he jan2006 state space controller

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m odel predictive control (MPC) has been thedominant technology for implementingadvanced process control (APC) in petroleumrefining and some petrochemical processes for approxi-

mately 20 years1. MPC evolved to satisfy requirements in

this industry segment and is being applied to an increas-

ingly diverse range of processes elsewhere. Often the tech-

nology is a natural fit, but can require significant customi-

sation for specific applications. In any case, MPC provides

a standard approach to address important APC design and

implementation issues.Recent advances have led to the development of a

new generation MPC. The technology uses state-space

models, replacing finite step response models used in tra-

ditional MPC. The state-space technology is designed to

address requirements typical in many chemical

processes, making it a more natural fit for the industry.

The technology implements explicit state estimation to

achieve better prediction and especially enables

improved rejection of process disturbances. An infinite

horizon controller formulation makes it feasible to address

issues that were outside the scope of previous

approaches. The development of this new technology is

more fully described elsewhere2.

Early implementations of state-space MPC by

AspenTech have demonstrated its viability and perfor-

mance in several chemical process units, including different

types of reactor systems. It has also been shown that the

technology can be packaged with an ease of use focus to

enable engineers without specialised control system exper-

tise to implement these controllers. The new technology

provides capabilities that are complementary to those ofexisting process controllers, hence adding to the MPC

alternatives available across the broad spectrum of the

process industries.

This article presents a brief case study based on an

initial application of the APC state-space controller

(a module of the aspenONE advanced

process control solution) and illustrates

how process characteristics have

played a key role in guiding the

development of the technology.

REPRINTED FROM HYDROCARBON ENGINEERING JANUARY 2006

Brian Froisy,Aspen Technology, USA, describes how new model predictive

control technology can offer significant performance benefits when applied to

a wide range of common chemical process units.

Figure 1. State-space MPC is a natural fit in manychemical processes.


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MPC basics

From a high level, the major steps in all approaches toMPC can be summarised with the following questions:

Where is the process now?

Where is it going, if there is no intervention?

Where do we want it to go?

What is the best plan to get it there?

MPC requires a process model that describes the

dynamic relationship between manipulated variables (MVs)

and controlled variables (CVs). Control calculations are

essentially an optimisation to determine the best trajectory

of future MVs that satisfies economic or operational objec-

tives, subject to physical and operating constraints. MVs

are typically valve positions or setpoints to low level regu-

latory PID (proportional, integral, derivative) controllers.

CVs include process measurements such as temperature,

pressure, flow, level and quality variables directly mea-

sured by online analysers or inferred via calculations.

Models usually come from empirical identification based on

step test data. An understanding of the underlying physics

normally supplements empirical results to help validate the

model. Sometimes, a physical model validated from

selected test data is the starting point.

Traditional MPC normally uses finite step response

models, at least for the internal representation. Finite

response models are limited in their ability to faithfully

describe a wide range of dynamics. The inherent approxi-

mations become severe when describing a mix of fastdynamics (e.g. valve positions, flows, pressures) with slow

dynamics (e.g. composition in high purity distillation). State-

space models overcome this issue completely. Dynamic

range is important in chemical processes since recycles

(both material and energy) often introduce long response

times and complex dynamics. Other features leading to

long (several hours or more) responses include high purity

distillation (hundreds of trays), impurities that must be

purged (a very small purge flow relative to total process vol-

ume), catalyst deactivation, and slow byproduct reactions.

These are almost always coupled with fast responding (a

few minutes or less) process variables.

Model representation is just a starting point. In particu-

lar, a state-space model describing the relationship

between MVs and CVs can be extended to help describe

how unmeasured disturbances affect the process. Early,

accurate disturbance detection is a prerequisite for superior

control. This critical disturbance model extension makes it

possible to build controllers with the potential to reject dis-

turbances faster and more reliably than with traditional

MPC. In terms of the basic MPC questions, an extended

model provides the means to help determine the current

process state and its future trajectory.

The third MPC question, where do we want it to go?,

must be answered by describing operational and economic

objectives along with physical or other constraints to be sat-

isfied. At a high level, this is an optimisation problem nor-

mally based on the controller internal model. External opti-misation, for example based on a rigorous online model

consistent with the internal controller model, is also an

option.

