Main

!! %blue%Background on Process Systems Engineering%black%

!! %blue%Optimization%black% with %blue%A%red%P%black%Monitor

There are many tools for process system engineering, so it is important to differentiate what a software tool can accomplish. Below are some of the key strengths of %blue%A%red%P%black%Monitor:

* %blue%A%red%P%black%Monitor Strengths

** modeling system for simulation, optimization, and control

** solution of differential and algebraic (DAE) equations

** efficient for large-scale systems

** algorithms for linear and nonlinear discrete and continuous optimization

** real-time optimization and control

*%blue%A%red%P%black%Monitor Areas Under Development

** solution of integral or PDE systems

** algorithms for global and stochastic optimization

** information management systems and data bases

** advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process from an initial process design to a minute to minute cycles of model predictive control.
~~** algorithms for linear and nonlinear discrete and continuous optimization~~
~~To complement the role of process design and synthesis, research in ~~process ~~operations seeks to improve existing operating processes. Through the development of strategies and analysis tools, improvements can be found through on-line optimization of a process, scheduling of operating strategies, changeovers and interactions between different processes, and overall planning of product productions to meet market ~~demands~~. The research tasks involved in this task take the following categories~~.

----

!! %blue%Estimation%black%

Estimation is the allignment of a process model with actual process measurements. This can be accomplished by adjusting model parameters or current state estimates. For linear models, the Kalman filter is a popular choice because of low computational requirements and ease of implementation. Moving Horizon Estimation (MHE), on the other hand, is an optimization approach that better handles problems with

* Constraints

* Nonlinear Models

* Infrequent Measurements

* Explicit Measurement Ranking

* Statistically Insignificant Noise and Outliers

Results of the estimation may also include a probability distribution of the current process state.
~~!!! Process Simulation~~

Challenges in process simulation include the incorporation of more difficult and detailed process models. These include modeling of process dynamics as well as steady state, incorporation of transport models for separation, the simulation of highly nonideal systems with multiple phases, and the development of rigorous, first principle reactor models. These models require simulators to evolve from modeling and solving algebraic systems of equations to differential algebraic models and also to consider PDEs. In addition, the availability and application of optimization methods has led to a powerful extension of simulation tools.

!!! Design under uncertainty

Over the life cycle of the process, input conditions and product demands change, feedstock and product specifications may vary and the process will be subject to short and long term uncertainties. Moreover, process models are also subject to uncertainty.

The challenge therefore is to develop a design that is tolerant to levels of uncertainty and exhibits a profitable expected performance. An important case is also the one of processes under multiperiod operation that are subjected to a finite number of process variations.

~~Typically the bread and butter of industrial designs, this task deals with the analysis of a given process. ~~Challenges in process simulation include the incorporation of more difficult and detailed process models. These include modeling of process dynamics as well as steady state, incorporation of transport models for separation, the simulation of highly nonideal systems with multiple phases, and the development of rigorous, first principle reactor models. These models require simulators to evolve from modeling and solving algebraic systems of equations to differential algebraic models and also to consider PDEs. In addition, the availability and application of optimization methods has led to a powerful extension of simulation tools.

!!! Flexibility and Operability

This task is devoted to the development quantitative measures of process flexibility as well as strategies that improve these measures for chemical processes. Here improvements in both design and operation can be considered to increase the process' tolerance to uncertainty. This also allows the process to deal with a wider range of operations and production scenarios. The formulation of flexibility problems, either in terms of deterministic or stochastic measures, leads to large, complex optimization problems and with challenges for the application on realistic processes.
~~#~~ modeling ~~systems~~ for simulation, optimization, and control

~~# algorithms for~~ differential and algebraic (DAE) equations

~~# algorithms~~ for ~~integral or PDE ~~systems

~~# algorithms for linear ~~and ~~nonlinear discrete and continuous optimization~~

#algorithms for ~~global and stochastic optimization~~

# information managementsystems ~~and data bases~~

# advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization~~, and control environment for differential and algebraic equation (DAE) models (items 1 & 2). The ~~%blue%A%red%P%black%Monitor software ~~does not attempt to solve problems in the areas 3-7. While these capabilities may change with future development efforts, there are likely better software tools for these activities~~. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation models.

!! %blue%Integration Of Design, Control And Operations%black%

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

!! %blue%Supporting Tools And Methods For Process Systems Engineering%black%

All the above areas in process systems engineering are supported by a large number of tools and algorithms which are the subject of active research efforts. These include

* modeling systems for simulation, optimization and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for linear and nonlinear discrete and continuous optimization

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation

----
~~!!! Integration Of Design, Control And Operations~~

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

## Process Systems Engineering

## Main.Background History

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(:title~~ Background on~~ Process Systems Engineering:)

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(:title Process Systems Engineering:)

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!! %blue%Background on Process Systems Engineering%black%

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Attach:frequency.png~~|~~'''Figure 1.''' The typical frequency ranges from once for process design to a minute by minute cycle for model predictive control. Sharing information between layers is a key to synergies for model development and refinement over the lifecycle of the process. %blue%A%red%P%black%Monitor facilitates the sharing of information by providing a common simulation environment.

to:

Attach:frequency.png

'''Figure 1.''' The typical frequency ranges from once for process design to a minute by minute cycle for model predictive control. Sharing information between layers is a key to synergies for model development and refinement over the lifecycle of the process. %blue%A%red%P%black%Monitor facilitates the sharing of information by providing a common simulation environment.

