Dynamic Optimization
Main.DynamicOptimization History
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(:title Dynamic Optimization for Engineering Design:)
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(:title Dynamic Optimization:)
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In order to apply dynamic optimization methods we must have a dynamic model to optimize. Obtaining a good dynamic model of the design problem is the most important step. A static model is often developed first and can often be augmented to include dynamic elements that relate how the system evolves with time. In this section we discuss some modeling concepts for dynamic systems that can help you develop models for optimization. We also discuss the formulation objectives, constraints, and dynamic data sets. See the [[https://apmonitor.com/do|Dynamic Optimization Course]] for additional content.
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* [[Attach:blood_glucose_optimal_control.zip|Download Exothermic Reactor Files]]
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* [[https://apmonitor.com/do/index.php/Main/NonlinearControl|Download Exothermic Reactor Files with Video Solutions]]
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!!! Reduce Pollution from an Exothermic Reactor
The objective is to reduce the concentration of the pollution from an exothermic reactor without exceeding an upper temperature limit. Python, MATLAB, and Simulink simulations are available for download at the link below.
Attach:cstr.png
* [[Attach:blood_glucose_optimal_control.zip|Download Exothermic Reactor Files]]
!!! Reduce Pollution from an Exothermic Reactor
The objective is to reduce the concentration of the pollution from an exothermic reactor without exceeding an upper temperature limit. Python, MATLAB, and Simulink simulations are available for download at the link below.
Attach:cstr.png
* [[Attach:blood_glucose_optimal_control.zip|Download Exothermic Reactor Files]]
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This 5 minute tutorial gives step-by-step instructions on how to simulate dynamic systems. Dynamic systems may have differential and algebraic equations (DAEs) or just differential equations (ODEs) that cause a time evolution of the response. The tutorial covers the same problem in both MATLAB and Python.
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This next tutorial covers how to simulate changing inputs over a time horizon with a dynamic model. The inputs change at regular intervals, causing a time varying response in the output. The same simulation is produced in both MATLAB and Python.
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!!! Insulin Injection Optimization for Diabetic Blood Glucose Regulation
Attach:blood_glucose_optimal_control.png
* [[Attach:blood_glucose_optimal_control.pdf|Blood Glucose Presentation]]
* [[Attach:blood_glucose_optimal_control.zip|Download Blood Glucose Simulink Files]]
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Attach:blood_glucose_optimal_control.png
* [[Attach:blood_glucose_optimal_control.pdf|Blood Glucose Presentation]]
* [[Attach:blood_glucose_optimal_control.zip|Download Blood Glucose Simulink Files]]
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The following files are a Simulink example of dynamic estimation and dynamic optimization. Separate blocks run the estimation and control algorithms for Model Predictive Control (MPC) with constrained nonlinear programming.
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https://www.youtube.com/watch?v=Oae-S5AzZCk&feature=share&list=PLLBUgWXdTBDjVLQVMnT80y6m_97XNhBZv&index=20
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* [[Attach:dynopt.zip|Download Excel, MATLAB, and Python Files for Dynamic Parameter Estimation (dynopt.zip)]]
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!!! Estimation and Control with APM in Simulink
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!!! Simulink Estimation and Control with APM
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!!! Estimation and Control with APM in Simulink
* [[Attach:apm_simulink.zip|Download APM Simulink Files (zip)]]
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!!! Introduction to Dynamic Modeling with MATLAB
*MATLAB.zip|Download MATLAB Simulation Files (zip)]]
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!!! Introduction to Dynamic Modeling with MATLAB and Python
* [[Attach:dynamic_sim_demo.zip|Download MATLAB and Python Simulation Files (zip)]]
* [[Attach:dynamic_sim_demo.zip|Download MATLAB and Python Simulation Files (zip)]]
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!!! Simulate Dynamic Data
*[[Attach:dynamic_data.zip|Download Dynamic Simulation Files (zip)]]
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!!! Introduction to Dynamic Modeling with MATLAB
* [[Attach:dynamic_sim_MATLAB.zip|Download MATLAB Simulation Files (zip)]]
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<iframe width="560" height="315" src="https://www.youtube.com/embed/-IDTagajoyA?rel=0" frameborder="0" allowfullscreen></iframe>
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!!! Simulate Dynamic Data with Python and MATLAB
* [[Attach:dynamic_sim_MATLAB.zip|Download MATLAB Simulation Files (zip)]]
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<iframe width="560" height="315" src="https://www.youtube.com/embed/-IDTagajoyA?rel=0" frameborder="0" allowfullscreen></iframe>
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!!! Simulate Dynamic Data with Python and MATLAB
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In order to apply dynamic optimization methods we must have a dynamic model to optimize. Obtaining a good dynamic model of the design problem is the most important step. A static model is often developed first and can often be augmented to include dynamic elements that relate how the system evolves with time. In this section we discuss some modeling concepts for dynamic systems that can help you develop models for optimization. We also discuss the formulation of data file, objectives, and constraints.
