Main
~~The APMonitor Modeling Language~~ is optimization software for mixed-integer and differential algebraic equations. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include data reconciliation, ~~real-time optimization, dynamic simulation~~, ~~and nonlinear predictive control. It is available through MATLAB, Python, or from a web browser interface~~.

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control.

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~~Attach:apmonitor_info.png %blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:~~

* Meet regulatory reporting requirements

* Flow assurance of oil and gas transport pipelines

* Visualize data from remote locations

* Reduce alarms by consolidating relevant information

* Provide soft sensing

* Automatic control of continuous and batch systems

* Increase production 3-5% without equipment changes

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes. A modeling language interface to MATLAB and Python extend the applicability for pre- and post-processing of the optimization solution results.

----

!!!! Range of usage

%blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

* Meet regulatory reporting requirements

* Flow assurance of oil and gas transport pipelines

* Visualize data from remote locations

* Reduce alarms by consolidating relevant information

* Provide soft sensing

* Automatic control of continuous and batch systems

* Increase production 3-5% without equipment changes

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes. A modeling language interface to MATLAB and Python extends the applicability for pre- and post-processing of the optimization solution results.
[[Main/MATLAB | ~~Attach:apm_matlab.png ~~Download Latest MATLAB Toolbox]]

[[Main/PythonApp |~~ Attach:apm_python.png~~ Download Latest Python Package]]

[[Main/MATLAB | Attach:apm_matlab.png Download Latest MATLAB Toolbox]]

[[Main/PythonApp | Attach:apm_python.png Download Latest Python Package]]

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~~----~~

~~----~~
~~----~~

!!! %blue%A%red%P%black%Monitor Overview

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in [[Main/Modes|nine solution modes]]. The DAE model does not have to be changed to switch between the modes. The same model is used for parameter fitting, dynamic simulation, optimization, and control. The user is required to define the model and the software automatically configures the various simulation options.

!!!! Chemical Process Flowsheets

A thermodynamic database and a number of prebuilt nonlinear models are available with %blue%A%red%P%black%Monitor. The chemical processing modeling package includes polymer reactors, distillation columns, compressors, valves, etc. These models are combined to form a flowsheet in an object-oriented environment.

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!! Documentation Overview

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited to %blue%A%red%P%black%Monitor as it allows for collaboration and continuing development.

!!!! Essential Files for Simulation

* %list list-page% '''[[Main/APM|model.apm]]''': To generate a new model, create a text file and save it with an '''apm''' extension.

* %list list-page% '''[[Main/INFO|model.info]]''': The '''info''' file contains designation of special variables for trending, data acquisition, and mode-specific actions. If no variables are treated specially, the '''info''' file can be blank.

* %list list-page% '''[[Main/DBS|model.dbs]]''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.
~~ <img src="http://groups.google.com/intl/en/images/logos/groups_logo_sm.gif"~~

height=30 width=140 alt="Google Groups">
~~!! ~~Attach:apmonitor_info.png %blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

<META NAME="Description" CONTENT="~~Simulation, optimization, estimation, ~~and ~~control with APMonitor~~">

~~APMonitor~~ is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:
~~%blue%A%red%P%black%Monitor, or "Advanced Process Monitor", is~~ a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

APMonitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

Meet regulatory reporting requirements

Flow assurance of oil and gas transport pipelines

Visualize data from remote locations

Reduce alarms by consolidating relevant information

Provide soft sensing

Automatic control of continuous and batch systems

Increase production 3-5% without equipment changes

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes.

----

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" includes a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

----

!!! Newton's Apple

Attach:apple.jpg

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.
~~APMonitor~~, or "Advanced Process Monitor", is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.
~~!!! Introduction to~~ Differential and Algebraic Equations
~~[[~~Attach:apmonitor_icon.~~jpg]]~~
~~!!! Newton's Apple~~

Attach:apple.jpg

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.

----

----

!!! Newton's Apple

Attach:apple.jpg

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.

* [[Main/APM|Model (apm)]]

* [[Main/INFO|Info (info)]]

* [[Main/DBS|Database (dbs)]]

** [[Main/DbsGlobal|Global]]

** [[Main/DbsVariable|Variables]]

* [[Main/CSV|Data (csv)]]

* [[Main/T0|Solution (t0)]]
~~# Steady~~-~~state~~ simulation (SS)

~~#~~ Model Parameter Update (MPU)

~~#~~ Real Time Optimization (RTO)

~~#~~ Dynamic simulation (SIM)

~~#~~ Moving horizon estimation (EST)

~~#~~ Nonlinear control (CTL)

"In that slight startle from his contemplation –

'Tis said (for I'll not answer above ground

For any sage's creed or calculation) –

A mode of proving that the earth turn'd round

In a most natural whirl, called "gravitation;"

And this is the sole mortal who could grapple,

Since Adam, with a fall or with an apple."

[--Don Juan (1821), Canto 10, Verse I. In Jerome J. McGann (ed.), Lord Byron: The Complete Poetical Works (1986), Vol. 5, 437--]

# Honeywell's NOVA Solver (version 4.0)

# Carnegie Mellon's IPOPT Solver (version 2.3)

# IBM's IPOPT Solver (version 3.5)

# Stanford's SNOPT Solver (version 6.1)

# Stanford's MINOS Solver (version 5.5)

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and less on data handling, model convergence, and on-line implementation.
~~The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''.~~

* Model Structure

** Parameters

** Variables

*** Algebraic

*** Differential

*** Constraints

*** Slack variables

*** Objective function variables

*** Variable scope

** Connections

** Intermediates

** Equations

** Arrays

** Objects

*** Feed

*** Flash

*** Flash_column

*** Lag

*** Massflow

*** Mixer

*** PID

*** Poly_reactor

*** Pump

*** Reactor

*** Splitter

*** Stage_1

*** Stage_2

*** Stream_lag

*** Vessel

*** Vesselm

** Object arrays

** Object variable connections

* Modes of Operation

** Steady-state Simulation (ss)

** Model Parameter Update (mpu)

** Real-time Optimization (rto)

** Dynamic Simulation (sim)

** Moving Horizon Estimation (est)

** Nonlinear Control (ctl)

* System files

** apm - Model file

** info - Information file

** dbs - Database file

** t0 - Restart solution file

* Obtaining Solutions

** Software demo

** Online interface

** DOS Command line

** MATLAB

The documentation is presented in a Wiki format to allow instant modification by anyone with permission to edit.