'''Figure 1.''' The typical frequency ranges from once for process design to a minute by minute cycle for model predictive control. Sharing information between layers is a key to synergies for model development and refinement over the lifecycle of the process. %blue%A%red%P%black%Monitor facilitates the sharing of information by providing a common simulation environment.

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(:title Background on Process Systems Engineering:)

(:keywords nonlinear, model, predictive control, APMonitor, differential, algebraic, modeling language:)

(:description Simulation, optimization, estimation, and control with APMonitor:)

(:keywords nonlinear, model, predictive control, APMonitor, differential, algebraic, modeling language:)

(:description Simulation, optimization, estimation, and control with APMonitor:)

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The areas of '''simulation''', '''estimation''', '''control''', and '''optimization''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. ~~There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.~~

* %blue%A%red%P%black%Monitor Strengths

** modeling system for simulation, optimization, and control

** solution of differential and algebraic (DAE) equations

** efficient for large-scale systems

** algorithms for linear and nonlinear discrete and continuous optimization

** real-time optimization and control

*%blue%A%red%P%black%Monitor Areas Under Development

** solution of integral or PDE systems

** algorithms for global and stochastic optimization

** information management systems and data bases

** advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process from an initial process design to a minute to minute cycles of model predictive control.

* %blue%A%red%P%black%Monitor Strengths

** modeling system for simulation, optimization, and control

** solution of differential and algebraic (DAE) equations

** efficient for large-scale systems

** algorithms for linear and nonlinear discrete and continuous optimization

** real-time optimization and control

*%blue%A%red%P%black%Monitor Areas Under Development

** solution of integral or PDE systems

** algorithms for global and stochastic optimization

** information management systems and data bases

** advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process from an initial process design to a minute to minute cycles of model predictive control.

to:

The areas of '''simulation''', '''estimation''', '''control''', and '''optimization''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently.

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!! %blue%Optimization%black% with %blue%A%red%P%black%Monitor

There are many tools for process system engineering, so it is important to differentiate what a software tool can accomplish. Below are some of the key strengths of %blue%A%red%P%black%Monitor:

* %blue%A%red%P%black%Monitor Strengths

** modeling system for simulation, optimization, and control

** solution of differential and algebraic (DAE) equations

** efficient for large-scale systems

** algorithms for linear and nonlinear discrete and continuous optimization

** real-time optimization and control

*%blue%A%red%P%black%Monitor Areas Under Development

** solution of integral or PDE systems

** algorithms for global and stochastic optimization

** information management systems and data bases

** advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process from an initial process design to a minute to minute cycles of model predictive control.

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** algorithms for linear and nonlinear discrete and continuous optimization

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to:

Improvements can be found through on-line optimization of a process, scheduling of operating strategies, changeovers and interactions between different processes, and overall planning of product productions to meet market demands.

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With ~~short term (e.g., hourly) changes in feedstock and product demands, the availability of detailed process~~ models ~~and powerful optimization tools, it is now possible~~ to ~~optimize steady state models on-line ~~and ~~to readjust the setpoints of the control system. This leads to processes that can adapt to daily fluctuations in inputs and uncertainties. These can therefore lead too much higher profits.~~ The current challenge is to deal with dynamic models in addition to steady state cases and also to provide a tighter coupling to the process control system.

to:

With changes in pricing structures or product demands it is often advantageous to optimize steady state models on-line. This leads to processes that can adapt to daily fluctuations in inputs and uncertainties. The current challenge is to deal with dynamic models in addition to steady state cases and also to provide a tighter coupling to the process control system.

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Scheduling of batch and continuous processes can have a major impact on the overall profitability of a process, as well as on the timely delivery of products. Major problems include sequencing, scheduling of equipment utilization and maintenance over a planning horizon, and inventory considerations of a process. Such problems ~~form perhaps~~ difficult combinatorial optimization problems but also contribute to high payoffs. Moreover, the results of this task have a major impact on the local operation of the process, and strong interactions exist between the scheduling, design and operation of the process.

to:

Scheduling of batch and continuous processes can have a major impact on the overall profitability of a process, as well as on the timely delivery of products. Major problems include sequencing, scheduling of equipment utilization and maintenance over a planning horizon, and inventory considerations of a process. Such problems may pose difficult combinatorial optimization problems but also contribute to high payoffs. Moreover, the results of this task have a major impact on the local operation of the process, and strong interactions exist between the scheduling, design and operation of the process.