The fourth question, what is the best plan to get

there?, is answered by solving yet another optimisation

problem, this time based on the infinite dynamic model and

controller objectives. A major technical breakthrough with

state-space MPC is the ability to calculate an infinite hori-

zon move plan that determines the true optimal MV action

plan. This is made possible by a combination of control the-

ory and numerical techniques.

The four MPC questions are answered at each con-

troller cycle, taking into account process measurementssince the last execution. Typical execution intervals range

from fractions of a minute to several minutes, depending on

the underlying process dynamics. Numerical optimisation

that exploits structure in this type of problem makes real

time solution practical.

Process exampleExtractive distillation illustrates the kind of process than can

benefit from the new technology. Multiple recycle streams

with both fast and slow dynamic responses makes it espe-

cially suitable for infinite state-space models. Economic

benefits come from maintaining stringent product qualities,

while maximising production rate and minimising energy.

Process disturbances tend to propagate due to material

and energy recycles. A control system that detects distur-

bance effects quickly and takes optimal corrective action

provides the foundation for realising economic benefits.

The process is highly interactive. Failure to account for

important interactive dynamics can actually cause a control

system to amplify disturbances, leading to plant operation

that is far from optimal.

Essential process features are illustrated in Figure 2.

Feed is a mixture of two close boiling components, denoted

by the red/green stream. Solvent (blue stream) vaporises

feed and separation takes place in the columns. Feed is

separated into individual, high purity products. Solvent is

recovered and recirculated. Recycle streams return mater-ial and energy to various points in the process, leading to

complex dynamics. Disturbances in recycles tend to upset

the entire unit, unless properly controlled. Long response

times (for compositions) are observed since there are


Figure 2. Extractive distillation process.

Figure 3. Step responses.


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hundreds of total trays. Short response times also exist

because of the solvent loop as well as various heat

exchangers, pressure effects and local level control loops

(these details are omitted from the diagram).

Step responses representative of this type of process

are shown in Figure 3, with a response time of four hours.

Some responses are fast, such as the CV1 response to a

step input for MV3 with important dynamics during the first

15 min. Others, such as the response of CV3 to MV2 take

approximately one hour to start and do not quite reach

steady state in four hours.

Another characteristic is the oscillatory tendency in sev-

eral responses, frequently caused by recycle effects. The

response of CV2 to MV3 is an example that also illustrates

how there can be a significant dynamic response without

any net final effect. Process recycles and feedback due to

lower level PID controllers can cause a zero gain

response like this one. Similar responses (CV1 to MV3)

have small non zero gains. The overall effect is that this is

a very difficult type of process to control.

The control strategy must honour an overall material

balance and ensure that products meet specification. This

requires a delicate balance between solvent rates and

product withdrawal, as well as the various internal flowsand energy exchange required to maintain internal stability

and material balances. MPC provides the framework to

achieve this basic operational objective. It can also imple-

ment optimisation by maximising production rate and min-

imising energy. These additional economic objectives are

demanding because optimal operation is normally at con-

straints (e.g. column pressure drop, heating or cooling lim-

its or flow limits as indicated by wide open valves). Control

near multiple interacting constraints is challenging. This is

where the capability of MPC becomes essential. For this

example the added dynamic response time range is well

accommodated using the state-space model formulation.

Measurements of process variables that are not explic-itly controlled are almost always available and can provide

valuable information about the process state. This is espe-

cially true for tightly integrated processes. Although inter-

actions cause control challenges, they can be exploited

with state estimation. Temperatures, pressure drop, internal

flows and levels are the types of measurements that pro-

vide supplemental information about the internal state of

the process. These are not independent inputs, nor are

they necessarily controlled to targets or within constraints.

They serve as a type of feedforward signal that can be

used with the process model to estimate the dynamic state

of the process. This helps to answer the first two basic MPC

questions. In control systems terminology, the estimate offuture CV behaviour is obtained using a so called Kalman

filter. This is markedly superior to the bias update approach

used by traditional MPC, which, by its formulation, does not

natively provide for use of extra dependent measurements.

The extended process model (i.e. disturbance model) is the

foundation for the Kalman filter.

