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Unformatted text preview: MEM 255: Introduction to Controls Midterm Examination #2 solution Problem statement: Refer to Problem 4.65 in the text and answer the. You will need Problems 2.55, and 1.17. Some of the numerical values have been changed and are presented below as for each team. A. Read Problem 1.17. You do not have to draw any block diagrams. B. Answer all the questions in Problem 2.55 (Use the TEAM specific numerical values for the mechanical elements given below.) In addition, obtain a single state space representation with the output matrix reflecting all the three variables {y cat , y h , and y caty h } of interest. Describe the stability of the system. Team K_ave K_s K_h Fv_h Fv_f M_h M_f 1 1.535E+ 6 8.23E+4 7.00E+3 130 30 9.1 17.2 2 1.535E+ 7 8.23E+4 7.00E+3 130 30 9.1 17.2 3 1.535E+ 8 8.23E+4 7.00E+3 130 30 9.1 17.2 4 1.535E+ 6 8.23E+5 7.00E+3 130 30 9.1 17.2 5 1.535E+ 6 8.23E+4 7.00E+3 260 30 9.1 17.2 6 1.535E+ 6 8.23E+4 7.00E+3 390 30 9.1 17.2 7 1.535E+ 6 8.23E+4 7.00E+3 130 30 91 17.2 8 1.535E+ 6 8.23E+4 7.00E+3 130 30 910 17.2 9 1.535E+ 6 8.23E+4 7.00E+3 130 30 9100 17.2 10 1.535E+ 6 8.23E+4 7.00E+3 130 30 9.1 172 11 1.535E+ 6 8.23E+4 7.00E+3 130 30 9.1 1720 12 1.535E+ 6 8.23E+4 7.00E+3 130 30 9.1 17200 13 1.535E+ 6 8.23E+4 7.00E+3 130 150 9.1 17.2 C. Problem 4.65. Answer all (a), (b), and (c). Would the answer to (a) be different if you use the other two transfer functions from part B above? Why, or why not? In (c) use the “full” transfer function from part B above. _________________________________________________________________________ Grade distribution: B: 50% C: 40% Report: 10% _________________________________________________________________________ Solution Introduction: The team “PantoPandas” has been assigned to analyze the dynamics of a Pantograph. In lieu of conducting on line experimentation the Team has chosen to understand the system via computer simulation. Such a simulation will not only reduce the time required, but also the expenses and the manpower mandatory of the online evaluations. A mathematical model of the pantograph is generated first. In stead of using the numerical values provided to the Team for the system parameters, we have chosen to work with symbolic representation of these parameters as far as possible to facilitate the accommodation of possible variations of these parameters in the future. In order to simplify the subsequent controller design problem (a task not asked of us) in the future, we have chosen to investigate the role of a reduced model (i.e., a model of less complexity) in capturing the salient features of the pantograph. Our steps, analyses, and conclusions are provided below. The system: The picture and a schematic and its schematic representation are given below in Figures 1 and 2.The simplified models in Figure 2 provide us with a starting point in our analysis....
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 Spring '08
 Yousuff
 state space representation, numerical values, Pantograph

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