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*%blue%A%red%P%black%Monitor Strengths

to:

* %blue%A%red%P%black%Monitor Strengths

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Attach:frequency.png|'''Figure~~:~~''' ~~Typical Frequency of Simulation, Control, and Optimization~~

to:

Attach:frequency.png|'''Figure 1.''' The typical frequency ranges from once for process design to a minute by minute cycle for model predictive control. Sharing information between layers is a key to synergies for model development and refinement over the lifecycle of the process. %blue%A%red%P%black%Monitor facilitates the sharing of information by providing a common simulation environment.

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Estimation is the allignment of a process model with actual process measurements. This can be accomplished by adjusting model parameters or current state estimates. For linear models, the Kalman filter is a popular choice because of low computational requirements and ease of implementation. Moving Horizon Estimation (MHE), on the other hand, is an optimization approach that better handles problems ~~with~~

to:

Estimation is the allignment of a process model with actual process measurements. This can be accomplished by adjusting model parameters or current state estimates. For linear models, the Kalman filter is a popular choice because of low computational requirements and ease of implementation. Moving Horizon Estimation (MHE), on the other hand, is an optimization approach that better handles problems with:

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Attach:frequency.png|~~Frequency of Process System Activities~~

to:

Attach:frequency.png|'''Figure:''' Typical Frequency of Simulation, Control, and Optimization

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Attach:frequency.~~png~~

to:

Attach:frequency.png|Frequency of Process System Activities

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The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process.

to:

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process from an initial process design to a minute to minute cycles of model predictive control.

Changed lines 18-20 from:

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for ~~industry or academia~~.

to:

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for the lifecycle of a process.

Attach:frequency.png

Attach:frequency.png

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Results of the estimation may also include a probability distribution of the current process state.

to:

Results of the estimation may also include a probability distribution of the current process state. This distribution may be in the form of a single statistical figure or as a population of probable outcomes.

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!! %blue%~~Integration Of Simulation, Optimization, and Control~~%black%

to:

!! %blue%Background on Process Systems Engineering%black%

Changed lines 3-4 from:

The areas of '''simulation''', '''control''', and '''optimization''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

to:

The areas of '''simulation''', '''estimation''', '''control''', and '''optimization''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

Added lines 32-45:

----

!! %blue%Estimation%black%

Estimation is the allignment of a process model with actual process measurements. This can be accomplished by adjusting model parameters or current state estimates. For linear models, the Kalman filter is a popular choice because of low computational requirements and ease of implementation. Moving Horizon Estimation (MHE), on the other hand, is an optimization approach that better handles problems with

* Constraints

* Nonlinear Models

* Infrequent Measurements

* Explicit Measurement Ranking

* Statistically Insignificant Noise and Outliers

Results of the estimation may also include a probability distribution of the current process state.

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!!! Nonlinear ~~Control~~

to:

!!! Nonlinear Control (NLC)

Changed lines 3-4 from:

The areas of '''simulation''', '''~~optimization~~''', and '''~~control~~''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

to:

The areas of '''simulation''', '''control''', and '''optimization''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

Deleted lines 32-40:

Challenges in process simulation include the incorporation of more difficult and detailed process models. These include modeling of process dynamics as well as steady state, incorporation of transport models for separation, the simulation of highly nonideal systems with multiple phases, and the development of rigorous, first principle reactor models. These models require simulators to evolve from modeling and solving algebraic systems of equations to differential algebraic models and also to consider PDEs. In addition, the availability and application of optimization methods has led to a powerful extension of simulation tools.

!!! Design under uncertainty

Over the life cycle of the process, input conditions and product demands change, feedstock and product specifications may vary and the process will be subject to short and long term uncertainties. Moreover, process models are also subject to uncertainty.

The challenge therefore is to develop a design that is tolerant to levels of uncertainty and exhibits a profitable expected performance. An important case is also the one of processes under multiperiod operation that are subjected to a finite number of process variations.

Added lines 35-48:

!! %blue%Control%black%

Process control has evolved into a strong discipline in process systems engineering. Traditionally this has been characterized by single loop PID controllers with incremental advances that lead to advanced elements in the control system. More recently, concepts from optimization, mathematical analysis and nonlinear dynamics have played important roles in developing more efficient and superior control strategies.

!!! Model Predictive Control (MPC)

Developed in the late 70s, MPC has shown significant advantages over structured PID control loops and has become the most widely used multivariable control strategy in industry. This approach is a generic strategy applied to large classes of unit operations, but was developed only with linear process models (usually derived empirically). Only recently have theoretical properties of these controllers been developed. Moreover, the discovery of many interesting properties for control and identification has led to direct results in tuning and design of these control systems in industry.

!!! Nonlinear Control

All processes are nonlinear and in many cases, linear model-based controllers are no longer satisfactory. To deal with this, geometric linearization strategies have been developed and lead to powerful insights in the design of control structures. Moreover, model predictive control can also be extended directly to deal with nonlinear dynamic models. Again, properties relating to the stability, robustness and performance of these controllers still need to be explored. Also, industry has had significant successes with these controllers on batch and semi-continuous processes.

