CHEN461_Project

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Mechanical Engineering

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Apr 3, 2024

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Heating Kit Group project Now that you have collected the data in Labs 02 and 03 (and we will provide you with the data from Labs 04 and 05; see attached excel files), in this project you will analyze those data and provide a lab report. Please format the lab report according to the following guidelines: • Length : The report should be between 2 and 3 pages in length single spaced, plus Title Page, references, figures and tables. In other words, the page limit is for the main part of the text: Introduction, Results/Discussion, and Conclusions. The title page, references, figures, tables, and appendices do not count towards your 3-page limit. Reports with main texts under 2 pages or exceeding 3 pages will have 20 points deducted. • Organization : Each submission should be a pdf and should contain the following sections: Title Page (including the date and the names of each contributing group member in alphabetical order by last name), Introduction, Results/Discussion, Conclusions, References, Figures, Tables (if applicable). The Appendix can be a separate pdf. • Formatting : The font should be Times New Roman 12 pt, single-spaced (not 1.15 spaced). Section and subsection headings should be 14 pt. Margins should be 1 inch on each side. Do not indent paragraphs. Place one extra hard return between each paragraph, including before (but not after) section headings. Remove all automatic spacing before and after all paragraphs. • References : References should be numbered in the text in the order they appear. • Figures and tables : Each figure and table should appear on its own page with the corresponding legend on the same page. o The pages for the figures and tables should come after the end of the references and do not count in the page limit. Embedding figures in the middle of the main text body, instead of after the references, will be a 5 point deduction. • Numbering : Equations, figures, and tables should be numbered and referenced in the text. • Appendix : Please submit the Appendix in a separate pdf from the main report. The Appendix could include scanned-in images of necessary calculations performed on engineering paper, or a marked-up word file of equations. • Software files : You must turn in Excel files and Matlab files with your numerical calculations. • Overall submission : All files (pdfs and software files) should be uploaded to the Canvas site in a zip file by one group member.

It is required to turn in a 2-3 page paper with Introduction, Results/Discussion, and Conclusions sections. You are also required to turn in an Appendix and any Excel file and Matlab code you use. In the Introduction, you must: (a) (10) Describe process control in general and why it is important. Describe the experimental set up, including how process control is applied. In the Results/Discussion section, you must: (b) (10) Describe in words how you performed the experiments for Labs 02 and 03. (c) (10) Describe in words how you performed the calculations from the data gathered from Labs 02 and 03 or from the data provided (Labs 04 and 05). In the Conclusions section, you must: (d) (10) Write a coherent conclusion paragraph that highlights the important aspects of process control in this system and summarizes what you learned from your analyses. In the Appendix you must provide: (e) (35) All hand-written calculations. You must also turn in: (f) (10) An Excel workbook detailing numerical calculations. This workbook should include separate sheets with the data from Labs 02, 03, 04, and 05. These sheets should also include the necessary calculations to analyze those data. Also, in general, your writing must be concise and clear (15 points). Please note that you need to justify your conclusions with support from material covered in this class. (Your target audience in that case should be a junior-level Chem E student.) The descriptions of the required analyses are on the following pages.

Lab02 analysis 1. Present a plot of the data you collected in Lab02. 2. For P control with Kc = 2 and set point change to 32  C, what was the steady-state offset? How did that change when integral action with  I = 2 was added? 3. For P control with Kc = 2 when the fans got turned off, what was the steady-state offset? How did that change when integral action was added? 4. Using the parameters of Problem 3 of Lab01, determine the experimental system's manipulated input first order plus time delay parameters: K,  , and D. Use these to determine the PI tuning (K c and  I ) using the Cohen-Coon method. 5. Present a plot with the above tuning with fan speed at 255 and the setpoint at 40. 6. Comment on the different tuning strategies used and justify which one is the best for this system.

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Lab03 analysis 1. Present a plot of the data you collected from the step change down in Lab03. Calculate the new steady-state value of the temperature measurement ystst_d by averaging the measurements from the time you reached steady state until the input changed. Calculate the corresponding process gain K_d. 2. Present a new plot of your data from the time u was decreased until the temperature measurement decreased by 1  C. Draw the tangent line on the plot with your response from the step change down and calculate D min _d =0.9 * (t corner_d -to_d) 3. Run a Solver optimization minimizing the sum of squared errors to determine D_d and tau_d constraining D_d  D min _d. Use D min _d and your Lab02 tau as your initial guesses. 4. Present a plot of the data you collected from the step change up in Lab03. Calculate the new steady-state value of the temperature measurement ystst_u by averaging the measurements from the time you reached steady state until the input changed. Calculate the corresponding process gain K_u. 5. Present a new plot of your data from the time u was increased until the temperature measurement increased by 1  C. Draw the tangent line on the plot with your response from the step change up and calculate D min _u =0.9 * (t corner_u -to_u) 6. Run a Solver optimization minimizing the sum of squared errors to determine D_u and tau_u constraining D_u  D min _u. Use D min _u and tau_d as your initial guesses. 7. Calculate the FOPTD parameters that will be used in future tests by averaging the parameters from the steps down and up. K = (K_d +K_u)/2  = (tau_d+tau_u)/2 D = (D_d+D_u)/2