!! Documentation Overview

The documentation is presented in a Wiki format to allow instant modification by anyone with permission to edit. The basic structure of the documentation is

* Basic Model Structure

* Parameters

* Variables

** Algebraic

** Differential

** Constraints

** Slack variables

** Objective function variables

* Intermediates

* Equations

* Intermediate Variables

* Arrays

* Objects

** Feed

** Flash

** Flash_column

** Lag

** Massflow

** Mixer

** PID

** Poly_reactor

** Pump

** Reactor

** Splitter

** Stage_1

** Stage_2

** Stream_lag

** Vessel

** Vesselm

Program generated, user edited:

APMonitor enables the use of the nonlinear DAE models directly in parameter estimation, optimization, and control applications.

A number of ~~prebuilt nonlinear models are available with the APMonitor product~~. ~~ The chemical processing modeling package includes polymer reactors, distillation columns, compressors, etc. ~~

!!!
~~DAE models are a natural expression of many systems. ~~APMonitor enables the use of the nonlinear DAE models directly in parameter estimation, optimization, and control applications.
~~ ~~Force = G * mass_1_ * mass_2_ / r^2^
~~A popular story claims that Newton was inspired to formulate his theory of universal gravitation by the fall of an apple from a tree. ~~

~~!! %blue%A%red%P%black%Monitor Wiki Homepage~~

!! %~~%~~blue~~%~~%APMonitor
~~Welcome to PmWiki!~~

A local copy of PmWiki's

documentation has been installed along with the software,

and is available via the [[PmWiki/documentation index]].

To continue setting up PmWiki, see [[PmWiki/initial setup tasks]].

The [[PmWiki/basic editing]] page describes how to create pages

in PmWiki. You can practice editing in the [[wiki sandbox]].

More information about PmWiki is available from http://www.pmwiki.org .

!! %%blue%%APMonitor

## APMonitor Documentation

## Main.HomePage History

Hide minor edits - Show changes to output

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Attach:apm_matlab.png [[Main/MATLAB | Download ~~Latest~~ MATLAB ~~Toolbox~~]]

to:

Attach:apm_matlab.png [[Main/MATLAB | Download latest MATLAB toolbox]]

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Attach:apm_python.png [[Main/PythonApp | Download ~~Latest~~ Python ~~Package~~]]

to:

Attach:apm_python.png [[Main/PythonApp | Download latest Python package]]

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Attach:apm_learn.png [[Main/CourseRegistration | Register for a course to get started]]

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Attach:apm_learn.png [[Main/CourseRegistration | Register for a course to get started]]

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%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" is optimization software for mixed-integer and differential algebraic equations. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include data reconciliation, moving horizon estimation, real-time optimization, dynamic simulation, and nonlinear predictive control with solution capabilities for high-index differential and algebraic (DAE) equations. It is available as a [[Main/MATLAB | MATLAB toolbox]], [[Main/PythonApp | Python]], or from a [[http://apmonitor.com/online/view_pass.php | web browser interface]].

Deleted lines 19-20:

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control.

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%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control~~. APMonitor does not solve the problems directly, but calls appropriate external solvers~~.

to:

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control.

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The APMonitor Modeling Language is optimization software for mixed-integer and differential algebraic equations. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include data reconciliation, real-time optimization, dynamic simulation, and nonlinear predictive control. It is available through MATLAB, Python, or from a web browser interface.

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* Meet regulatory reporting requirements

* Flow assurance of oil and gas transport pipelines

* Visualize data from remote locations

* Reduce alarms by consolidating relevant information

* Provide soft sensing

* Automatic control of continuous and batch systems

* Increase production 3-5% without equipment changes

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes. A modeling language interface to MATLAB and Python extend the applicability for pre- and post-processing of the optimization solution results.

----

Added lines 64-77:

!!!! Range of usage

%blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

* Meet regulatory reporting requirements

* Flow assurance of oil and gas transport pipelines

* Visualize data from remote locations

* Reduce alarms by consolidating relevant information

* Provide soft sensing

* Automatic control of continuous and batch systems

* Increase production 3-5% without equipment changes

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes. A modeling language interface to MATLAB and Python extends the applicability for pre- and post-processing of the optimization solution results.

Changed lines 5-6 from:

to:

Attach:apm_matlab.png [[Main/MATLAB | Download Latest MATLAB Toolbox]]

Attach:apm_python.png [[Main/PythonApp | Download Latest Python Package]]

Attach:apm_python.png [[Main/PythonApp | Download Latest Python Package]]

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(:title APMonitor~~ Modeling Language~~ Documentation:)

to:

(:title APMonitor Documentation:)

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[[Main/MATLAB | Attach:apm_matlab.png Download Latest MATLAB Toolbox]]

[[Main/PythonApp | Attach:apm_python.png Download Latest Python Package]]

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Deleted line 54:

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!!! %blue%A%red%P%black%Monitor Overview

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in [[Main/Modes|nine solution modes]]. The DAE model does not have to be changed to switch between the modes. The same model is used for parameter fitting, dynamic simulation, optimization, and control. The user is required to define the model and the software automatically configures the various simulation options.

Deleted lines 61-66:

!!!! Chemical Process Flowsheets

A thermodynamic database and a number of prebuilt nonlinear models are available with %blue%A%red%P%black%Monitor. The chemical processing modeling package includes polymer reactors, distillation columns, compressors, valves, etc. These models are combined to form a flowsheet in an object-oriented environment.

----

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Software Technical Reference

* %list list-page% J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.

* %list list-page% J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.

to:

!!!! Software Technical Reference

* %list list-page% J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, [[http://www.sciencedirect.com/science/article/pii/S0098135414001306|Nonlinear Modeling, Estimation and Predictive Control in APMonitor]], Computers & Chemical Engineering, 2014.

* %list list-page% J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, [[http://www.sciencedirect.com/science/article/pii/S0098135414001306|Nonlinear Modeling, Estimation and Predictive Control in APMonitor]], Computers & Chemical Engineering, 2014.

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A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes.

to:

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes. A modeling language interface to MATLAB and Python extend the applicability for pre- and post-processing of the optimization solution results.

Added lines 19-22:

Software Technical Reference

* %list list-page% J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.

* %list list-page% J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.