----

Process control has evolved into a strong discipline in process systems engineering. Traditionally this has been characterized by single loop PID controllers with incremental advances that lead to advanced elements in the control system. More recently, concepts from optimization, mathematical analysis and nonlinear dynamics have played important roles in developing more efficient and superior control strategies.

!!! Model Predictive Control (MPC)

Developed in the late 70s, MPC has shown significant advantages over structured PID control loops and has become the most widely used multivariable control strategy in industry. This approach is a generic strategy applied to large classes of unit operations, but was developed only with linear process models (usually derived empirically). Only recently have theoretical properties of these controllers been developed. Moreover, the discovery of many interesting properties for control and identification has led to direct results in tuning and design of these control systems in industry.

!!! Nonlinear Control

All processes are nonlinear and in many cases, linear model-based controllers are no longer satisfactory. To deal with this, geometric linearization strategies have been developed and lead to powerful insights in the design of control structures. Moreover, model predictive control can also be extended directly to deal with nonlinear dynamic models. Again, properties relating to the stability, robustness and performance of these controllers still need to be explored. Also, industry has had significant successes with these controllers on batch and semi-continuous processes.

----

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!!! On-line Optimization

to:

!!! On-line Optimization (Hourly/Daily)

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!!! Process Scheduling

to:

!!! Process Scheduling (Weekly)

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!!! Planning and Supply Chain Management

Production planning and supply chain management provide the decision support systems for the logistics in the long range operation of networks of plants, and their coordination with marketing and business considerations. These problems give rise to very large multiperiod optimization problems where a major challenge lies in the effective aggregation of more detailed scheduling and operational models.~~ ~~

----

!! %blue%Control%black%

Process control has evolved into a strong discipline in process systems engineering. Traditionally this has been characterized by single loop PID controllers with incremental advances that lead to advanced elements in the control system. More recently, concepts from optimization, mathematical analysis and nonlinear dynamics have played important roles in developing more efficient and superior control strategies. Areas of research can be classified as follows:

!!! Model Predictive Control (MPC)

Developed in the late 70s, MPC has shown significant advantages over structured PID control loops and has become the most widely used multivariable control strategy in industry. This approach is a generic strategy applied to large classes of unit operations, but was developed only with linear process models (usually derived empirically). Only recently have theoretical properties of these controllers been developed. Moreover, the discovery of many interesting properties for control and identification has led to direct results in tuning and design of these control systems in industry.

!!! Nonlinear Control

All processes are nonlinear and in many cases, linear model-based controllers are no longer satisfactory. To deal with this, geometric linearization strategies have been developed and lead to powerful insights in the design of control structures. Moreover, model predictive control can also be extended directly to deal with nonlinear dynamic models. Again, properties relating to the stability, robustness and performance of these controllers still need to be explored. Also, industry has had significant successes with these controllers on batch and semi-continuous processes.

Production

----

!! %blue%Control%black%

Process control has evolved into a strong discipline in process systems engineering. Traditionally this has been characterized by single loop PID controllers with incremental advances that lead to advanced elements in the control system. More recently, concepts from optimization, mathematical analysis and nonlinear dynamics have played important roles in developing more efficient and superior control strategies. Areas of research can be classified as follows:

!!! Model Predictive Control (MPC)

Developed in the late 70s, MPC has shown significant advantages over structured PID control loops and has become the most widely used multivariable control strategy in industry. This approach is a generic strategy applied to large classes of unit operations, but was developed only with linear process models (usually derived empirically). Only recently have theoretical properties of these controllers been developed. Moreover, the discovery of many interesting properties for control and identification has led to direct results in tuning and design of these control systems in industry.

!!! Nonlinear Control

All processes are nonlinear and in many cases, linear model-based controllers are no longer satisfactory. To deal with this, geometric linearization strategies have been developed and lead to powerful insights in the design of control structures. Moreover, model predictive control can also be extended directly to deal with nonlinear dynamic models. Again, properties relating to the stability, robustness and performance of these controllers still need to be explored. Also, industry has had significant successes with these controllers on batch and semi-continuous processes.

to:

!!! Planning and Supply Chain Management (Yearly)

Production planning and supply chain management provide the decision support systems for the logistics in the long range operation of networks of plants, and their coordination with marketing and business considerations. These problems give rise to very large multiperiod optimization problems where a major challenge lies in the effective aggregation of more detailed scheduling and operational models.

Production planning and supply chain management provide the decision support systems for the logistics in the long range operation of networks of plants, and their coordination with marketing and business considerations. These problems give rise to very large multiperiod optimization problems where a major challenge lies in the effective aggregation of more detailed scheduling and operational models.

