of possible control structures with respect to the number of
variables, a complete dynamic evaluation of all alternative
control structures is impractical for any realistic process. To
deal with this disadvantage, several researchers decomposed
the problem into a hierarchy of decisions,206–209 motivated
by Douglas’s hierarchical procedure for conceptual process
design.210 In this approach, some alternatives are eliminated
according to economic, environmental, or controllability considerations
at each level of hierarchy. Simulation-based
frameworks as listed above make use of exhaustive closedloop
dynamic simulations for controllability tests that allows
for realistic ranking of alternative designs. This type of
framework requires extended time for performing several
runs. Although a dynamic simulation is used, initially some
important and complex dynamic behavior may not be
observed for the specified conditions due to the limited number
of simulation tests that can be performed. When the process
comprises fast and slow modes, this approach is inefficient
and potentially not inclusive.
Recently, Molina et al. presented a new systematic methodology
for synthesizing a plant-wide control structure based
on retaining the most useful ideas provided by process-based
experience, engineering judgment and a rigorous mathematical
framework, applied to a simple flowsheet.211 The results
shown that this approach is helpful in deciding whether the
equipment sizing is suitable for guaranteeing plant-wide controllability.
This approach also gave useful guidelines for
analysis of the effects of process structures and control structures
on the operability or controllability of plant-wide processes
and the improvement that controllability characteristics
may reach. In the meantime, further study is required before
applying it to complex flowsheets.
Remarks
Generally, the integrated design methods can be classified
into two sets. The first set of approaches uses methods that
enable the screening of alternative designs for controllability.
The first step in these methods is the consideration of the
steady-state operation that will be most desirable. They then
seek to develop steady-state designs that are economically
optimal but are also dynamically operable in a region around
the specified steady-states. The final decision will be determined
by a trade-off between an economic performance
measure and controllability indices, as listed in Table 1. The
main disadvantage is that the results are only reliable around
the specific steady state and it is usually not clear how controllability
indices are related to the real performance
requirements. The second set of approaches are dynamic
approaches212–214 that take the view that all processes are
inherently dynamic and that dynamic operation is inevitable
or in some cases preferable to steady-state operation. Therefore,
they explicitly consider the dynamic performance using
dynamic models at the design stage. These methods are not
restricted to a small operating region around steady-states,
thus the final decision drawn are reliable over a large region
of operation in the face of disturbances. Although uncertainty
or disturbances seem to be solved in the design stages,
uncertainty in the models will arise in practice. Moreover, as
the cost of obtaining a ‘‘detailed’’ dynamic model is expensive
and the computational effort required is significant, their
applications are currently restricted to small scale problems.
181
Therefore, it is desirable that a method should be one that
only uses open-loop steady-state data as considering dynamic
characteristics of a process design. The bifurcation analysisbased
methods discussed in the next section, which use only
the open-loop steady-state data, can predict some dynamic
characteristics of a process design, so can also provide important
guidance for making processes more controllable by
eliminating or avoiding some undesirable behaviors.
Bifurcation Analysis-Based Method
for Process Design
Bifurcation analysis, a method for studying how qualitative
behavior of a nonlinear system changes as the parameters
vary, is a powerful nonlinear analysis tool that characterizes
complex nonlinearities and examines the causes of
steady-state multiplicity and periodic operations by using
only steady-state data and applying this to process design.
The applications of bifurcation analysis as a powerful nonlinear
system analysis tool for chemical processes have been
widely reported.215–225 Morari suggested that bifurcation
analysis should be used in controllability analysis for nonlinear
systems.226 Input/output multiplicity is a complex phenomenon
that can be encountered in chemical processes and
will adversely affect the performance of the closed-loop system,
subject to the changing operating conditions. Russo and
Bequette studied the effect of design parameters on the multiplicity
behavior of jacketed exothermic CSTRs.217 Gudekar
and Riggs performed open-loop and closed-loop nonlinear
stability analyses of an industrial ethylene oxide reactor
using bifurcation analysis.227 The nonlinear stability analysis
indicated that an ethylene oxide process with a detuned temperature
controller is most prone to reactor runaway. Much
research has shown that nonlinear dynamic phenomena due
to input multiplicity can compromise the robustness of a
control system. Kuhlman and Bogle addressed the question
of the relationship between input multiplicity and nonminimum
phase behavior and between controllability and optimal
operation for nonlinear SISO systems.228 Bifurcation analysis
could be sufficient to obtain a qualitative picture of the solution
space for a nonlinear process as a parameter of the process
variables at the design stage. This can be used to identify
the potential control difficulties determined by the process
design and to investigate the influences of the design
and operating parameters and disturbances on control, hence
providing guidance to eliminate control difficulties by modifying
the process design at the design stage. Bifurcation
analysis gives a guideline for modifying a process to avoid
undesirable behavior.