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%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in ~~seven~~ solution modes~~:~~

* %list list-cat% [[Main/SteadyState|Steady-State (SS)]]

* [[Main/ParameterFit|Parameter Fit (MPU)]]

* [[Main/Optimization|Optimization (RTO)]]

* [[Main/Simulation|Simulation (SIM)]]

* [[Main/Estimation|Estimation (EST)]]

* [[Main/Control|Control (CTL)]]

* [[Main/Sequential|Sequential (SQS)]]

The DAE model does not have to be changed to switch between the modes. The same model is used for parameter fitting, dynamic simulation, optimization, and control. The user is required to define the model and the software automatically configures the various simulation options.

* %list list-cat% [[Main/SteadyState|Steady-State (SS)]]

* [[Main/ParameterFit|Parameter Fit (MPU)]]

* [[Main/Optimization|Optimization (RTO)]]

* [[Main/Simulation|Simulation (SIM)]]

* [[Main/Estimation|Estimation (EST)]]

* [[Main/Control|Control (CTL)]]

* [[Main/Sequential|Sequential (SQS)]]

The DAE model does not have to be changed to switch between the modes. The same model is used for parameter fitting, dynamic simulation, optimization, and control. The user is required to define the model and the software automatically configures the various simulation options.

to:

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in [[Main/Modes|nine solution modes]]. The DAE model does not have to be changed to switch between the modes. The same model is used for parameter fitting, dynamic simulation, optimization, and control. The user is required to define the model and the software automatically configures the various simulation options.

Deleted lines 68-73:

----

!! Documentation Overview

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited to %blue%A%red%P%black%Monitor as it allows for collaboration and continuing development.

Deleted lines 78-83:

!!!! Essential Files for Simulation

* %list list-page% '''[[Main/APM|model.apm]]''': To generate a new model, create a text file and save it with an '''apm''' extension.

* %list list-page% '''[[Main/INFO|model.info]]''': The '''info''' file contains designation of special variables for trending, data acquisition, and mode-specific actions. If no variables are treated specially, the '''info''' file can be blank.

* %list list-page% '''[[Main/DBS|model.dbs]]''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

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!!!! Discussion Group

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(:htmlend:)

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!!!! YouTube Channel

(:html:)

<script src="https://apis.google.com/js/platform.js"></script>

<div class="g-ytsubscribe" data-channel="APMonitorCom" data-layout="full" data-count="default"></div>

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!!!! YouTube Channel

(:html:)

<script src="https://apis.google.com/js/platform.js"></script>

<div class="g-ytsubscribe" data-channel="APMonitorCom" data-layout="full" data-count="default"></div>

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%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" ~~includes~~ a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

to:

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

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<b>Subscribe to ~~apmonitor~~</b>

to:

<b>Subscribe to APMonitor E-mail List</b>

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height=30 width=140 alt="Google Groups">

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%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in ~~six~~ solution modes:

to:

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in seven solution modes:

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* [[Main/Sequential|Sequential (SQS)]]

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

to:

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

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to:

Attach:apmonitor_info.png %blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

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!! Attach:apmonitor_info.png

%blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

%blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

to:

!! Attach:apmonitor_info.png %blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

Changed lines 5-6 from:

!! ~~%blue%A%red%P%black%Monitor ~~Attach:apmonitor_~~icon~~.~~jpg~~

----

----

to:

!! Attach:apmonitor_info.png

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(:~~html~~:)~~<head>~~

<title>APMonitor Modeling Language</title>

<META NAME="Keywords" CONTENT="Nonlinear Model Predictive Control APMonitor Analytic First Derivatives Nonlinear Differential Algebraic Modeling Language">

<META NAME="Description" CONTENT="APMonitor~~ Documentation and Nonlinear Model Library">~~

<META NAME="Author" CONTENT="support@apmonitor.com">

</head>(:~~htmlend:~~)

<title>APMonitor Modeling Language</title>

<META NAME="Keywords" CONTENT="Nonlinear Model Predictive Control APMonitor Analytic First Derivatives Nonlinear Differential Algebraic Modeling Language">

<META NAME="Description" CONTENT="

<META NAME="Author" CONTENT="support@apmonitor.com">

</head>(

to:

(:title APMonitor Modeling Language Documentation:)

(: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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<META NAME="Description" CONTENT="APMonitor Documentation and Nonlinear Model Library">

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(:html:)<head>

<title>APMonitor Modeling Language</title>

<META NAME="Keywords" CONTENT="Nonlinear Model Predictive Control APMonitor Analytic First Derivatives Nonlinear Differential Algebraic Modeling Language">

<META NAME="Description" CONTENT="Simulation, optimization, estimation, and control with APMonitor">

<META NAME="Author" CONTENT="support@apmonitor.com">

</head>(:htmlend:)

<title>APMonitor Modeling Language</title>

<META NAME="Keywords" CONTENT="Nonlinear Model Predictive Control APMonitor Analytic First Derivatives Nonlinear Differential Algebraic Modeling Language">

<META NAME="Description" CONTENT="Simulation, optimization, estimation, and control with APMonitor">

<META NAME="Author" CONTENT="support@apmonitor.com">

</head>(:htmlend:)

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%blue%A%red%P%black%Monitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

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Meet regulatory reporting requirements

Flow assurance of oil and gas transport pipelines

Visualize data from remote locations

Reduce alarms by consolidating relevant information

Provide soft sensing

Automatic control of continuous and batch systems

Increase production 3-5% without equipment changes

Flow assurance of oil and gas transport pipelines

Visualize data from remote locations

Reduce alarms by consolidating relevant information

Provide soft sensing

Automatic control of continuous and batch systems

Increase production 3-5% without equipment changes

to:

* Meet regulatory reporting requirements

* Flow assurance of oil and gas transport pipelines

* Visualize data from remote locations

* Reduce alarms by consolidating relevant information

* Provide soft sensing

* Automatic control of continuous and batch systems

* Increase production 3-5% without equipment changes

* Flow assurance of oil and gas transport pipelines

* Visualize data from remote locations

* Reduce alarms by consolidating relevant information

* Provide soft sensing

* Automatic control of continuous and batch systems

* Increase production 3-5% without equipment changes

Changed lines 3-18 from:

to:

APMonitor is advanced process control and optimization software for industrial-scale systems. The software interfaces to live systems to provide advanced diagnostics, meet safety and environmental constraints, and drive the process to economic optimum. With rapidly changing feedstock and commodity pricing, this application enables instant and continual realignment to real operating objectives. These may include:

Meet regulatory reporting requirements

Flow assurance of oil and gas transport pipelines

Visualize data from remote locations

Reduce alarms by consolidating relevant information

Provide soft sensing

Automatic control of continuous and batch systems

Increase production 3-5% without equipment changes

A number of prebuilt asset models are available with the APMonitor software. The chemical processing modeling package includes reactors, distillation columns, and compressors necessary for industrial scale processes.