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The ~~creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction~~ of ~~the design time as well as the development of better designs that incorporate life cycle features~~ of ~~the process. These features include, of course, a highly profitable and competitive process, as well as a ~~process ~~that is easy to control and operate. Moreover, it must be environmentally benign and safe~~.

to:

The objective of process simulation is to create a virtual process that can be investigated or manipulated to give desirable results. Some common objectives of simulation activities are:

* development of better designs that incorporate life cycle features of the process

* reduction of design time and engineering effort

* maximize profitability while observing environmental constraints

* ease of control and operation

Because process parameters are rarely exactly known, the design under uncertainty gives a method to address probabilities. While process simulation often provides an single answer, design under uncertainty provides aides in decision making with imperfect information.

* development of better designs that incorporate life cycle features of the process

* reduction of design time and engineering effort

* maximize profitability while observing environmental constraints

* ease of control and operation

Because process parameters are rarely exactly known, the design under uncertainty gives a method to address probabilities. While process simulation often provides an single answer, design under uncertainty provides aides in decision making with imperfect information.

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to:

Challenges in process simulation include the incorporation of more difficult and detailed process models. These include modeling of process dynamics as well as steady state, incorporation of transport models for separation, the simulation of highly nonideal systems with multiple phases, and the development of rigorous, first principle reactor models. These models require simulators to evolve from modeling and solving algebraic systems of equations to differential algebraic models and also to consider PDEs. In addition, the availability and application of optimization methods has led to a powerful extension of simulation tools.

Added line 38:

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The areas of '''simulation''', '''optimization''', and '''control''' are naturally synergistic because of their reliance on process ~~modeling~~. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

to:

The areas of '''simulation''', '''optimization''', and '''control''' are naturally synergistic because of their reliance on process models. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

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!! %blue%~~Process Design and ~~Simulation%black%

to:

!! %blue%Simulation%black%

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The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities ~~may change~~ with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

to:

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities will expand with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

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!! %blue%Process Design%black%

The creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction of the design time as well as the development of better designs that incorporate life cycle features of the process. These features include, of course, a highly profitable and competitive process, as well as a process that is easy to control and operate. Moreover, it must be environmentally benign and safe.~~ The research tasks involved in this task take the following categories: ~~

The creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction of the design time as well as the development of better designs that incorporate life cycle features of the process. These features include, of course, a highly profitable and competitive process, as well as a process that is easy to control and operate. Moreover, it must be environmentally benign and safe.

to:

!! %blue%Process Design and Simulation%black%

The creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction of the design time as well as the development of better designs that incorporate life cycle features of the process. These features include, of course, a highly profitable and competitive process, as well as a process that is easy to control and operate. Moreover, it must be environmentally benign and safe.

The creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction of the design time as well as the development of better designs that incorporate life cycle features of the process. These features include, of course, a highly profitable and competitive process, as well as a process that is easy to control and operate. Moreover, it must be environmentally benign and safe.

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!! %blue%~~Operations~~%black%

to:

!! %blue%Optimization%black%

Deleted lines 38-41:

!!! Flexibility and Operability

This task is devoted to the development quantitative measures of process flexibility as well as strategies that improve these measures for chemical processes. Here improvements in both design and operation can be considered to increase the process' tolerance to uncertainty. This also allows the process to deal with a wider range of operations and production scenarios. The formulation of flexibility problems, either in terms of deterministic or stochastic measures, leads to large, complex optimization problems and with challenges for the application on realistic processes.

Changed line 12 from:

** ~~algorithms for~~ integral or PDE systems

to:

** solution of integral or PDE systems

Changed line 3 from:

The areas of '''simulation''', '''optimization''', and '''control''' are naturally synergistic because of their reliance on process modeling. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.~~ Many of these tools are the subject of active research and development efforts. These include~~

to:

The areas of '''simulation''', '''optimization''', and '''control''' are naturally synergistic because of their reliance on process modeling. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish.

Changed lines 5-13 from:

#

# information management

# advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation,

to:

*%blue%A%red%P%black%Monitor Strengths

** modeling system for simulation, optimization, and control

** solution of differential and algebraic (DAE) equations

** efficient for large-scale systems

** real-time optimization and control

*%blue%A%red%P%black%Monitor Areas Under Development

** algorithms for integral or PDE systems

** algorithms for linear and nonlinear discrete and continuous optimization

** algorithms for global and stochastic optimization

** information management systems and data bases

** advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities may change with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

** modeling system for simulation, optimization, and control

** solution of differential and algebraic (DAE) equations

** efficient for large-scale systems

** real-time optimization and control

*%blue%A%red%P%black%Monitor Areas Under Development

** algorithms for integral or PDE systems

** algorithms for linear and nonlinear discrete and continuous optimization

** algorithms for global and stochastic optimization

** information management systems and data bases

** advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models. The capabilities may change with future development effort. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

Changed lines 1-15 from:

!! %blue%Integration Of ~~Design~~, ~~Operations~~, and Control%black%

The~~ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads ~~to ~~problem formulations that directly consider ~~the ~~interactions~~ of ~~'''process design''', '''operations''', and '''control'''. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility ~~and ~~operability and the solution of large optimization problems with both continuous ~~and ~~discrete decision variables.~~

!! %blue%Tools For Process Systems Engineering%black%

All the above areas in process systems ~~engineering are supported by a large number of tools and ~~algorithms ~~which are the subject of active research efforts. These include~~

* modeling systems for simulation, optimization, and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for ~~linear~~ and ~~nonlinear discrete and continuous optimization~~

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation models.

