Modeling and Optimization of Real Systems

Transcription

1 Modeling and Optimization of Real Systems CRC Seminar Presentation Fernando Garcia University of Notre Dame February 5, 2014 Fernando Garcia Modeling and Optimization of Real Systems 1 / 24

2 Motivation Explore the procedure required to turn process models of engineering problems into software applications. Fernando Garcia Modeling and Optimization of Real Systems 2 / 24

3 Modeling and Optimization of Real Systems Main Topics 1 Formulation of a first-principles mathematical model for an engineering system and programming of its dynamics. 2 Performing parameter tuning and optimization to achieve process targets and goals. 3 Development of Graphical User Interfaces (GUIs) for ease-of-interaction with the model. 4 Deployment of software tools via shareable and standalone applications. Fernando Garcia Modeling and Optimization of Real Systems 3 / 24

4 What is Matlab? A numerical computing environment that allows for matrix manipulations, plotting functions and data, and coding of complex algorithms. Features Extensive toolbox set geared to many types of different modeling applications. Powerful graphics and fast algorithm development. Figure : Contour Plot in Matlab Fernando Garcia Modeling and Optimization of Real Systems 4 / 24

5 Typical Applications found in Matlab Matlab users come from various disciplines, including the physical sciences, engineering and economics. Figure : Modeling Applications Fernando Garcia Modeling and Optimization of Real Systems 5 / 24

6 Development of Applications Development Model Formulation Deployment Matlab Application Parameter Tuning GUI Development Standalone Application Optimization Figure : Stages of Software Development Fernando Garcia Modeling and Optimization of Real Systems 6 / 24

7 Step 1. Formulating a Model Let us start by assuming that we would like to model the dynamics of a Continuous Stirred-Tank Reactor (CSTR) with an exothermic first-order reaction A B. Figure : Cooled CSTR Diagram Fernando Garcia Modeling and Optimization of Real Systems 7 / 24

8 Basic Assumptions 1 The kinetics of a first order, irreversible reaction are given by r A = kc A. The reaction rate constant is given by Arrhenius equation k = k 0 exp( E a RT ) (1) 2 A mass balance on a simple tank reactor is given by the following law [Accumulation] = [In] [Out] + [Generation] (2) 3 The volume of the tank is constant. 4 The coolant is at a uniform temperature T c. 5 The rate of heat transfer from the reactor contents to the coolant is 6 Shaft work and heat losses can be neglected. Q = UA(T c T ) (3) Fernando Garcia Modeling and Optimization of Real Systems 8 / 24

9 Equations We can write the following mass balance for the CSTR. V dc A dt = q(c Ai C A ) VkC A (4) The energy balance is V ρc p dt dt = qc p(t i T ) + ( H R )VkC A + UA(T c T ) (5) Fernando Garcia Modeling and Optimization of Real Systems 9 / 24

10 Step 2. Building a Dynamic Model Simulink is an additional package within Matlab used for building dynamic models and enabling control logic and automation. Features Extensive library of math functions, control design and sequential or decision logic. Powerful graphical interface, consisting of hierarchical of blocks with subsystems embedded in them. Ability to create portable and shareable files that can be modified to increase the degree of complexity of the model. Fernando Garcia Modeling and Optimization of Real Systems 10 / 24

11 Implementing Control Logic Let s suppose that we wanted to design a PID controller in our CSTR to keep its temperature and concentration at a desired set point. The manipulated variable in this case is the temperature of the coolant T c. Figure : PID Control for a CSTR Fernando Garcia Modeling and Optimization of Real Systems 11 / 24

12 CSTR Control in Simulink Figure : PID Control in Simulink Fernando Garcia Modeling and Optimization of Real Systems 12 / 24

13 Step 3. Performing Process Optimization The purpose of an optimization algorithm is to obtain optimal values for process parameters by enforcing certain operating constraints to meet a design objective. Can an optimization routine climb Mount Washington to the top? Fernando Garcia Modeling and Optimization of Real Systems 13 / 24

14 Your Time vs. Computer Time Matlab has an additional package called the parallel computing toolbox that can be leveraged to make efficient use of the architecture of modern computers. The parallel computing toolbox can be scaled up for computation on grids, high-performance clusters and clouds (e.g. CRC s HPC facility). Figure : Parallel Computing Capabilities in Matlab Fernando Garcia Modeling and Optimization of Real Systems 14 / 24

15 Speeding up Optimization Figure : Optimization Speedup Fernando Garcia Modeling and Optimization of Real Systems 15 / 24

16 Step 4. Building a Graphical User Interface A Graphical User Interface (GUI) is a visual computer program that enables a person to communicate with a computer. 1 The interface is simple and easy to use; It is composed primarily of screens, panels and buttons. 2 The user does not need to interact/manipulate the source code. 3 Retrieve simulation results in real time, can adjust/change initial conditions. Fernando Garcia Modeling and Optimization of Real Systems 16 / 24

17 Tips for Building GUIs Each of the screens and buttons should be clearly labeled. Do not let any room for guess work. The GUI should contain a user guide with installation instructions, typical usage and expected output. Obtain feedback from your user group. They are the most valuable tool in the development process. Fernando Garcia Modeling and Optimization of Real Systems 17 / 24

18 Step 5. Build a Shareable Application Matlab allows for their GUIs, code and Simulink models to be turned into applications for ease-of-transfer with other users. There are two types 1 Matlab Apps 2 Standalone Applications Fernando Garcia Modeling and Optimization of Real Systems 18 / 24

19 Matlab s Compiling Capabilities Figure : Building Applications in Matlab Fernando Garcia Modeling and Optimization of Real Systems 19 / 24

20 Demonstration Fernando Garcia Modeling and Optimization of Real Systems 20 / 24

21 Conclusions 1 It is easy to develop applications in Matlab and Simulink. 2 Matlab offers incredible flexibility for deploying these applications accross different platforms. Fernando Garcia Modeling and Optimization of Real Systems 21 / 24

22 Acknowledgments Center for Research Computing. Professor Jeffrey Kantor. Amgen, Inc. Fernando Garcia Modeling and Optimization of Real Systems 22 / 24

23 Acknowledgments The Audience. Fernando Garcia Modeling and Optimization of Real Systems 23 / 24

24 Questions? Fernando Garcia Modeling and Optimization of Real Systems 24 / 24