----

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor" includes a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

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----

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height=30 width=140 alt="Google Groups">

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<b>Subscribe to apmonitor</b>

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<form action="http://groups.google.com/group/apmonitor/boxsubscribe">

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Email: <input type=text name=email>

<input type=submit name="sub" value="Subscribe">

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<tr><td align=right>

<a href="http://groups.google.com/group/apmonitor">Visit this group</a>

</td></tr>

</table>

(:htmlend:)

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<img src="http://groups.google.com/intl/en/images/logos/groups_logo_sm.gif"

height=30 width=140 alt="Google Groups">

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<b>Subscribe to apmonitor</b>

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<form action="http://groups.google.com/group/apmonitor/boxsubscribe">

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Email: <input type=text name=email>

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<a href="http://groups.google.com/group/apmonitor">Visit this group</a>

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!!! %blue%A%red%P%black%Monitor ~~in a Nutshell~~

to:

!!! %blue%A%red%P%black%Monitor Overview

Deleted lines 35-49:

----

!!! Newton's Apple

Attach:apple.jpg

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.

Changed line 3 from:

%blue%A%red%P%black%~~MonitorAPMonitor~~, or "Advanced Process Monitor", is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

to:

%blue%A%red%P%black%Monitor, or "Advanced Process Monitor", is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

Changed line 3 from:

to:

%blue%A%red%P%black%MonitorAPMonitor, or "Advanced Process Monitor", is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

Changed lines 3-5 from:

to:

APMonitor, or "Advanced Process Monitor", is a modeling language for differential and algebraic (DAE) equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls appropriate external solvers.

----

!!! Differential and Algebraic Equations

----

!!! Differential and Algebraic Equations

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

Attach:apmonitor_icon.jpg

Attach:apmonitor_icon.jpg

to:

!! %blue%A%red%P%black%Monitor Attach:apmonitor_icon.jpg

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to:

Attach:apmonitor_icon.jpg

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!! %blue%A%red%P%black%Monitor~~ ~~[[Attach:apmonitor_icon.jpg]]

to:

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

[[Attach:apmonitor_icon.jpg]]

[[Attach:apmonitor_icon.jpg]]

Changed line 1 from:

!! %blue%A%red%P%black%Monitor [[Attach:~~apmonitor42~~.jpg]]

to:

!! %blue%A%red%P%black%Monitor [[Attach:apmonitor_icon.jpg]]

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!! %blue%A%red%P%black%Monitor [[Attach:~~apmonitor~~.jpg]]

to:

!! %blue%A%red%P%black%Monitor [[Attach:apmonitor42.jpg]]

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!! %blue%A%red%P%black%Monitor ~~Documentation~~

to:

!! %blue%A%red%P%black%Monitor [[Attach:apmonitor.jpg]]

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Attach:apple.jpg

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.

----

Added lines 35-49:

----

!!! Newton's Apple

Attach:apple.jpg

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.

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!! %blue%A%red%P%black%Monitor ~~Documentation Wiki~~

to:

!! %blue%A%red%P%black%Monitor Documentation

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!! %blue%A%red%P%black%Monitor Documentation ~~Homepage~~

to:

!! %blue%A%red%P%black%Monitor Documentation Wiki

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----

to:

----

Changed line 20 from:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. DAE models are generally easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. ~~Analytic solution~~ of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is less restrictive.

to:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. DAE models are generally easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is less restrictive.

Deleted lines 44-51:

* [[Main/APM|Model (apm)]]

* [[Main/INFO|Info (info)]]

* [[Main/DBS|Database (dbs)]]

** [[Main/DbsGlobal|Global]]

** [[Main/DbsVariable|Variables]]

* [[Main/CSV|Data (csv)]]

* [[Main/T0|Solution (t0)]]

Changed lines 46-48 from:

* ~~%list list-page% '''model.~~apm~~''': To generate a new model, create a text file and save it with an ~~'''apm''' ~~extension.~~

* %list list-page% '''model~~.info''': The '''info'''~~ file ~~contains designation of special variables for trending, data acquisition, and mode~~-~~specific actions~~.~~ If no variables are treated specially, the '''info''' file can be blank. ~~

* %list list-page%'''~~model.dbs~~''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

* %list list-page% '''

* %list list-page%

to:

* [[Main/APM|Model (apm)]]

* [[Main/INFO|Info (info)]]

* [[Main/DBS|Database (dbs)]]

** [[Main/DbsGlobal|Global]]

** [[Main/DbsVariable|Variables]]

* [[Main/CSV|Data (csv)]]

* [[Main/T0|Solution (t0)]]

* %list list-page% '''[[Main/APM|model.apm]]''': To generate a new model, create a text file and save it with an '''apm''' extension.

* %list list-page% '''[[Main/INFO|model.info]]''': The '''info''' file contains designation of special variables for trending, data acquisition, and mode-specific actions. If no variables are treated specially, the '''info''' file can be blank.

* %list list-page% '''[[Main/DBS|model.dbs]]''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

* [[Main/INFO|Info (info)]]

* [[Main/DBS|Database (dbs)]]

** [[Main/DbsGlobal|Global]]

** [[Main/DbsVariable|Variables]]

* [[Main/CSV|Data (csv)]]

* [[Main/T0|Solution (t0)]]

* %list list-page% '''[[Main/APM|model.apm]]''': To generate a new model, create a text file and save it with an '''apm''' extension.

* %list list-page% '''[[Main/INFO|model.info]]''': The '''info''' file contains designation of special variables for trending, data acquisition, and mode-specific actions. If no variables are treated specially, the '''info''' file can be blank.