The

!! %blue%Tools For Process Systems Engineering%black%

All the above areas in process

* modeling systems for simulation, optimization, and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation models

to:

!! %blue%Integration Of Simulation, Optimization, and Control%black%

The areas of '''simulation''', '''optimization''', and '''control''' are naturally synergistic because of their reliance on process modeling. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish. Many of these tools are the subject of active research and development efforts. These include

# modeling systems for simulation, optimization, and control

# algorithms for differential and algebraic (DAE) equations

# algorithms for integral or PDE systems

# algorithms for linear and nonlinear discrete and continuous optimization

# algorithms for global and stochastic optimization

# information management systems and data bases

# advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models (items 1 & 2). The %blue%A%red%P%black%Monitor software does not attempt to solve problems in the areas 3-7. While these capabilities may change with future development efforts, there are likely better software tools for these activities. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

The areas of '''simulation''', '''optimization''', and '''control''' are naturally synergistic because of their reliance on process modeling. One key to integrating these activities is the development of software tools that can solve large-scale, complex models efficiently. There are many tools for process system engineering, so it is important to differentiate what a software tool can and cannot accomplish. Many of these tools are the subject of active research and development efforts. These include

# modeling systems for simulation, optimization, and control

# algorithms for differential and algebraic (DAE) equations

# algorithms for integral or PDE systems

# algorithms for linear and nonlinear discrete and continuous optimization

# algorithms for global and stochastic optimization

# information management systems and data bases

# advanced computer architectures for parallel computation

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation (DAE) models (items 1 & 2). The %blue%A%red%P%black%Monitor software does not attempt to solve problems in the areas 3-7. While these capabilities may change with future development efforts, there are likely better software tools for these activities. For models of large-scale DAE systems, %blue%A%red%P%black%Monitor is an efficient and user-friendly software tool for industry or academia.

Added lines 14-15:

The %blue%A%red%P%black%Monitor software is a simulation, optimization, and control environment for differential and algebraic equation models.

Changed line 1 from:

!! %blue%Integration Of Design, ~~Control And ~~Operations%black%

to:

!! %blue%Integration Of Design, Operations, and Control%black%

Changed lines 1-2 from:

!! %blue%~~Process~~ Design And ~~Synthesis~~%black%

to:

!! %blue%Integration Of Design, Control And Operations%black%

The ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of '''process design''', '''operations''', and '''control'''. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

!! %blue%Tools For Process Systems Engineering%black%

All the above areas in process systems engineering are supported by a large number of tools and algorithms which are the subject of active research efforts. These include

* modeling systems for simulation, optimization, and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for linear and nonlinear discrete and continuous optimization

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation

----

!! %blue%Process Design%black%

The ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of '''process design''', '''operations''', and '''control'''. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

!! %blue%Tools For Process Systems Engineering%black%

All the above areas in process systems engineering are supported by a large number of tools and algorithms which are the subject of active research efforts. These include

* modeling systems for simulation, optimization, and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for linear and nonlinear discrete and continuous optimization

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation

----

!! %blue%Process Design%black%

Changed lines 31-32 from:

!! %blue%~~Process ~~Operations%black%

to:

!! %blue%Operations%black%

Changed lines 53-54 from:

!! %blue%~~Process ~~Control%black%

to:

!! %blue%Control%black%

Deleted lines 65-80:

!! %blue%Integration Of Design, Control And Operations%black%

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

!! %blue%Supporting Tools And Methods For Process Systems Engineering%black%

All the above areas in process systems engineering are supported by a large number of tools and algorithms which are the subject of active research efforts. These include

* modeling systems for simulation, optimization and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for linear and nonlinear discrete and continuous optimization

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation

----

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* advanced computer architectures for parallel ~~computation.~~

to:

* advanced computer architectures for parallel computation

Changed lines 15-16 from:

!! Process Operations

to:

!! %blue%Process Operations%black%

Changed lines 37-38 from:

!! Process Control

to:

!! %blue%Process Control%black%

Deleted lines 48-51:

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

Changed lines 51-55 from:

!! ~~Supporting Tools And Methods For Process Systems Engineering~~

to:

!! %blue%Integration Of Design, Control And Operations%black%

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

!! %blue%Supporting Tools And Methods For Process Systems Engineering%black%

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

!! %blue%Supporting Tools And Methods For Process Systems Engineering%black%

Changed line 1 from:

!! Process Design And ~~Synthesis~~

to:

!! %blue%Process Design And Synthesis%black%

Added lines 1-63:

