Final Exam Take-Home Portion
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CHME4415 – Process Dynamics and Control – Fall 2021
To:
CHME 4415 Students
From:
CHME 4415 Instructor
Subject: Final Exam – Take Home Portion
Date:
December 7, 2021
This take-home portion of the final exam is an extension of the analysis conducted for Homework #5. You will apply Root Locus and Bode analysis to the system analyzed in Homework #5. A copy of the instructor solution is posted with this assignment for you to use and you should use the values of process parameters from the instructor solution. The analysis conducted here will focus on application of Root Locus and Bode analysis. Assignment is to be submitted to Canvas by 11:59 pm Monday December 13th.
1.
For the system in Homework #5, use Matlab to create a root locus plot for the process. Remember that the dead time must be approximated using the Pade approximation. From the root locus, estimate the ultimate gain and frequency for the process. Make a second Root Locus plot using the tuning results from the instructor solution for the PI case and including the integral control transfer function { (τ
I
s + 1)/ τ
I
s }. Using the root locus plot, identify the value of controller gain that now makes the system unstable. Compare this to the one found without the
integral control transfer functions and discuss any differences.
2.
For the system in Homework #5, using the Bode (frequency response) workbook included with the assignment, create a Bode diagram for your process. Determine the ultimate gain and period of oscillation using this tool. Compare to what you obtained by root locus method.
What to submit:
Please include a pdf copy of your spreadsheet, formatted to fit (no reduced print, please) on 4 pages or less. When preparing the pdf pay attention to formatting so figures and tables are not split across multiple pages. The work should be documented to make it clear what was done, using textboxes for the more extensive comments. You may include small versions of plots from Matlab to document your work and to explain your choice of tuning parameters. A copy of your Excel workbook is also to be submitted for review.
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Related Questions
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-The exam is open adopted textbook, open class notes (posted notes and solutions on the class' Canvas site only) and you may use
Matlab's build-in help system, but only to look up Matlab syntax questions;
- no collaboration is allowed; no help, including the tutoring center, may be sought to solve the problems;
- exam questions may only be asked to the instructor via private Ed Discussion posts or during the instructor's office hours;
- for non Matlab Grader problems, document all steps you took to solve the problem. This can be handwritten, but must be legible
for credit. If the problem states 'By hand', do not use any script/function to actually solve the problem, however, you may use a
non-programmable calculator or script/functions coded in this class to help in verifying the numerical results of individual steps;
- on Gradescope associate/select your answer pages with the corresponding problem numbers. Failure to do so may result in
no points given initially and will require a…
arrow_forward
Don't Use Chat GPT Will Upvote And Give Handwritten Solution Please
arrow_forward
Learning Goal:
To use transformation equations to calculate the plane state of stress in a rotated coordinate system.
The normal and shear stresses for a state of stress depend on the orientation of the axes. If the stresses are
given in one coordinate system (Figure 1), the equivalent stresses in a rotated coordinate system (Figure 2) can
be calculated using a set of transformation equations. Both sets of stresses describe the same state of stress.
In order to use the transformation equations, a sign convention must be chosen for the normal stresses, shear
stresses, and the rotation angle. For the equations below, a positive normal stress acts outward on a face. A
positive Try acts in the positive y-direction on the face whose outward normal is in the positive x-direction. The
positive direction for the rotation is also shown in the second figure.
The stresses in the rotated coordinate system are given by the following equations:
στ
σy
+
cos 20+Try sin 20
2
2
σετ συ
=
σy'
cos 20-Try…
arrow_forward
Scenario
You are assigned a role as a mechanical engineer for a vehicle design manufacturing company. Your
department has a software to perform numerical differentiation and integration. To be able to verify the
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Q: is the last two digits of your student Id number. If your number is (20110092) then Q=92.
P: is the last digit of your student Id Number. If your number is (20110092) then P=2,
If that digit equals zero then use P=1. Example: If your number is (20110040) then P=1.
Task 1
Determine the gradient of following functions at the given points:
a) x(t) = (2t7 + P t-2)² + (6vi – 5) when t = 1
5s+7
b) v(s) =
when s = 3
(s²-P)2
c) i(t) = 5(1 – In(2t – 1) )
when t= 1 sec.
d) V(t) =5sin(100nt + 0.2) Volts , find i(t) = 10 × x10-6 dV©)
Ampere when t= 1ms.
dt
e) y(t) = e¬(t-n) sin(Qt + P)
when t = n radian
f)…
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Question number 1
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Motiyo
Add explanation
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Learning Goal:
To use equilibrium to calculate the plane state of stress in a rotated coordinate system.
In general, the three-dimensional state of stress at a point requires six stress components to be fully described: three normal stresses and three shear stresses (Figure 1). When the external loadings are coplanar, however, the resulting internal stresses can be treated as plane stress and described using a simpler, two-dimensional analysis with just two normal stresses and one shear stress (Figure 2). The third normal stress and two other shear stresses are assumed to be zero.
The normal and shear stresses for a state of stress depend on the orientation of the axes. If the stresses are given in one coordinate system (Figure 3), the equivalent stresses in a rotated coordinate system (Figure 4) can be calculated using the equations of static equilibrium. Both sets of stresses describe the same state of stress.