* %list list-page% '''[[Main/DBS|model.dbs]]''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

Changed lines 27-32 from:

* %list list-cat% Steady-~~state simulation ~~(SS)

* ~~Model Parameter Update ~~(MPU)

* ~~Real Time Optimization ~~(RTO)

* ~~Dynamic simulation ~~(SIM)

* ~~Moving horizon estimation ~~(EST)

* ~~Nonlinear control ~~(CTL)

to:

* %list list-cat% [[Main/SteadyState|Steady-State (SS)]]

* [[Main/ParameterFit|Parameter Fit (MPU)]]

* [[Main/Optimization|Optimization (RTO)]]

* [[Main/Simulation|Simulation (SIM)]]

* [[Main/Estimation|Estimation (EST)]]

* [[Main/Control|Control (CTL)]]

* [[Main/ParameterFit|Parameter Fit (MPU)]]

* [[Main/Optimization|Optimization (RTO)]]

* [[Main/Simulation|Simulation (SIM)]]

* [[Main/Estimation|Estimation (EST)]]

* [[Main/Control|Control (CTL)]]

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%list list-cat%

* Steady-state simulation (SS)

*

to:

* %list list-cat% Steady-state simulation (SS)

Changed lines 27-32 from:

to:

%list list-cat%

* Steady-state simulation (SS)

* Model Parameter Update (MPU)

* Real Time Optimization (RTO)

* Dynamic simulation (SIM)

* Moving horizon estimation (EST)

* Nonlinear control (CTL)

* Steady-state simulation (SS)

* Model Parameter Update (MPU)

* Real Time Optimization (RTO)

* Dynamic simulation (SIM)

* Moving horizon estimation (EST)

* Nonlinear control (CTL)

Changed lines 20-21 from:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. DAE models are generally easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is ~~least~~ restrictive.

to:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. DAE models are generally easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is less restrictive.

Changed lines 34-35 from:

The DAE model does not have to be changed to switch between the modes. The model is ~~defined once to facilitate the exchange of information between parameter fitting, dynamic simulation, optimization, and control~~.

to:

The DAE model does not have to be changed to switch between the modes. The same model is used for parameter fitting, dynamic simulation, optimization, and control. The user is required to define the model and the software automatically configures the various simulation options.

Changed lines 38-39 from:

%blue%A%red%P%black%Monitor uses a simultaneous solution approach ~~(versus a sequential approach) to solve the~~ differential equations~~. The differential~~ equations ~~are converted to algebraic equations and solved with large-scale sparse~~ solvers~~. There are a variety of solvers that are available depending on the user's license. These solvers range~~ from free and open-source to commercial.

to:

%blue%A%red%P%black%Monitor uses a simultaneous solution approach to solve the differential equations. The differential equations are converted to algebraic equations and solved with large-scale sparse solvers. There are an assortment of solvers available with various user's licenses, ranging from free and open-source to commercial.

Changed lines 44-51 from:

!!!! ~~Esssential~~ Files for Simulation

~~The model is contained in the text file with an ~~'''apm''' ~~extension. The '''info''' file contains designation of variables that are treated differently depending on the simulation mode~~. ~~If no variables are treated specially, the ~~'''info''' ~~file can be blank. Finally, the '''dbs''' file contains all of the user~~-~~defined options that control how the solution is performed. When no ~~'''~~dbs~~''' file ~~is present, a new file is generated with default parameters~~.

*'''~~apm'''~~: ~~Main model file~~

*'''~~info~~'''~~: Information ~~file ~~to indicate variable types~~

* '''dbs''': Database of options and model inputs

*

*

* '''dbs''': Database of options and model inputs

to:

!!!! Essential Files for Simulation

* %list list-page% '''model.apm''': To generate a new model, create a text file and save it with an '''apm''' extension.

* %list list-page% '''model.info''': The '''info''' file contains designation of special variables for trending, data acquisition, and mode-specific actions. If no variables are treated specially, the '''info''' file can be blank.

* %list list-page% '''model.dbs''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

* %list list-page% '''model.apm''': To generate a new model, create a text file and save it with an '''apm''' extension.

* %list list-page% '''model.info''': The '''info''' file contains designation of special variables for trending, data acquisition, and mode-specific actions. If no variables are treated specially, the '''info''' file can be blank.

* %list list-page% '''model.dbs''': The '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

Changed line 54 from:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited ~~for a software product that is under intensive ~~and ~~collaborative~~ development.

to:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited to %blue%A%red%P%black%Monitor as it allows for collaboration and continuing development.

Deleted lines 6-14:

"In that slight startle from his contemplation –

'Tis said (for I'll not answer above ground

For any sage's creed or calculation) –

A mode of proving that the earth turn'd round

In a most natural whirl, called "gravitation;"

And this is the sole mortal who could grapple,

Since Adam, with a fall or with an apple."

[--Don Juan (1821), Canto 10, Verse I. In Jerome J. McGann (ed.), Lord Byron: The Complete Poetical Works (1986), Vol. 5, 437--]

Changed line 24 from:

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and ~~the push and pull of data to and from~~ live systems.

to:

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and interface with live systems.

Changed line 65 from:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited for a software product that is under intensive development.

to:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited for a software product that is under intensive and collaborative development.

Changed line 65 from:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is ~~better~~ suited for a software product that is under intensive development.

to:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is well suited for a software product that is under intensive development.

Added line 62:

Changed lines 65-67 from:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is better suited for a software product that is under intensive development.

to:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is better suited for a software product that is under intensive development.

----

----

Deleted lines 47-52:

# Honeywell's NOVA Solver (version 4.0)

# Carnegie Mellon's IPOPT Solver (version 2.3)

# IBM's IPOPT Solver (version 3.5)

# Stanford's SNOPT Solver (version 6.1)

# Stanford's MINOS Solver (version 5.5)

Changed line 24 from:

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and ~~less on~~ data handling, model convergence, and ~~on-line implementation~~.

to:

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and let %blue%A%red%P%black%Monitor perform data handling, model convergence, and the push and pull of data to and from live systems.

Changed lines 52-53 from:

# Stanford's SNOPT Solver (version 6.~~5~~)

# Stanford's MINOS Solver (version 5.~~0~~)

# Stanford's MINOS Solver (version 5.

to:

# Stanford's SNOPT Solver (version 6.1)

# Stanford's MINOS Solver (version 5.5)

# Stanford's MINOS Solver (version 5.5)

Changed lines 17-18 from:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (1) and the motion of the apple (2).

to:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (Equation 1) and the motion of the apple (Equation 2).