!! Process Design And Synthesis

The creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction of the design time as well as the development of better designs that incorporate life cycle features of the process. These features include, of course, a highly profitable and competitive process, as well as a process that is easy to control and operate. Moreover, it must be environmentally benign and safe. The research tasks involved in this task take the following categories:

!!! Process Simulation

Typically the bread and butter of industrial designs, this task deals with the analysis of a given process. Challenges in process simulation include the incorporation of more difficult and detailed process models. These include modeling of process dynamics as well as steady state, incorporation of transport models for separation, the simulation of highly nonideal systems with multiple phases, and the development of rigorous, first principle reactor models. These models require simulators to evolve from modeling and solving algebraic systems of equations to differential algebraic models and also to consider PDEs. In addition, the availability and application of optimization methods has led to a powerful extension of simulation tools.

!!! Design under uncertainty

Over the life cycle of the process, input conditions and product demands change, feedstock and product specifications may vary and the process will be subject to short and long term uncertainties. Moreover, process models are also subject to uncertainty.

The challenge therefore is to develop a design that is tolerant to levels of uncertainty and exhibits a profitable expected performance. An important case is also the one of processes under multiperiod operation that are subjected to a finite number of process variations.

----

!! Process Operations

To complement the role of process design and synthesis, research in process operations seeks to improve existing operating processes. Through the development of strategies and analysis tools, improvements can be found through on-line optimization of a process, scheduling of operating strategies, changeovers and interactions between different processes, and overall planning of product productions to meet market demands. The research tasks involved in this task take the following categories.

!!! Flexibility and Operability

This task is devoted to the development quantitative measures of process flexibility as well as strategies that improve these measures for chemical processes. Here improvements in both design and operation can be considered to increase the process' tolerance to uncertainty. This also allows the process to deal with a wider range of operations and production scenarios. The formulation of flexibility problems, either in terms of deterministic or stochastic measures, leads to large, complex optimization problems and with challenges for the application on realistic processes.

!!! On-line Optimization

With short term (e.g., hourly) changes in feedstock and product demands, the availability of detailed process models and powerful optimization tools, it is now possible to optimize steady state models on-line and to readjust the setpoints of the control system. This leads to processes that can adapt to daily fluctuations in inputs and uncertainties. These can therefore lead too much higher profits. The current challenge is to deal with dynamic models in addition to steady state cases and also to provide a tighter coupling to the process control system.

!!! Process Scheduling

Scheduling of batch and continuous processes can have a major impact on the overall profitability of a process, as well as on the timely delivery of products. Major problems include sequencing, scheduling of equipment utilization and maintenance over a planning horizon, and inventory considerations of a process. Such problems form perhaps difficult combinatorial optimization problems but also contribute to high payoffs. Moreover, the results of this task have a major impact on the local operation of the process, and strong interactions exist between the scheduling, design and operation of the process.

!!! Planning and Supply Chain Management

Production planning and supply chain management provide the decision support systems for the logistics in the long range operation of networks of plants, and their coordination with marketing and business considerations. These problems give rise to very large multiperiod optimization problems where a major challenge lies in the effective aggregation of more detailed scheduling and operational models.

----

!! Process Control

Process control has evolved into a strong discipline in process systems engineering. Traditionally this has been characterized by single loop PID controllers with incremental advances that lead to advanced elements in the control system. More recently, concepts from optimization, mathematical analysis and nonlinear dynamics have played important roles in developing more efficient and superior control strategies. Areas of research can be classified as follows:

!!! Model Predictive Control (MPC)

Developed in the late 70s, MPC has shown significant advantages over structured PID control loops and has become the most widely used multivariable control strategy in industry. This approach is a generic strategy applied to large classes of unit operations, but was developed only with linear process models (usually derived empirically). Only recently have theoretical properties of these controllers been developed. Moreover, the discovery of many interesting properties for control and identification has led to direct results in tuning and design of these control systems in industry.

!!! Nonlinear Control

All processes are nonlinear and in many cases, linear model-based controllers are no longer satisfactory. To deal with this, geometric linearization strategies have been developed and lead to powerful insights in the design of control structures. Moreover, model predictive control can also be extended directly to deal with nonlinear dynamic models. Again, properties relating to the stability, robustness and performance of these controllers still need to be explored. Also, industry has had significant successes with these controllers on batch and semi-continuous processes.

!!! Integration Of Design, Control And Operations

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

----

!! Supporting Tools And Methods For Process Systems Engineering

All the above areas in process systems engineering are supported by a large number of tools and algorithms which are the subject of active research efforts. These include

* modeling systems for simulation, optimization and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for linear and nonlinear discrete and continuous optimization

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation.