Lab04 analysis Using the K, tau and D from Lab03 calculate the following: a) PI tuning parameters with Cohen and Coon b) PI tuning parameters for ITAE minimization method for disturbance (load) changes c) PI tuning parameters for ITAE minimization method for set-point changes d) PID tuning parameters for ITAE minimization method for disturbance (load) changes Imagine you used the above values to tune the heating kit system and obtained the data in Lab04.xlsx. Use those data to answer the questions below. 1. Show a plot of the experimental system response to PI tuning with Cohen and Coon. 2. Show a plot of the experimental system response to PI tuning with ITAE minimization method for disturbance (load) changes. 3. Show a plot of the experimental system response to PI tuning with ITAE minimization method for set-point changes. 4. Show a plot of the experimental system response to PID tuning with ITAE minimization method for disturbance (load) changes. 5. Tune a PI controller using the ITAE minimization method for set-point changes 6. Comment on the use of different strategies. Which one is best for this system? Justify

Lab05 analysis Imagine you performed the following experiment: Part 1 Turn the heating element on and start the Arduino app. Switch to automatic mode with the best tuning parameters obtained from Lab04. Wait until steady state has been reached at T = 37  C. Both the temperature measurement and the manipulated input u (% Heater On) should have reached approximately constant values. If oscillations persist for a long time, decrease K c by 50%. Part 2 Change the mode to manual. Wait until the temperature reading flattens. The manipulated input (% Power) will stay constant at the last value it had on automatic mode. Record this value. This is your nominal manipulated input value, u o . Part 3 Decrease the %power value by 3% (for example, reduce it from 10 to 7%). Record the time t o at which the manipulated input was decreased and the temperature measurement at that time. Part 4 Watch your data and wait until the temperature measurement decreased by 3  C (to around 34  C). Then change the % Power. Increase it by 6% (e.g., from 7 to 13%) and record the time t 1 of this change. Part 5 Watch your data and wait until the temperature measurement increased by 6  C (to around 40  C). Then change the % Power. Decrease it by 3% returning it to its original value (e.g., from 13 to 10%) and record the time t 2 of this change. Part 6 Collect data for about 8 minutes. The data from this experiment are provided in Lab05.xlsx. 1. Determine the beginning steady state measurement value y o by averaging the temperature measurements for times where the data are almost flat before or just after t o. If there is no time at which the temperatures are almost flat, use as y o the last value before the input change. Then use the plot of your experimental data to draw a

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tangent line at the inflection point after the first decrease in % Power and from that determine the time delay, D tangent . Present a screenshot of the plot of the tangent line. 2. You can decompose the pulse changes as a sum of three step changes, i.e., u' = u 1 ' + u 2 ' + u 3 '. Then: y' = y 1 ' + y 2 ' + y 3 ', … where each y i ' is a FOPDT step response. Set up Excel with column for the predicted y 1 ', y 2 ', y 3 ', y (= y o + y') and a column for the corresponding errors squared. Set a cell to calculate the performance measure, the sum of the errors squared. Use Solver to find the values of K,  , and D that minimize the sum of errors squared subject to the constraints D ≥ 0.9 D tangent , K ≥ 0.8 and K  1.6. The process gain is constrained close to the value determined by the energy balance model since pulse response data do not contain steady-state information. Present a screen shot of an Excel plot with the experimental data as points and the model prediction as a line. 3. Repeat (2) fitting an overdamped Second Order Plus Deadtime model. (Use the same D and K constraints) 4. Using the transfer function from (2) determine the tuning of a PI controller using the ITAE tuning for disturbance changes. 5. Using the transfer function from (2) determine the tuning of a PI controller using the ITAE tuning for set-point changes. 6. Using the transfer function from problem 2 determine the tuning of a PID controller using the ITAE tuning for disturbance changes and  F = 0.2  D .

ITAE Tuning Rules Design Relations: 𝑌 = ? ∙ ( 𝜃 𝜏 ) 𝐵 Here, 𝑌 = 𝐾 ∙ 𝐾 𝑐 for proportional mode 𝑌 = 𝜏 𝜏 𝐼 for the integral mode 𝑌 = 𝜏 𝐷 𝜏 for the derivative mode *For set-point changes, design relation for integral mode is 𝜏 𝜏 𝐼 = ? + ? ∙ ( 𝜃 𝜏 ) Type of Input Type of controller Mode A B Disturbance PI P 0.859 -0.977 I 0.674 -0.680 Disturbance PID P 1.357 -0.947 I 0.842 -0.738 D 0.381 0.995 Set point PI P 0.586 -0.916 I 1.03* -0.165* Set point PID P 0.965 -0.85 I 0.796* -0.1465* D 0.308 0.929 Example 1: ITAE Disturbance PI For 𝐾 𝑐 : A = 0.859, B = -0.977 𝑌 = 𝐾 ∙ 𝐾 𝑐 = 0.859 ∙ ( 𝐷 𝜏 ) −0.977 Rearranging, 𝐾 𝑐 = 0.859 𝐾 ∙ ( 𝐷 𝜏 ) −0.977 For 𝜏 𝐼 : A = 0.674, B = -0.680 𝑌 = 𝜏 𝜏 𝐼 = 0.674 ∙ ( 𝐷 𝜏 ) −0.680 𝜏 𝐼 = 𝜏 0.674 ∙ ( 𝐷 𝜏 ) −0.680

Example 2: ITAE Set-point PI For 𝐾 𝑐 : A = 0.586, B = -0.916 𝑌 = 𝐾 ∙ 𝐾 𝑐 = 0.586 ∙ ( 𝐷 𝜏 ) −0.916 Rearranging, 𝐾 𝑐 = 0.586 𝐾 ∙ ( 𝐷 𝜏 ) −0.916 For 𝜏 𝐼 : A = 0.674, B = -0.680 𝑌 = 𝜏 𝜏 𝐼 = 1.03 + (−0.165) ∙ ( 𝐷 𝜏 ) 𝜏 𝐼 = 𝜏 1.03 + (−0.165) ∙ ( 𝐷 𝜏 )

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