Added lines 23-24:

Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The %blue%A%red%P%black%Monitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With %blue%A%red%P%black%Monitor, the user can concentrate more on the difficult task of building the mathematical relationships and less on data handling, model convergence, and on-line implementation.

Changed line 17 from:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree~~. Newton's theory revolutionized the way his society viewed the movement of celestial bodies~~. A simple equation defines the gravitational force between two objects (1) and the motion of the apple (2).

to:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. A simple equation defines the gravitational force between two objects (1) and the motion of the apple (2).

Changed lines 68-120 from:

* Model Structure

** Parameters

** Variables

*** Algebraic

*** Differential

*** Constraints

*** Slack variables

*** Objective function variables

*** Variable scope

** Connections

** Intermediates

** Equations

** Arrays

** Objects

*** Feed

*** Flash

*** Flash_column

*** Lag

*** Massflow

*** Mixer

*** PID

*** Poly_reactor

*** Pump

*** Reactor

*** Splitter

*** Stage_1

*** Stage_2

*** Stream_lag

*** Vessel

*** Vesselm

** Object arrays

** Object variable connections

* Modes of Operation

** Steady-state Simulation (ss)

** Model Parameter Update (mpu)

** Real-time Optimization (rto)

** Dynamic Simulation (sim)

** Moving Horizon Estimation (est)

** Nonlinear Control (ctl)

* System files

** apm - Model file

** info - Information file

** dbs - Database file

** t0 - Restart solution file

* Obtaining Solutions

** Software demo

** Online interface

** DOS Command line

** MATLAB

The documentation is presented in a Wiki format to allow instant modification by anyone with permission to edit.

to:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''. The documentation is presented in a Wiki format to allow collaborative modification by any user. This format is better suited for a software product that is under intensive development.

Changed line 68 from:

The basic structure of the documentation is outlined into four main sections: ~~!!!~~model structure~~!!!~~, ~~!!!~~modes of operation~~!!!~~, ~~!!!~~system files~~!!!~~, and ~~!!!~~obtaining solutions~~!!!~~.

to:

The basic structure of the documentation is outlined into four main sections: '''model structure''', '''modes of operation''', '''system files''', and '''obtaining solutions'''.

Changed lines 68-69 from:

The ~~documentation is presented in a Wiki format to allow instant modification by anyone with permission to edit. The basic structure of the documentation is ~~

to:

The basic structure of the documentation is outlined into four main sections: !!!model structure!!!, !!!modes of operation!!!, !!!system files!!!, and !!!obtaining solutions!!!.

Added line 120:

The documentation is presented in a Wiki format to allow instant modification by anyone with permission to edit.

Changed line 114 from:

* ~~Solution options~~

to:

* Obtaining Solutions

Changed line 27 from:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. ~~The problem with DAE models is that they are~~ easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is least restrictive.

to:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. DAE models are generally easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is least restrictive.

Changed line 34 from:

# Steady-state ~~simulation~~

to:

# Steady-state simulation (SS)

Changed lines 37-39 from:

# Dynamic simulation

~~# Moving horizon estimation ~~(~~MHE~~)

#~~Nonlinear control ~~(~~NLC~~)

#

to:

# Dynamic simulation (SIM)

# Moving horizon estimation (EST)

# Nonlinear control (CTL)

# Moving horizon estimation (EST)

# Nonlinear control (CTL)

Added lines 102-108:

* Modes of Operation

** Steady-state Simulation (ss)

** Model Parameter Update (mpu)

** Real-time Optimization (rto)

** Dynamic Simulation (sim)

** Moving Horizon Estimation (est)

** Nonlinear Control (ctl)

** Steady-state Simulation (ss)

** Model Parameter Update (mpu)

** Real-time Optimization (rto)

** Dynamic Simulation (sim)

** Moving Horizon Estimation (est)

** Nonlinear Control (ctl)

Changed lines 70-102 from:

* ~~Basic ~~Model Structure

* Parameters

* Variables

** Algebraic

** Differential

** Constraints

** Slack variables

** Objective function variables

** Variable scope

* Connections

* Intermediates

* Equations

* Intermediate variables and equations

* Arrays

* Objects

** Feed

** Flash

** Flash_column

** Lag

** Massflow

** Mixer

** PID

** Poly_reactor

** Pump

** Reactor

** Splitter

** Stage_1

** Stage_2

** Stream_lag

** Vessel

** Vesselm

* Object arrays

* Object variable connections

* Parameters

* Variables

** Algebraic

** Differential

** Constraints

** Slack variables

** Objective function variables

** Variable scope

* Connections

* Intermediates

* Equations

* Intermediate variables and equations

* Arrays

* Objects

** Feed

** Flash

** Flash_column

** Lag

** Massflow

** Mixer

** PID

** Poly_reactor

** Pump

** Reactor

** Splitter

** Stage_1

** Stage_2

** Stream_lag

** Vessel

** Vesselm

* Object arrays

* Object variable connections

to:

* Model Structure

** Parameters

** Variables

*** Algebraic

*** Differential

*** Constraints

*** Slack variables

*** Objective function variables

*** Variable scope

** Connections

** Intermediates

** Equations

** Intermediate variables and equations

** Arrays

** Objects

*** Feed

*** Flash

*** Flash_column

*** Lag

*** Massflow

*** Mixer

*** PID

*** Poly_reactor

*** Pump

*** Reactor

*** Splitter

*** Stage_1

*** Stage_2

*** Stream_lag

*** Vessel

*** Vesselm

** Object arrays

** Object variable connections

** Parameters

** Variables

*** Algebraic

*** Differential

*** Constraints

*** Slack variables

*** Objective function variables

*** Variable scope

** Connections

** Intermediates

** Equations

** Intermediate variables and equations

** Arrays

** Objects

*** Feed

*** Flash

*** Flash_column

*** Lag

*** Massflow

*** Mixer

*** PID

*** Poly_reactor

*** Pump

*** Reactor

*** Splitter

*** Stage_1

*** Stage_2

*** Stream_lag

*** Vessel

*** Vesselm

** Object arrays

** Object variable connections

Added lines 78-79:

** Variable scope

* Connections

* Connections

Added line 102:

* Object variable connections

Changed line 80 from:

* Intermediate ~~Variables~~

to:

* Intermediate variables and equations

Added line 99:

* Object arrays

Added lines 99-107:

