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Unformatted text preview: MINI COURSE PROJECT EGM 3401 MOTIVATION Many engineers in industry are good at solving welldefined problems (the same is true of engineering college students!). However, far fewer are good at formulating appropriate problem statements and associated physical system models for openended design situations. Common mistakes are the inability to define what should be quantified with the model, or the creation of an excessively complex model for the problem at hand. The intuitive side of engineering involves being able to identify what is and is not important in a particular problem, and to use this information to develop the simplest model that can address the problem. DETAILS In light of this situation, the final homework assignment will be a mini course project. The goal of this project is to give you the opportunity to perform the following general tasks in an engineering design situation: 1) Identify an openended engineering problem related to either the chaotic pendulum or the magnetic pendulum (pick one of these two systems to model and simulate). Be creative in coming up with a problem to solve. 2) Formulate a specific problem statement defining the unknown quantities you desire to find. 3) Define an appropriate dynamical system model. 4) Perform the full range of tasks required to develop a forward dynamic simulation of the nominal system. 5) Identify and vary one parameter of the nominal system to evaluate its effect on design performance. The table on the next page provides a list of items that you will be required to turn in with your completed mini project: All items will be due on the last day of class, and NO LATES will be accepted for this assignment. Note that cramming does not work for an openended project, since time is required to ruminate on different approaches for addressing the problem and for formulating the dynamics equations for the system to be studied. So START NOW and give yourself the time you need for the rumination process. As a general comment, please note that the goal of this project is NOT to make you create a large report, but rather to take you through the steps involved in solving a realworld problem. Therefore, you should endeavor to write no more than necessary for each of the items below. SUGGESTIONS Below are several suggestions to help you with the various steps required to perform a nominal forward dynamic simulation and an associated a sensitivity study. 1) Use Autolev to derive the equations of motion for the system you choose. 2) Use the CODE ODE() command in Autolev to perform all necessary forward dynamic simulations. 2 3) Change the value of one constant parameter in your dynamic system model (e.g., a mass value, a magnet strength value, an initial condition, a length, a damping value) to perform the required sensitivity study. The additional forward dynamic simulations will predict the resulting change in the motion of your system. The goal is to make a plot that shows how varying this one parameter influences some quantity of interest in your system. Thus, you will need to be able to measure how this quantity changes when the parameter of interest is changed. Useful measures often include maximum or minimum values, average values, and rootmeansquare values. 4) The following mass measurements may be helpful for modeling your selected system: Chaotic pendulum: Mass of head = 8 g, Mass of one arm = 2 g. Magnetic pendulum: Mass of 1 magnet = ~2.5 g, mass of 9 magnets = ~23 g. Item Problem Statement Description One paragraph describing in general terms the design problem you wish to study. You should mention the physical system involved in the design problem (e.g., a person walking, a satellite, a bicycle, etc.), preliminary ideas for variables that can be used to quantify some aspect of the design (e.g., control torque magnitudes), and preliminary ideas for a system parameter that when varied may affect these quantities (e.g., the length of a rigid body in the model). The description of the physical system to be modeled should be in a form similar to a homework or exam problem (e.g., Body B is the frame of the bicycle, with a set of righthanded mutuallyperpendicular unit vectors . . .). Include a sketch of the system, and state clearly what the constants, variables, knowns, and unknowns are in the problem. The simulation algorithm should outline the solution process to be followed to produce a forward dynamic simulation. Inputs to and outputs from each step of the process should be listed explicitly. For simplicity, the algorithm description can be reported in the form of a flowchart if desired. Provide dynamic simulation results for the nominal system model over the specified time period. Results should be plotted and include input and output quantities of interest, and in particular, the quantities defined in the problem statement as a measure of system performance. This nominal simulation must utilize forward dynamics. Sensitivity results produced by performing a forward dynamic simulation repeatedly for several values of the selected system parameter. Results should be plotted with the system parameter as the independent variable. Dependent variables should be quantities that describe one aspect of an entire curve, such as maximum value, minimum value, average value, range, rootmeansquare error, total simulation time, etc. System Description Simulation Algorithm Nominal Simulation Sensitivity Study ...
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- Spring '08