Ma and Bogle presented an approach for modifying a process
design to improve its controllability based on bifurcation
analysis and optimization.229–231 In their work, based on
bifurcation analysis, they first developed a methodology for
determining potential control problems associated with the
inherent characteristics of a nonlinear process over the entire
operating region of interest and analyzing the parameter
effects on these problems. They then presented a method for
modifying an existing process design to improve controllability,
as keeping modifications as minor as possible.
of possible control structures with respect to the number of
variables, a complete dynamic evaluation of all alternative
control structures is impractical for any realistic process. To
deal with this disadvantage, several researchers decomposed
the problem into a hierarchy of decisions,206–209 motivated
by Douglas’s hierarchical procedure for conceptual process
design.210 In this approach, some alternatives are eliminated
according to economic, environmental, or controllability considerations
at each level of hierarchy. Simulation-based
frameworks as listed above make use of exhaustive closedloop
dynamic simulations for controllability tests that allows
for realistic ranking of alternative designs. This type of
framework requires extended time for performing several
runs. Although a dynamic simulation is used, initially some
important and complex dynamic behavior may not be
observed for the specified conditions due to the limited number
of simulation tests that can be performed. When the process
comprises fast and slow modes, this approach is inefficient
and potentially not inclusive.
Recently, Molina et al. presented a new systematic methodology
for synthesizing a plant-wide control structure based
on retaining the most useful ideas provided by process-based
experience, engineering judgment and a rigorous mathematical
framework, applied to a simple flowsheet.211 The results
shown that this approach is helpful in deciding whether the
equipment sizing is suitable for guaranteeing plant-wide controllability.
This approach also gave useful guidelines for
analysis of the effects of process structures and control structures
on the operability or controllability of plant-wide processes
and the improvement that controllability characteristics
may reach. In the meantime, further study is required before
applying it to complex flowsheets.
Remarks
Generally, the integrated design methods can be classified
into two sets. The first set of approaches uses methods that
enable the screening of alternative designs for controllability.
The first step in these methods is the consideration of the
steady-state operation that will be most desirable. They then
seek to develop steady-state designs that are economically
optimal but are also dynamically operable in a region around
the specified steady-states. The final decision will be determined
by a trade-off between an economic performance
measure and controllability indices, as listed in Table 1. The
main disadvantage is that the results are only reliable around
the specific steady state and it is usually not clear how controllability
indices are related to the real performance
requirements. The second set of approaches are dynamic
approaches212–214 that take the view that all processes are
inherently dynamic and that dynamic operation is inevitable
or in some cases preferable to steady-state operation. Therefore,
they explicitly consider the dynamic performance using
dynamic models at the design stage. These methods are not
restricted to a small operating region around steady-states,
thus the final decision drawn are reliable over a large region
of operation in the face of disturbances. Although uncertainty
or disturbances seem to be solved in the design stages,
uncertainty in the models will arise in practice. Moreover, as
the cost of obtaining a ‘‘detailed’’ dynamic model is expensive
and the computational effort required is significant, their
applications are currently restricted to small scale problems.
181
Therefore, it is desirable that a method should be one that
only uses open-loop steady-state data as considering dynamic
characteristics of a process design. The bifurcation analysisbased
methods discussed in the next section, which use only
the open-loop steady-state data, can predict some dynamic
characteristics of a process design, so can also provide important
guidance for making processes more controllable by
eliminating or avoiding some undesirable behaviors.
Bifurcation Analysis-Based Method
for Process Design
Bifurcation analysis, a method for studying how qualitative
behavior of a nonlinear system changes as the parameters
vary, is a powerful nonlinear analysis tool that characterizes
complex nonlinearities and examines the causes of
steady-state multiplicity and periodic operations by using
only steady-state data and applying this to process design.
The applications of bifurcation analysis as a powerful nonlinear
system analysis tool for chemical processes have been
widely reported.215–225 Morari suggested that bifurcation
analysis should be used in controllability analysis for nonlinear
systems.226 Input/output multiplicity is a complex phenomenon
that can be encountered in chemical processes and
will adversely affect the performance of the closed-loop system,
subject to the changing operating conditions. Russo and
Bequette studied the effect of design parameters on the multiplicity
behavior of jacketed exothermic CSTRs.217 Gudekar
and Riggs performed open-loop and closed-loop nonlinear
stability analyses of an industrial ethylene oxide reactor
using bifurcation analysis.227 The nonlinear stability analysis
indicated that an ethylene oxide process with a detuned temperature
controller is most prone to reactor runaway. Much
research has shown that nonlinear dynamic phenomena due
to input multiplicity can compromise the robustness of a
control system. Kuhlman and Bogle addressed the question
of the relationship between input multiplicity and nonminimum
phase behavior and between controllability and optimal
operation for nonlinear SISO systems.228 Bifurcation analysis
could be sufficient to obtain a qualitative picture of the solution
space for a nonlinear process as a parameter of the process
variables at the design stage. This can be used to identify
the potential control difficulties determined by the process
design and to investigate the influences of the design
and operating parameters and disturbances on control, hence
providing guidance to eliminate control difficulties by modifying
the process design at the design stage. Bifurcation
analysis gives a guideline for modifying a process to avoid
undesirable behavior.
Ma and Bogle presented an approach for modifying a process
design to improve its controllability based on bifurcation
analysis and optimization.229–231 In their work, based on
bifurcation analysis, they first developed a methodology for
determining potential control problems associated with the
inherent characteristics of a nonlinear process over the entire
operating region of interest and analyzing the parameter
effects on these problems. They then presented a method for
modifying an existing process design to improve controllability,
as keeping modifications as minor as possible.
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