Controller performanceThe actual application that formed the basis for this case

study has approximately 10 MVs and 25 CVs. There were

also five measured (traditional feedforward) disturbance

variables and approximately 25 additional measured

dependent variables. These, combined with basic MVs and

CVs, are included in the extended model to detect unmea-sured disturbances. The complete real world application

has too much detail to explain in this article. Instead, a sim-

ulation based on a simpler process fragment with similar

characteristics will provide an illustration of how controller

structure, state estimation in particular, can impact con-

troller performance.

Figure 4 is a block diagram of a distillation column. The

objective is to control the composition (A) using reboiler

heat input (F). The dynamic response between the reboiler

and composition includes a significant time delay. An inter-

mediate column temperature (T) is available but does not

have a specific control objective.

Disturbances can enter the process in various ways.Potential candidates include:

Heating medium temperature or steam quality.

Fuel heating value (for a fired reboiler).

Upstream pressure (assuming valve position is directly

manipulated).

Valve malfunction (sticky valve).

The control system must reject these and other distur-

bance effects quickly and reliably.

Figure 5 illustrates disturbance rejection performance

with three MPC structures corresponding to the numbered

response curves.

Case 1: Traditional MPC bias update is used for the dis-turbance model. There is no state estimation.

Case 2: State estimation with a disturbance model that

looks for disturbances entering at the reboiler, but with-

out an early warning variable.


Figure 4. Simulation process example.

Figure 5. Disturbance rejection comparison.


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Case 3: State estimation as in Case 2, with additional

use of the intermediate temperature as an early warn-

ing mechanism.

The plant model is identical for all cases, with the provi-

sion that Case 1 does not (due to its natural formulation)

include the extended disturbance model. Controller tuning

is also identical. Different responses are a result of the

state estimation structure only.

An unmeasured (reboiler) disturbance enters at time

zero. Disturbance rejection with traditional MPC is sluggishdue to the time delay between the disturbance event and

observing it via the composition deviation. Additionally, the

(implied) disturbance model that expects disturbances to

enter directly into the CV measurement does not match the

underlying physics.

The benefit of an explicit disturbance model and state

estimation is apparent in Case 2. There is still a time delay,

but quick effective action is taken once the CV measure-

ment deviates from its setpoint. Note that MV action is nec-

essarily more aggressive to counteract the disturbance.

The third case shows what happens when the interme-

diate temperature is included. Temperature is not con-

trolled, but provides the early warning to enhance state

estimation, resulting in even more effective disturbance

rejection. Due to the quick action, MV movement does not

have to be aggressive as in the second case.

State estimation with the intermediate temperature is

somewhat like cascade control in classical APC, with simi-

lar early warning benefits. The Kalman filter state estima-

tion approach, however, handles the general multivariable

case including the ability to use many intermediate vari-

ables (the slave loop in traditional cascade control).

Traditional cascade control also requires that the slave loop

response be much faster than the master loop (composition

in this case). The state-space MPC approach eliminates

this restriction.

ConclusionThe wide range of process characteristics in the chemical

industry translates into numerous control system chal-

lenges. It is not economically feasible to design and imple-

ment custom control solutions from scratch for each type ofprocess. MPC products address the issue, in part, by pro-

viding a mechanism for tailoring specific solutions without

starting from scratch. The availability of the new state-

space controller technology now makes it possible to

address a wider range of applications, such as the case

study presented here, with minimal customisation.

Moreover, this can be achieved while offering significant

performance enhancements compared with earlier genera-

tion technology. Reduced customisation also offers the

considerable additional benefit of long term maintainability.

Using a standard framework makes it possible to amortise

training across multiple applications and eases mainte-

nance costs as engineers are reassigned within anorganisation.

References1. QIN, S.J., and BADGWELL, T. A.l, A Survey of Industrial Model

Predictive Control Technology, Control Engineering Practice, 11/7,

733 - 764, (2003).

2. FROISY, J. B., Model Predictive Control - Building a Bridge Between

Theory and Practice, Proceedings of the Seventh International

Conference on Chemical Process Control, Lake Louise, Alberta

Canada, January 2006.__________________________________


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