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APMonitor, 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 MATLAB toolbox, a Python module, a Julia package, or from a web browser interface.
APMonitor, 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 MATLAB toolbox, a Python module, a Julia package, or from a web browser interface.
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
APMonitor uses a simultaneous or sequential solution approach to solve the differential and algebraic 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. APMonitor provides Nonlinear Programming Solvers (such as APOPT, BPOPT, IPOPT, MINOS, SNOPT) are accessed by switching APM.SOLVER. It provides the required information to the solvers by compiling the model to byte code with automatic differentiation for derivatives in sparse form.
APMonitor uses a simultaneous or sequential solution approach to solve the differential and algebraic 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. APMonitor provides Nonlinear Programming Solvers (such as APOPT, BPOPT, IPOPT, MINOS, SNOPT) are accessed by switching APM.SOLVER. It provides the required information to the solvers by compiling the model to byte code with automatic differentiation for derivatives in sparse form.
APM.IMODE 1-3 modes are steady state options with all derivatives set equal to zero. Modes 4-6 are dynamic modes where the differential equations define how the variables change with time. Modes 7-9 are the same as 4-6 except the solution is performed with a sequential versus a simultaneous approach. Each mode for simulation, estimation, and optimization has a steady state and dynamic option.
APM.IMODE 1-3 modes are steady state options with all derivatives set equal to zero. Modes 4-6 are dynamic modes where the differential equations define how the variables change with time. Modes 7-9 are the same as 4-6 except the solution is performed with a sequential versus a simultaneous approach. Each mode for simulation, estimation, and optimization has a steady state and dynamic option. There are many additional application configuration options and parameter and variable options that can be set or retrieved in MATLAB or Python.
APMonitor uses a simultaneous or sequential solution approach to solve the differential and algebraic 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. APMonitor provides the following to a Nonlinear Programming Solver (such as APOPT, BPOPT, IPOPT, MINOS, SNOPT) in sparse form:
APMonitor uses a simultaneous or sequential solution approach to solve the differential and algebraic 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. APMonitor provides Nonlinear Programming Solvers (such as APOPT, BPOPT, IPOPT, MINOS, SNOPT) are accessed by switching APM.SOLVER. It provides the required information to the solvers by compiling the model to byte code with automatic differentiation for derivatives in sparse form.
When the system of equations does not converge, APMonitor produces a convergence report in infeasibilities.txt. There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.DIAGLEVEL to higher levels (0-10) gives more output to the user. Setting APM.COLDSTART to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
When the system of equations does not converge, APMonitor produces a convergence report in infeasibilities.txt that can be retrieved with apm_get(s,a,'infeasibilities.txt'). There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.DIAGLEVEL to higher levels (0-10) gives more output to the user. Setting APM.COLDSTART to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
APMonitor compiles a model to byte-code and performs model reduction based on analysis of the sparsity structure (incidence of variables in equations or objective function) of the model. For differential and algebraic equation systems, orthogonal collocation on finite elements is used to transcribe the problem into a purely algebraic system of equations. APMonitor has several modes of operation, adjustable with the imode parameter. The core of all modes is the nonlinear model. Each mode interacts with the nonlinear model to receive or provide information. The 9 modes of operation are:
APMonitor compiles a model to byte-code and performs model reduction based on analysis of the sparsity structure (incidence of variables in equations or objective function) of the model. For differential and algebraic equation systems, orthogonal collocation on finite elements is used to transcribe the problem into a purely algebraic system of equations.
Modes of Operation
APMonitor has several modes of operation, adjustable with the APM.IMODE parameter. The core of all modes is the model (linear or nonlinear). Each mode interacts with the nonlinear model to receive or provide information. The 9 modes of operation are:
Modes 1-3 are steady state modes with all derivatives set equal to zero. Modes 4-6 are dynamic modes where the differential equations define how the variables change with time. Modes 7-9 are the same as 4-6 except the solution is performed with a sequential versus a simultaneous approach. Each mode for simulation, estimation, and optimization has a steady state and dynamic option.
APMonitor provides the following to a Nonlinear Programming Solver (APOPT, BPOPT, IPOPT, MINOS, SNOPT) in sparse form:
APM.IMODE 1-3 modes are steady state options with all derivatives set equal to zero. Modes 4-6 are dynamic modes where the differential equations define how the variables change with time. Modes 7-9 are the same as 4-6 except the solution is performed with a sequential versus a simultaneous approach. Each mode for simulation, estimation, and optimization has a steady state and dynamic option.
