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HW8_solution

# HW8_solution - Temperature Controller Simulation Coded by...

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Unformatted text preview: Temperature Controller Simulation Coded by Dan Frey, 2 July 1998 This Mathcad sheet reproduces the results from Padke, "Quality Engineering Using Robust Design" chapter 9. The sheet is intended to facilitate deeper explorartion of the case study and to help 16.881 students complete homework #8 -- "Design of Dynamic Systems". ORIGIN := 1 The first index of all vectors and matrices will be one. Define the governing equations of the temperature controller circuit. An explanation of the circuit can be found on pg. 214-216 of Phadke. The governing equations are on page 218. Define the System Model E o := 10 The supply voltage is not a control factor, so its nominal value is set right up front. There will be noise induced about the nominal however. This is the governing equation for RT-ON found in Phadke. R T_ON ( R 1 , R 2 , R 3 , R 4 , E o , E z ) := R 3 R 2 ( E z R 4 + E o R 1 ) R 1 ( E z R 2 + E z R 4 - E o R 2 ) This second equation defines the value of RT-ON as a function of vectors of signal factors (SF), noise factors (NF), and control factors (NF). R T_ON2 (SF , NF , CF) := R T_ON ( NF 1 CF 1 , NF 2 CF 2 , SF , NF 3 CF 3 , NF 4 E o , NF 5 CF 4 ) This is the governing equation for RT-OFF found in Phadke. R T_OFF ( R 1 , R 2 , R 3 , R 4 , E o , E z ) := R 3 R 2 R 4 R 1 ( R 2 + R 4 ) This second equation defines the value of RT-OFF as a function of vectors of signal factors (SF), noise factors (NF), and control factors (NF). R T_OFF2 (SF , NF , CF) := R T_OFF ( NF 1 CF 1 , NF 2 CF 2 , SF , NF 3 CF 3 , NF 4 E o , NF 5 CF 4 ) 1 Choose Noise, Control, and Signal Factor Levels These are the noise levels defined in Table 9.1 on page 220. I've switched the ordering so that the column numbers correspond to the compound noise factor levels defined on page 221. 1.0204 1 0.9796 0.9796 1 1.0204 noise_levels := 1.0204 1 0.9796 0.9796 1 1.0204 Ł 1.0204 1 0.9796 ł Here are the signal factor levels as defined in Table 9.2. 0.5 signal_levels := 1 Ł 1.5 ł Here are the control factor level assignements within the L18 as defined by Tables 9.3 and 9.4. 1 2 3 1 2 3 2.668 4.0 6.0 5.336 8.0 12.0 cf_level := 26.68 40 60 1 2 3 4.8 6 7.2 Ł 1 2 3 ł This command forms the L18 matrix. Ø 1 1 1 1 1 1 1 1 Ø 1 3 1 2 1 3 2 3 2 2 1 2 3 1 3 2 øø Œ 1 1 2 2 2 2 2 2 Œ 1 3 2 3 2 1 3 1 2 2 2 3 1 2 1 3 œœ Œ Œ œœ 1 1 3 3 3 3 3 3 , stack Œ 1 3 3 1 3 2 1 2 2 2 3 1 2 3 2 1 œœ L 18 := stack Œ Œ 1 2 1 1 2 2 3 3 Œ 2 1 1 3 3 2 2 1 , 2 3 1 3 2 3 1 2 œœ Œ 1 2 2 2 3 3 1 1 Œ 2 1 2 1 1 3 3 2 2 3 2 1 3 1 2 3 œœ Œ Œ œœ ºŁ 1 2 3 3 1 1 2 2 ł ºŁ 2 1 3 2 2 1 1 3 ł Ł 2 3 3 2 1 2 3 1 łßß 2 Perform the Experiment For every row of the experiment, compute the values of RT-ON. The values of RT_ON are made by running a full factorial on the signal factor and the compound noise factor. This is easily accomplished with nested FOR loops. Within the FOR loops, single values of RT-ON are computed using the L18 matrix and control factor level table....
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HW8_solution - Temperature Controller Simulation Coded by...

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