* System files

** apm - Model file

** info - Information file

** dbs - Database file

** t0 - Restart solution file

* Solution options

** Software demo

** Online interface

** DOS Command line

** apm - Model file

** info - Information file

** dbs - Database file

** t0 - Restart solution file

* Solution options

** Software demo

** Online interface

** DOS Command line

Added line 3:

----

Added line 24:

----

Added line 29:

----

Added line 65:

----

Added lines 61-95:

!! Documentation Overview

The documentation is presented in a Wiki format to allow instant modification by anyone with permission to edit. The basic structure of the documentation is

* Basic Model Structure

* Parameters

* Variables

** Algebraic

** Differential

** Constraints

** Slack variables

** Objective function variables

* Intermediates

* Equations

* Intermediate Variables

* Arrays

* Objects

** Feed

** Flash

** Flash_column

** Lag

** Massflow

** Mixer

** PID

** Poly_reactor

** Pump

** Reactor

** Splitter

** Stage_1

** Stage_2

** Stream_lag

** Vessel

** Vesselm

Changed lines 42-43 from:

%blue%A%red%P%black%Monitor uses a simultaneous solution approach (versus a sequential approach) to solve the differential equations.

to:

%blue%A%red%P%black%Monitor uses a simultaneous solution approach (versus a sequential approach) to solve the differential equations. The differential equations are converted to algebraic equations and solved with large-scale sparse solvers. There are a variety of solvers that are available depending on the user's license. These solvers range from free and open-source to commercial.

# Honeywell's NOVA Solver (version 4.0)

# Carnegie Mellon's IPOPT Solver (version 2.3)

# IBM's IPOPT Solver (version 3.5)

# Stanford's SNOPT Solver (version 6.5)

# Stanford's MINOS Solver (version 5.0)

# Honeywell's NOVA Solver (version 4.0)

# Carnegie Mellon's IPOPT Solver (version 2.3)

# IBM's IPOPT Solver (version 3.5)

# Stanford's SNOPT Solver (version 6.5)

# Stanford's MINOS Solver (version 5.0)

Deleted lines 53-55:

Changed line 56 from:

The model is contained in the text file with an '''apm''' extension. The '''info''' file contains designation of variables that are treated differently depending on the simulation mode. Finally, the '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

to:

The model is contained in the text file with an '''apm''' extension. The '''info''' file contains designation of variables that are treated differently depending on the simulation mode. If no variables are treated specially, the '''info''' file can be blank. Finally, the '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

Changed lines 21-22 from:

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as ~~an ~~algebraic and differential ~~equation~~. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

to:

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as algebraic and differential equations. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

Changed line 25 from:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. The problem with DAE models is that they are easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems.

to:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. The problem with DAE models is that they are easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. %blue%A%red%P%black%Monitor allows an open-equation format that is least restrictive.

Changed lines 55-57 from:

* '''apm''' Main model file

* '''info''' Information file to indicate variable types

* '''dbs''' Database of options and model inputs

* '''info''' Information file to indicate variable types

* '''dbs''' Database of options and model inputs

to:

* '''apm''': Main model file

* '''info''': Information file to indicate variable types

* '''dbs''': Database of options and model inputs

* '''info''': Information file to indicate variable types

* '''dbs''': Database of options and model inputs

Changed lines 55-57 from:

* apm ~~ - Main model ~~file

* info~~- ~~Information file to indicate variable types

* dbs~~ -~~ Database of options and model inputs

* info

* dbs

to:

* '''apm''' Main model file

* '''info''' Information file to indicate variable types

* '''dbs''' Database of options and model inputs

* '''info''' Information file to indicate variable types

* '''dbs''' Database of options and model inputs

Changed lines 55-57 from:

* ~~*.~~apm - Main model file

*~~*.~~info - Information file to indicate variable types

*~~*.~~dbs - Database of options and

*

*

to:

* apm - Main model file

* info - Information file to indicate variable types

* dbs - Database of options and model inputs

* info - Information file to indicate variable types

* dbs - Database of options and model inputs

Added lines 48-50:

Changed lines 53-55 from:

The model is contained in the text file with an '~~apm~~'~~ extension example.~~apm.

User generated~~:~~

User

to:

The model is contained in the text file with an '''apm''' extension. The '''info''' file contains designation of variables that are treated differently depending on the simulation mode. Finally, the '''dbs''' file contains all of the user-defined options that control how the solution is performed. When no '''dbs''' file is present, a new file is generated with default parameters.

Deleted lines 55-56:

Program generated, user edited:

Changed lines 38-49 from:

APMonitor enables the use of the nonlinear DAE models directly in parameter estimation, optimization, and control applications.

A number

to:

The DAE model does not have to be changed to switch between the modes. The model is defined once to facilitate the exchange of information between parameter fitting, dynamic simulation, optimization, and control.

!!!! Solution options

%blue%A%red%P%black%Monitor uses a simultaneous solution approach (versus a sequential approach) to solve the differential equations.

!!!! Chemical Process Flowsheets

A thermodynamic database and a number of prebuilt nonlinear models are available with %blue%A%red%P%black%Monitor. The chemical processing modeling package includes polymer reactors, distillation columns, compressors, valves, etc. These models are combined to form a flowsheet in an object-oriented environment.

!!!! Esssential Files for Simulation

The model is contained in the text file with an 'apm' extension example.apm.

User generated:

* *.apm - Main model file

Program generated, user edited:

* *.info - Information file to indicate variable types

* *.dbs - Database of options and

!!!! Solution options

%blue%A%red%P%black%Monitor uses a simultaneous solution approach (versus a sequential approach) to solve the differential equations.

!!!! Chemical Process Flowsheets

A thermodynamic database and a number of prebuilt nonlinear models are available with %blue%A%red%P%black%Monitor. The chemical processing modeling package includes polymer reactors, distillation columns, compressors, valves, etc. These models are combined to form a flowsheet in an object-oriented environment.

!!!! Esssential Files for Simulation

The model is contained in the text file with an 'apm' extension example.apm.

User generated:

* *.apm - Main model file

Program generated, user edited:

* *.info - Information file to indicate variable types

* *.dbs - Database of options and

Changed lines 25-28 from:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. ~~ ~~

%blue%A%red%P%black%Monitor software is ~~a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs).~~

%blue%A%red%P%black%Monitor software

to:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways. The problem with DAE models is that they are easy to write but often difficult to solve analytically. Entire university level courses are devoted to the solution of particular types of differential equations in analytic form. Analytic solution of more complex systems is better handled through numeric approaches. There are many software packages that can solve DAE models for small and medium size problems. %blue%A%red%P%black%Monitor is designed to solve large-scale problems.