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 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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
Nonlinear and Mixed Integer Solvers
APMonitor uses a simultaneous or sequential solution approach to solve the differential and algebraic 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. APMonitor provides the following to a Nonlinear Programming Solver (such as APOPT, BPOPT, IPOPT, MINOS, SNOPT) in sparse form:
Once the solution is complete, APMonitor writes the results in results.csv that is available for transfer from the apm_sol(s,a) function in MATLAB or Python. It also creates several web-interface pages that are accessed with apm_web(s,a). The web-interface includes a sensitivity analysis if APM.SENSITIVITY = 1 (ON). When the system of equations does not converge, APMonitor produces a convergence report in ‘infeasibilities.txt’. There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.DIAGLEVEL to higher levels (0-10) gives more output to the user. Setting APM.COLDSTART to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
Reference to Cite
Viewing Results
Once the solution is complete, APMonitor writes the results in results.csv that is available for transfer from the apm_sol(s,a) function in MATLAB or Python. It also creates several web-interface pages that are accessed with apm_web(s,a). The web-interface includes a sensitivity analysis if APM.SENSITIVITY = 1 (ON).
Advanced Diagnostics
When the system of equations does not converge, APMonitor produces a convergence report in infeasibilities.txt. There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.DIAGLEVEL to higher levels (0-10) gives more output to the user. Setting APM.COLDSTART to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
Range of Usage
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. A modeling language interface to MATLAB and Python extends the applicability for pre- and post-processing of the optimization solution results.
References to Cite
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 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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
Solution options
APMonitor 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.
Range of usage
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. A modeling language interface to MATLAB and Python extends the applicability for pre- and post-processing of the optimization solution results.
Once the solution is complete, APMonitor writes the results in results.csv that is available for transfer from the apm_sol(s,a) function in MATLAB or Python. It also creates several web-interface pages that are accessed with apm_web(s,a). The web-interface includes a sensitivity analysis if APM.SENSITIVITY = 1 (ON).
Once the solution is complete, APMonitor writes the results in results.csv that is available for transfer from the apm_sol(s,a) function in MATLAB or Python. It also creates several web-interface pages that are accessed with apm_web(s,a). The web-interface includes a sensitivity analysis if APM.sensitivity? = 1 (ON). When the system of equations does not converge, APMonitor produces a convergence report in ‘infeasibilities.txt’. There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.diaglevel to higher levels (0-10) gives more output to the user. Setting APM.coldstart to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
When the system of equations does not converge, APMonitor produces a convergence report in ‘infeasibilities.txt’. There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.DIAGLEVEL to higher levels (0-10) gives more output to the user. Setting APM.COLDSTART to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
APMonitor provides the following to a Nonlinear Programming Solver (APOPT, BPOPT, IPOPT, MINOS, SNOPT) in sparse form:
- Variables with default values and constraints
- Objective function
- Equations
- Evaluation of equation residuals
- Sparsity structure
- Gradients (1st derivatives)
- Gradient of the equations
- Gradient of the objective function
- Hessian of the Lagrangian (2nd derivatives)
- 2nd Derivative of the equations
- 2nd Derivative of the objective function
Once the solution is complete, APMonitor writes the results in results.csv that is available for transfer from the apm_sol(s,a) function in MATLAB or Python. It also creates several web-interface pages that are accessed with apm_web(s,a). The web-interface includes a sensitivity analysis if APM.sensitivity? = 1 (ON). When the system of equations does not converge, APMonitor produces a convergence report in ‘infeasibilities.txt’. There are other levels of debugging that help expose the steps that APMonitor is taking to analyze or solve the problem. Setting APM.diaglevel to higher levels (0-10) gives more output to the user. Setting APM.coldstart to 2 decomposes the problem into irreducible sets of variables and equations to identify infeasible equations or properly initialize a model.
