgwell, T. A. (1996). An overview of industrial model predictive control technology. In J., Kantor, C., Garcia (Eds.), Chemical process control V. Ricker, N. L. (1990). Model predictive control with state estimation. Industrial and Engineering Chemistry Research, 29, 374. Samad, T., & Weyrauch, J. (Eds.) (2000). Automation, control and complexity: An integrated view. Chichester, UK: Wiley. Sheehan, B., & Reid, L. (1997). Robust controls optimize productivity, Chemical Engineering. Skogestad, S., & Truls, L. (1998). A review of plantwide control. Internal Report. Smith, F. B. (1993). An FCCU multivariable predictive control application in a DCS. Proceedings of the 48th annual symposium on instrumentation for the process industries. Verne, T., & Escarcega, J. (1998). Multi-unit refinery optimization: minimum investment, maximum return. The second international conference and exhibition on process optimization, Houston, Texas (pp. 1–7). Watano, T., et al. (1993). Integration of production, planning, operations and engineering at Idemistu Petrochemical Company. A.I.Ch.E. National Spring Meeting. Houston, Texas, April. Wijck, M., & Bassett, S. (1999). Oil terminal load distribution control and optimization. Hydrocarbon Engineering.