!!! %blue%A%red%P%black%Monitor in a Nutshell

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in six solution modes:

# Steady-state simulation

# Model Parameter Update (MPU)

# Real Time Optimization (RTO)

# Dynamic simulation

# Moving horizon estimation (MHE)

# Nonlinear control (NLC)

!!! %blue%A%red%P%black%Monitor in a Nutshell

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in six solution modes:

# Steady-state simulation

# Model Parameter Update (MPU)

# Real Time Optimization (RTO)

# Dynamic simulation

# Moving horizon estimation (MHE)

# Nonlinear control (NLC)

Changed lines 14-21 from:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. Newton's theory revolutionized the way his society viewed the movement of celestial bodies. A simple equation defines the gravitational force between two objects~~,~~

F =(~~G m'_1_' m'_2_') / r'^2^'~~

and the ~~velocity of the apple as it decends to earth,~~

F = m dv/dt

F =

and

F = m dv/dt

to:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. Newton's theory revolutionized the way his society viewed the movement of celestial bodies. A simple equation defines the gravitational force between two objects (1) and the motion of the apple (2).

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

# F = (G m'_1_' m'_2_') / r'^2^'

# F = m dv/dt

Changed line 23 from:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as ~~a reaction network~~.

to:

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as biological metabolic pathways.

Changed lines 14-19 from:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. Newton's theory revolutionized the way his society viewed the movement of celestial bodies. A simple equation defines the gravitational force between two objects~~.~~

Force = G ~~* mass~~'_1_' ~~* mass~~'_2_' / r'^2^'

Force

to:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. Newton's theory revolutionized the way his society viewed the movement of celestial bodies. A simple equation defines the gravitational force between two objects,

F = (G m'_1_' m'_2_') / r'^2^'

and the velocity of the apple as it decends to earth,

F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as an algebraic and differential equation. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

!!! Introduction to Differential and Algebraic Equations

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as a reaction network.

F = (G m'_1_' m'_2_') / r'^2^'

and the velocity of the apple as it decends to earth,

F = m dv/dt

The apple falling from a tree is simply approximated by these two equations. These two equations are solved together as an algebraic and differential equation. The solution of these two equations defines the velocity of the apple and the force the earth and apple exert on each other.

!!! Introduction to Differential and Algebraic Equations

Differential and algebraic (DAE) models are a natural expression of systems that change with time. These dynamic systems may be as simple as a falling apple or as complex as a reaction network.

Changed line 33 from:

to:

APMonitor enables the use of the nonlinear DAE models directly in parameter estimation, optimization, and control applications.

Changed line 16 from:

Force = G * mass_1_ * mass_2_ / r^2^

to:

Force = G * mass'_1_' * mass'_2_' / r'^2^'

Changed line 16 from:

to:

Force = G * mass_1_ * mass_2_ / r^2^

Deleted lines 4-5:

Added lines 14-16:

A popular story claims that Sir Isaac Newton was inspired to formulate his theory of universal gravitation by observing an apple fall from a tree. Newton's theory revolutionized the way his society viewed the movement of celestial bodies. A simple equation defines the gravitational force between two objects.

Force = G * mass_1_ * mass_2_ / r^2^

Force = G * mass_1_ * mass_2_ / r^2^

Changed line 5 from:

In that slight startle from his contemplation –

to:

"In that slight startle from his contemplation –

Changed lines 11-14 from:

Since Adam, with a fall or with an apple.

to:

Since Adam, with a fall or with an apple."

[--Don Juan (1821), Canto 10, Verse I. In Jerome J. McGann (ed.), Lord Byron: The Complete Poetical Works (1986), Vol. 5, 437--]

[--Don Juan (1821), Canto 10, Verse I. In Jerome J. McGann (ed.), Lord Byron: The Complete Poetical Works (1986), Vol. 5, 437--]

Changed lines 1-26 from:

to:

!! %blue%A%red%P%black%Monitor Documentation Homepage

A popular story claims that Newton was inspired to formulate his theory of universal gravitation by the fall of an apple from a tree.

In that slight startle from his contemplation –

'Tis said (for I'll not answer above ground

For any sage's creed or calculation) –

A mode of proving that the earth turn'd round

In a most natural whirl, called "gravitation;"

And this is the sole mortal who could grapple,

Since Adam, with a fall or with an apple.

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs).

DAE models are a natural expression of many systems. APMonitor enables the use of the nonlinear DAE models directly in parameter estimation, optimization, and control applications.

A number of prebuilt nonlinear models are available with the APMonitor product. The chemical processing modeling package includes polymer reactors, distillation columns, compressors, etc.

!!!

A popular story claims that Newton was inspired to formulate his theory of universal gravitation by the fall of an apple from a tree.

In that slight startle from his contemplation –

'Tis said (for I'll not answer above ground

For any sage's creed or calculation) –

A mode of proving that the earth turn'd round

In a most natural whirl, called "gravitation;"

And this is the sole mortal who could grapple,

Since Adam, with a fall or with an apple.

%blue%A%red%P%black%Monitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs).

DAE models are a natural expression of many systems. APMonitor enables the use of the nonlinear DAE models directly in parameter estimation, optimization, and control applications.

A number of prebuilt nonlinear models are available with the APMonitor product. The chemical processing modeling package includes polymer reactors, distillation columns, compressors, etc.

!!!

Changed line 1 from:

!! %blue%A%red%P%black%~~Monitor~~

to:

!! %blue%A%red%P%black%Monitor Wiki Homepage

Changed line 1 from:

!! %blue%~~APMonitor~~

to:

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

Changed lines 1-2 from:

to:

!! %blue%APMonitor

Changed lines 1-12 from:

A local copy of PmWiki's

documentation has been installed along with the software,

and is available via the [[PmWiki/documentation index]].

To continue setting up PmWiki, see [[PmWiki/initial setup tasks]].

The [[PmWiki/basic editing]] page describes how to create pages

in PmWiki. You can practice editing in the [[wiki sandbox]].

More information about PmWiki is available from http://www.pmwiki.org .

to:

!! %%blue%%APMonitor