The creation, evaluation and optimization of a chemical process is the central task in process systems engineering. In industry, the goal has been reduction of the design time as well as the development of better designs that incorporate life cycle features of the process. These features include, of course, a highly profitable and competitive process, as well as a process that is easy to control and operate. Moreover, it must be environmentally benign and safe. The research tasks involved in this task take the following categories:

!!! Process Simulation

Typically the bread and butter of industrial designs, this task deals with the analysis of a given process. Challenges in process simulation include the incorporation of more difficult and detailed process models. These include modeling of process dynamics as well as steady state, incorporation of transport models for separation, the simulation of highly nonideal systems with multiple phases, and the development of rigorous, first principle reactor models. These models require simulators to evolve from modeling and solving algebraic systems of equations to differential algebraic models and also to consider PDEs. In addition, the availability and application of optimization methods has led to a powerful extension of simulation tools.

!!! Design under uncertainty

Over the life cycle of the process, input conditions and product demands change, feedstock and product specifications may vary and the process will be subject to short and long term uncertainties. Moreover, process models are also subject to uncertainty.

The challenge therefore is to develop a design that is tolerant to levels of uncertainty and exhibits a profitable expected performance. An important case is also the one of processes under multiperiod operation that are subjected to a finite number of process variations.

----

!! Process Operations

To complement the role of process design and synthesis, research in process operations seeks to improve existing operating processes. Through the development of strategies and analysis tools, improvements can be found through on-line optimization of a process, scheduling of operating strategies, changeovers and interactions between different processes, and overall planning of product productions to meet market demands. The research tasks involved in this task take the following categories.

!!! Flexibility and Operability

This task is devoted to the development quantitative measures of process flexibility as well as strategies that improve these measures for chemical processes. Here improvements in both design and operation can be considered to increase the process' tolerance to uncertainty. This also allows the process to deal with a wider range of operations and production scenarios. The formulation of flexibility problems, either in terms of deterministic or stochastic measures, leads to large, complex optimization problems and with challenges for the application on realistic processes.

!!! On-line Optimization

With short term (e.g., hourly) changes in feedstock and product demands, the availability of detailed process models and powerful optimization tools, it is now possible to optimize steady state models on-line and to readjust the setpoints of the control system. This leads to processes that can adapt to daily fluctuations in inputs and uncertainties. These can therefore lead too much higher profits. The current challenge is to deal with dynamic models in addition to steady state cases and also to provide a tighter coupling to the process control system.

!!! Process Scheduling

Scheduling of batch and continuous processes can have a major impact on the overall profitability of a process, as well as on the timely delivery of products. Major problems include sequencing, scheduling of equipment utilization and maintenance over a planning horizon, and inventory considerations of a process. Such problems form perhaps difficult combinatorial optimization problems but also contribute to high payoffs. Moreover, the results of this task have a major impact on the local operation of the process, and strong interactions exist between the scheduling, design and operation of the process.

!!! Planning and Supply Chain Management

Production planning and supply chain management provide the decision support systems for the logistics in the long range operation of networks of plants, and their coordination with marketing and business considerations. These problems give rise to very large multiperiod optimization problems where a major challenge lies in the effective aggregation of more detailed scheduling and operational models.

----

!! Process Control

Process control has evolved into a strong discipline in process systems engineering. Traditionally this has been characterized by single loop PID controllers with incremental advances that lead to advanced elements in the control system. More recently, concepts from optimization, mathematical analysis and nonlinear dynamics have played important roles in developing more efficient and superior control strategies. Areas of research can be classified as follows:

!!! Model Predictive Control (MPC)

Developed in the late 70s, MPC has shown significant advantages over structured PID control loops and has become the most widely used multivariable control strategy in industry. This approach is a generic strategy applied to large classes of unit operations, but was developed only with linear process models (usually derived empirically). Only recently have theoretical properties of these controllers been developed. Moreover, the discovery of many interesting properties for control and identification has led to direct results in tuning and design of these control systems in industry.

!!! Nonlinear Control

All processes are nonlinear and in many cases, linear model-based controllers are no longer satisfactory. To deal with this, geometric linearization strategies have been developed and lead to powerful insights in the design of control structures. Moreover, model predictive control can also be extended directly to deal with nonlinear dynamic models. Again, properties relating to the stability, robustness and performance of these controllers still need to be explored. Also, industry has had significant successes with these controllers on batch and semi-continuous processes.

!!! Integration Of Design, Control And Operations

Finally, the ability to develop large steady state and dynamic process models and to solve large and complex optimization problems naturally leads to problem formulations that directly consider the interactions of process design, control and operations. The results of this approach lead to powerful synergies among these tasks, better performance of the process and improvements in profitability, efficiency and environmental impact. Challenges related to this approach include the modeling of quantitative metrics for control, flexibility and operability and the solution of large optimization problems with both continuous and discrete decision variables.

----

!! Supporting Tools And Methods For Process Systems Engineering

All the above areas in process systems engineering are supported by a large number of tools and algorithms which are the subject of active research efforts. These include

* modeling systems for simulation, optimization and control

* algorithms for algebraic/differential equations and integral/PDE systems

* algorithms for linear and nonlinear discrete and continuous optimization

* algorithms for global and stochastic optimization; information management systems and data bases

* advanced computer architectures for parallel computation.