The APMonitor modeling language is a high-level abstraction of mathematical optimization problems. Values in the models are defined by Constants, Parameters, and Variables. The values are related to each other by Intermediates or Equations. Objective functions are defined to maximize or minimize certain values. Objects are built-in collections of values (constants, parameters, and variables) and relationships (intermediates, equations, and objective functions). Objects can build upon other objects with object-oriented relationships. APMonitor compiles a model to byte-code and performs model reduction based on analysis of the sparsity structure (incidence of variables in equations or objective function) of the model. For differential and algebraic equation systems, orthogonal collocation on finite elements is used to transcribe the problem into a purely algebraic system of equations. APMonitor has several modes of operation, adjustable with the imode parameter. The core of all modes is the nonlinear model. Each mode interacts with the nonlinear model to receive or provide information. The 9 modes of operation are:
- Steady-state simulation (SS)
- Model parameter update (MPU)
- Real-time optimization (RTO)
- Dynamic simulation (SIM)
- Moving horizon estimation (EST)
- Nonlinear control / dynamic optimization (CTL)
- Sequential dynamic simulation (SQS)
- Sequential dynamic estimation (SQE)
- Sequential dynamic optimization (SQO)
Modes 1-3 are steady state modes with all derivatives set equal to zero. Modes 4-6 are dynamic modes where the differential equations define how the variables change with time. Modes 7-9 are the same as 4-6 except the solution is performed with a sequential versus a simultaneous approach. Each mode for simulation, estimation, and optimization has a steady state and dynamic option.
Software Technical Reference
- J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.
Reference to Cite
Please consider citing the following article for the APMonitor Optimization Suite.
- Hedengren, J. D. and Asgharzadeh Shishavan, R., Powell, K.M., and Edgar, T.F., Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers and Chemical Engineering, Volume 70, pg. 133–148, 2014, DOI: 10.1016/j.compchemeng.2014.04.013. Article - Preprint - BibTeX - RIS
Other applications of APMonitor are listed on the references page. Please send a note to support@apmonitor.com if you'd like to add a reference to the list.
APMonitor, 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 MATLAB toolbox, Python, or from a web browser interface.
APMonitor, 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 MATLAB toolbox, a Python module, a Julia package, or from a web browser interface.
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.
APMonitor, 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 MATLAB toolbox, Python, or from a web browser interface.
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, 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, 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.
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.
- 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
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. A modeling language interface to MATLAB and Python extends the applicability for pre- and post-processing of the optimization solution results.
Attach:apm_matlab.png Download Latest MATLAB Toolbox Attach:apm_python.png Download Latest Python Package
(:title APMonitor Modeling Language Documentation:)
(:title APMonitor Documentation:)
APMonitor Overview
APMonitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in 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 APMonitor. 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.
Software Technical Reference
- J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.
Software Technical Reference
- J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.
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 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.
Software Technical Reference
- J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell, T.F. Edgar, Nonlinear Modeling, Estimation and Predictive Control in APMonitor, Computers & Chemical Engineering, 2014.
APMonitor 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:
- Steady-State (SS)
- Parameter Fit (MPU)
- Optimization (RTO)
- Simulation (SIM)
- Estimation (EST)
- Control (CTL)
- 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.
APMonitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs). These models are employed in 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.
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 APMonitor as it allows for collaboration and continuing development.
Essential Files for Simulation
- model.apm: To generate a new model, create a text file and save it with an apm extension.
- 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.
- 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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APMonitor, 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.
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.
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APMonitor 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:
APMonitor 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:
(:description Simulation, optimization, estimation, and control with APMonitor:)
(:description APMonitor Documentation: Simulation, optimization, estimation, and control:)
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:
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:
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:
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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:
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
- 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
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.
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.
APMonitor, 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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Newton's Apple
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 APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, the user can concentrate more on the difficult task of building the mathematical relationships and let APMonitor perform data handling, model convergence, and interface with live systems.
APMonitorAPMonitor, 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, 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, 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.
APMonitorAPMonitor, 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
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
Newton's Apple
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 APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, the user can concentrate more on the difficult task of building the mathematical relationships and let APMonitor perform data handling, model convergence, and interface with live systems.
Newton's Apple
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 APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, the user can concentrate more on the difficult task of building the mathematical relationships and let APMonitor perform data handling, model convergence, and interface with live systems.
APMonitor Documentation Wiki
APMonitor Documentation
APMonitor Documentation Homepage
APMonitor Documentation Wiki
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
- model.apm: To generate a new model, create a text file and save it with an apm extension.
- 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.
- 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.
- Model (apm)
- Info (info)
- Database (dbs)
- Data (csv)
- Solution (t0)
- model.apm: To generate a new model, create a text file and save it with an apm extension.