to:
In order to apply dynamic optimization methods we must have a dynamic model to optimize. Obtaining a good dynamic model of the design problem is the most important step. A static model is often developed first and can often be augmented to include dynamic elements that relate how the system evolves with time. In this section we discuss some modeling concepts for dynamic systems that can help you develop models for optimization. We also discuss the formulation objectives, constraints, and dynamic data sets.
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* [[Attach:dynamic_data.zip|Download Dynamic Simulation Files (zip)]]
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(:title Dynamic Optimization for Engineering Design:)
(:keywords mathematical modeling, dynamic, nonlinear, optimization, engineering optimization, interior point, active set, differential, algebraic, modeling language, university course:)
(:description Dynamic optimization uses differential and algebraic equations to solve systems that have a time-varying component. Using dynamic models opens the analysis to systems that may not be stationary or at steady-state.:)
!!! Introduction
In order to apply dynamic optimization methods we must have a dynamic model to optimize. Obtaining a good dynamic model of the design problem is the most important step. A static model is often developed first and can often be augmented to include dynamic elements that relate how the system evolves with time. In this section we discuss some modeling concepts for dynamic systems that can help you develop models for optimization. We also discuss the formulation of data file, objectives, and constraints.
!!! Fitting Physical Models to Experimental Data
Dynamic models are often constructed with physical models and tuned with experimental data. Physical models are based on the underlying physical principles that govern the problem and result from expressions such as a force or momentum balance and may include quantities such as velocity, acceleration, and position. Other quantities of interest may include anything that changes with respect to time such as reactor composition, temperature, mole fraction, etc. Models likely contain both physical and experimental elements. We will discuss how to reconcile experimental data with the physical model through parameter estimation. A final activity will be to use the physical model to then optimize a particular objective.
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!!! Simulate Dynamic Data
<iframe width="560" height="315" src="https://www.youtube.com/embed/-3FaZEfu7vE?rel=0" frameborder="0" allowfullscreen></iframe>
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(:keywords mathematical modeling, dynamic, nonlinear, optimization, engineering optimization, interior point, active set, differential, algebraic, modeling language, university course:)
(:description Dynamic optimization uses differential and algebraic equations to solve systems that have a time-varying component. Using dynamic models opens the analysis to systems that may not be stationary or at steady-state.:)
!!! Introduction
In order to apply dynamic optimization methods we must have a dynamic model to optimize. Obtaining a good dynamic model of the design problem is the most important step. A static model is often developed first and can often be augmented to include dynamic elements that relate how the system evolves with time. In this section we discuss some modeling concepts for dynamic systems that can help you develop models for optimization. We also discuss the formulation of data file, objectives, and constraints.
!!! Fitting Physical Models to Experimental Data
Dynamic models are often constructed with physical models and tuned with experimental data. Physical models are based on the underlying physical principles that govern the problem and result from expressions such as a force or momentum balance and may include quantities such as velocity, acceleration, and position. Other quantities of interest may include anything that changes with respect to time such as reactor composition, temperature, mole fraction, etc. Models likely contain both physical and experimental elements. We will discuss how to reconcile experimental data with the physical model through parameter estimation. A final activity will be to use the physical model to then optimize a particular objective.
----
!!! Simulate Dynamic Data
<iframe width="560" height="315" src="https://www.youtube.com/embed/-3FaZEfu7vE?rel=0" frameborder="0" allowfullscreen></iframe>
----
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