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% Define Keplerian Elements
a = 29599.8; e = 0.0001; i = 0.9774; Omega = 1.3549; w = 0; M = 0.2645;
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wire coil
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Matlab function (just call it using its name process). The only difference between a .p and a .m file is that the source code of the .p
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(1)
Figure 1: Water tank inside an elevator
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OFocus
4:20 AM
28°C Mostly clear
3/26/2022
LG
CVENUENS
THANOS
BOBBLEHEAD
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YOP! AVENGES
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INFINITY WAR
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THANOS
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IGENA ERANLIA P COs CA AN
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P Comments
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S Replace
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ding 2
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1.
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- -The exam is open adopted textbook, open class notes (posted notes and solutions on the class' Canvas site only) and you may use Matlab's build-in help system, but only to look up Matlab syntax questions; - no collaboration is allowed; no help, including the tutoring center, may be sought to solve the problems; - exam questions may only be asked to the instructor via private Ed Discussion posts or during the instructor's office hours; - for non Matlab Grader problems, document all steps you took to solve the problem. This can be handwritten, but must be legible for credit. If the problem states 'By hand', do not use any script/function to actually solve the problem, however, you may use a non-programmable calculator or script/functions coded in this class to help in verifying the numerical results of individual steps; - on Gradescope associate/select your answer pages with the corresponding problem numbers. Failure to do so may result in no points given initially and will require a…arrow_forwardDon't Use Chat GPT Will Upvote And Give Handwritten Solution Pleasearrow_forwardLearning Goal: To use transformation equations to calculate the plane state of stress in a rotated coordinate system. The normal and shear stresses for a state of stress depend on the orientation of the axes. If the stresses are given in one coordinate system (Figure 1), the equivalent stresses in a rotated coordinate system (Figure 2) can be calculated using a set of transformation equations. Both sets of stresses describe the same state of stress. In order to use the transformation equations, a sign convention must be chosen for the normal stresses, shear stresses, and the rotation angle. For the equations below, a positive normal stress acts outward on a face. A positive Try acts in the positive y-direction on the face whose outward normal is in the positive x-direction. The positive direction for the rotation is also shown in the second figure. The stresses in the rotated coordinate system are given by the following equations: στ σy + cos 20+Try sin 20 2 2 σετ συ = σy' cos 20-Try…arrow_forward
- Scenario You are assigned a role as a mechanical engineer for a vehicle design manufacturing company. Your department has a software to perform numerical differentiation and integration. To be able to verify the results of using the software and validate these results, your department manager has asked you to analytically perform some tasks to validate the results generated by the software. Q: is the last two digits of your student Id number. If your number is (20110092) then Q=92. P: is the last digit of your student Id Number. If your number is (20110092) then P=2, If that digit equals zero then use P=1. Example: If your number is (20110040) then P=1. Task 1 Determine the gradient of following functions at the given points: a) x(t) = (2t7 + P t-2)² + (6vi – 5) when t = 1 5s+7 b) v(s) = when s = 3 (s²-P)2 c) i(t) = 5(1 – In(2t – 1) ) when t= 1 sec. d) V(t) =5sin(100nt + 0.2) Volts , find i(t) = 10 × x10-6 dV©) Ampere when t= 1ms. dt e) y(t) = e¬(t-n) sin(Qt + P) when t = n radian f)…arrow_forwardYou are a biomedical engineer working for a small orthopaedic firm that fabricates rectangular shaped fracture fixation plates from titanium alloy (model = "Ti Fix-It") materials. A recent clinical report documents some problems with the plates implanted into fractured limbs. Specifically, some plates have become permanently bent while patients are in rehab and doing partial weight bearing activities. Your boss asks you to review the technical report that was generated by the previous test engineer (whose job you now have!) and used to verify the design. The brief report states the following... "Ti Fix-It plates were manufactured from Ti-6Al-4V (grade 5) and machined into solid 150 mm long beams with a 4 mm thick and 15 mm wide cross section. Each Ti Fix-It plate was loaded in equilibrium in a 4-point bending test (set-up configuration is provided in drawing below), with an applied load of 1000N. The maximum stress in this set-up was less than the yield stress for the Ti-6Al-4V…arrow_forwardYou are assigned as the head of the engineering team to work on selecting the right-sized blower that will go on your new line of hybrid vehicles.The fan circulates the warm air on the inside of the windshield to stop condensation of water vapor and allow for maximum visibility during wintertime (see images). You have been provided with some info. and are asked to pick from the bottom table, the right model number(s) that will satisfy the requirement. Your car is equipped with a fan blower setting that allow you to choose between speeds 0, 1,2 and 3. Variation of the convection heat transfer coefficient is dependent upon multiple factors, including the size and the blower configuration.You can only use the following parameters:arrow_forward
- Question number 1arrow_forwardMotiyo Add explanationarrow_forwardLearning Goal: To use equilibrium to calculate the plane state of stress in a rotated coordinate system. In general, the three-dimensional state of stress at a point requires six stress components to be fully described: three normal stresses and three shear stresses (Figure 1). When the external loadings are coplanar, however, the resulting internal stresses can be treated as plane stress and described using a simpler, two-dimensional analysis with just two normal stresses and one shear stress (Figure 2). The third normal stress and two other shear stresses are assumed to be zero. The normal and shear stresses for a state of stress depend on the orientation of the axes. If the stresses are given in one coordinate system (Figure 3), the equivalent stresses in a rotated coordinate system (Figure 4) can be calculated using the equations of static equilibrium. Both sets of stresses describe the same state of stress. The stresses σx′and τx′y′ can be found by considering the free-body…arrow_forward
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