- 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.
- 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.
- 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)
- Steady-state simulation (SS)
- 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)
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is least restrictive.
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is less restrictive.
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.
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.
APMonitor 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.
APMonitor 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.
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
Essential Files for Simulation
- model.apm: To generate a new model, create a text file and save it with an apm extension.
- 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.
- 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.
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.
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 APMonitor as it allows for collaboration and continuing development.
"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
Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, the user can concentrate more on the difficult task of building the mathematical relationships and let APMonitor perform data handling, model convergence, and the push and pull of data to and from live systems.
Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, the user can concentrate more on the difficult task of building the mathematical relationships and let APMonitor perform data handling, model convergence, and interface with live systems.
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.
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.
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.
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.
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.
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.
- 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 APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, 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.
Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, the user can concentrate more on the difficult task of building the mathematical relationships and let APMonitor perform data handling, model convergence, and the push and pull of data to and from live systems.
- Stanford's SNOPT Solver (version 6.5)
- Stanford's MINOS Solver (version 5.0)
- Stanford's SNOPT Solver (version 6.1)
- Stanford's MINOS Solver (version 5.5)
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).
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).
Like Newton, it takes a trained mind to formulate, test, and validate mathematical models from observation of physical systems. The APMonitor software gives users a model development platform for simulation, data reconciliation, and optimization for both steady-state and dynamic systems. With APMonitor, 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.
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).
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).
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.
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.
The basic structure of the documentation is outlined into four main sections: !!!model structure!!!, !!!modes of operation!!!, !!!system files!!!, and !!!obtaining solutions!!!.
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 instant modification by anyone with permission to edit. The basic structure of the documentation is
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 instant modification by anyone with permission to edit.
- Solution options
- Obtaining Solutions
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is least restrictive.
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is least restrictive.
- Steady-state simulation
- Steady-state simulation (SS)
- Dynamic simulation
- Moving horizon estimation (MHE)
- Nonlinear control (NLC)
- Dynamic simulation (SIM)
- Moving horizon estimation (EST)
- Nonlinear control (CTL)
- 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)
- 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
- 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
- Variable scope
- Connections
- Object variable connections
- Intermediate Variables
- Intermediate variables and equations
- Object arrays
- System files
- apm - Model file
- info - Information file
- dbs - Database file
- t0 - Restart solution file
- Solution options
- Software demo
- Online interface
- DOS Command line
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
APMonitor uses a simultaneous solution approach (versus a sequential approach) to solve the differential equations.
APMonitor 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)
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.
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.
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.
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.
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. APMonitor is designed to solve large-scale problems.
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. APMonitor is designed to solve large-scale problems. Additionally, other software packages often require the user to reformulate the equations into a restrictive form. APMonitor allows an open-equation format that is least restrictive.
- apm Main model file
- info Information file to indicate variable types
- dbs Database of options and model inputs
- apm: Main model file
- info: Information file to indicate variable types
- dbs: Database of options and model inputs
- apm - Main model file
- info - Information file to indicate variable types
- dbs - Database of options and model inputs
- apm Main model file
- info Information file to indicate variable types
- dbs Database of options and model inputs
- *.apm - Main model file
- *.info - Information file to indicate variable types
- *.dbs - Database of options and
- apm - Main model file
- info - Information file to indicate variable types
- dbs - Database of options and model inputs
The model is contained in the text file with an 'apm' extension example.apm.
User generated:
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.
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.
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
APMonitor 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 APMonitor. 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
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.
APMonitor software is a modeling, simulation, and optimization environment for large-scale models of differential and algebraic equations (DAEs).
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. APMonitor is designed to solve large-scale problems.
APMonitor in a Nutshell
APMonitor 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)
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
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
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.
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.
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}
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.
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.
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^
Force = G * mass_{1} * mass_{2} / r^{2}
Force = G * mass_1_ * mass_2_ / r^2^
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.
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^
In that slight startle from his contemplation –
"In that slight startle from his contemplation –
Since Adam, with a fall or with an apple.
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
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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.
APMonitor 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.
Welcome to PmWiki!
A local copy of PmWiki's documentation has been installed along with the software, and is available via the documentation index.
To continue setting up PmWiki, see initial setup tasks.
The 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 https://www.pmwiki.org .