Will the stability of this system be any different than that of the standard feedback system? Why?

Chemical Engineering
Process_5_Modelling Assignment_2021 Page 1 of 4
SHC4032 Process Control Coursework: Modelling and Systems Analysis Assignment

Present all equations, substitutions and place a box around the final answer, where
applicable.
1. A model for a batch reactor has been derived as follows:
𝑑𝑦
𝑑𝑑 = (𝐼𝐷5)𝑦 βˆ’ (𝐼𝐷6)𝑦2
𝑑π‘₯
𝑑𝑑 = (𝐼𝐷7)𝑦
where the initial values of x and y are 0 and 0.03, respectively.
Using MS Excel, determine y(1) using the following:
a) Euler’s method
b) Fourth Order Runge Kutta method
2. The following chemical reaction takes place in a CSTR:
𝐴
π‘˜1
β‡Œ
π‘˜2
𝐡
π‘˜3
β‡Œ
π‘˜4
𝐢
where the rate constants are as follows:
k1 = (ID4) min–1 k2 = (ID5) min–1
k3 = (ID6) min–1 k4 = (ID7) min–1
Determine the following:
a) Rate expressions for components A, B and C.
b) Final steady state concentrations of Component B and C using the Euler
method.
Process_5_Modelling Assignment_2021 Page 2 of 4
3. Determine 𝑦(2) from the following 2nd order differential equation:
𝑑2𝑦
𝑑𝑑2 + 𝑑𝑦
𝑑𝑑 + 𝑦 = (𝐼𝐷7)
where 𝑦(0) = 𝑦′(0) = 0. Use:
a) Euler method
b) Fourth Order Runge Kutta method
4. (Bequette, 2003) Use the initial and final value theorems to determine the initial and
final values of the process output for a unit step input change for the following
transfer functions:
a) 5𝑠+12
7𝑠+4
b) (7𝑠2+4𝑠+2)(6𝑠+4)
(4𝑠2+4𝑠+1)(16𝑠2+4𝑠+1)
c) 4𝑠2+2𝑠+1
8𝑠2+4𝑠+0.5
5. (Bequette, 2003) Derive the closed loop transfer function between L(s)and Y(s) for
the following control block diagram (this is known as a feed forward / feedback
controller).
Figure 0-1 Feedforward / Feedback Control Loop
a) Describe how you would be able to check for stability for this closed loop system.
b) Will the stability of this system be any different than that of the standard feedback
system? Why?
Process_5_Modelling Assignment_2021 Page 3 of 4
6. (Bequette, 2003) A process has the following transfer function:
𝐺𝑃(𝑠) = 2(βˆ’3𝑠 + 1)
(5𝑠 + 1)
a) Using a P-controller, find the range of the controller gain that will yield a stable
closed loop system.
b) Simulate the process with the P controller to confirm the range of stability as
determined in part (a).
7. Consider the open-loop unstable process transfer function:
𝐺𝑃(𝑠) = 1
(𝑠 + 2)(𝑠 βˆ’ 1)
a) Find the range of KC for a P-only controller that will stabilize this process.
b) As it turns out, 𝐾𝐢 = 4 will yield a stable closed-loop (does this match with your
answer in part (a)?). Typically, there is a measurement lag in the feedback loop.
Assuming a first-order lag on the measurement, find the maximum measurement
time constant which is allowed before the system (with 𝐾𝐢 = 4) is destabilized.
c) Confirm all of your calculations with the system reproduced using
MATLAB/Simulink. Print out your results.
8. A PI controller is used on the following second order process:
𝐺𝑃(𝑠) = 𝐾𝑃
𝜏2𝑠2 + 2πœπœπ‘  + 1
The process parameters are:
𝐾𝑃 = 1, 𝜏 = 2, 𝜁 = 0.7
The tuning parameters are:
𝐾𝐢 = 5, 𝜏𝐼 = 0.2
a) Determine if the process is closed-loop stable.
b) Reproduce your results using MATLAB/Simulink and print out your results.
Process_5_Modelling Assignment_2021 Page 4 of 4
9. (Marlin, 2000) The process shown below consists of a mixing tank, mixing pipe, and
continuously stirred tank reactor. The following assumptions are applied to the
system:
I. Both tanks are well mixed and have constant volume and temperature.
II. All pipes are short with negligible transportation delay.
III. All flows and densities are constant.
IV. The first tank is a mixing tank.
V. The mixing pipe has no accumulation, and the concentration, CA3, is
constant.
VI. The second tank, CSTR, with 𝐴 β†’ π‘ƒπ‘Ÿπ‘œπ‘‘π‘’π‘π‘‘π‘ , and π‘Ÿπ΄ = βˆ’π‘˜π΄πΆπ΄
3 2⁄ .Mixing
Point
q1
CA0
q2
CA2
q3
CA3
q4
CA4
q5
CA5
V1
V2
Mixing
Tank
CSTR
Figure 0-2 Mixing tank, mixing pipe, and CSTR Process
a. Derive a linearized model relating 𝐢𝐴2
β€² (𝑑) to 𝐢𝐴0
β€² (𝑑).
b. Derive a linearized model relating 𝐢𝐴4
β€² (𝑑) to 𝐢𝐴2
β€² (𝑑).
c. Derive a linearized model relating 𝐢𝐴5
β€² (𝑑) to 𝐢𝐴4
β€² (𝑑).
d. Combine the models in (a) to (c) into one equation 𝐢𝐴5
β€² (𝑑) to 𝐢𝐴0
β€² (𝑑) using
Laplace transforms.

See also  What was the problem? How, exactly, did you solve it, and what inspired your creative solution?

Custompaper.help is an academic writing platform that provides students and professionals with quality services to ease their assignment challenges. With a wide range of services, the platform has become one of the leading academic writing service providers in the market due to its reliability and affordability. Below, we shall discuss some of the services which Custompaper.help provides:

Essay Writing Service
The essay writing service provides customers with quality essays on any subject or topic they requested within a given deadline. The writers at custompaper are experts in their respective fields, and they ensure customer satisfaction by producing original content with thorough research involved backed up with strong evidence from reliable sources available online or offline. All essays come with free plagiarism reports as well as revisions if needed so that customers can trust that they are getting high-quality work for their money’s worth.

Research Paper Writing Service
This is another popular service offered by custom paper help wherein customers are assisted in conducting research papers according to their needs and requirements within specified deadlines. Writers at custom paper help have vast knowledge about various topics belonging to different disciplines such as Management, Arts & Humanities, History etc., allowing them to craft impeccable research papers every time regardless of the complexity or urgency level requested by customers. Additionally, all our research papers come along with proper citation formats which ensures customer’s safety when it comes to plagiarism issues while also helping them save time on formatting procedures thus improving overall efficiency even further!

See also  Who does he see as his audience, and what does he want them to do?

Dissertation Writing Service
CustomPaperHelp also offers dissertation writing assistance for those who need it most – students preparing for graduation or professionals wanting to further refine their skills through higher education levels such as Master/PhD degrees etc, Our team of writers consists of experienced individuals having Master’s/PhD degrees themselves so you can rest assured that your dissertation will be handled expertly from the start till the end! Furthermore, we offer unlimited revisions until your complete satisfaction is achieved, along with regular checkups being done throughout the process just so everything goes according to course without any hiccups!

Editing And Proofreading Services
If you already have written an essay but want professional feedback before submitting it, then CustomPaperHelp also offers editing & proofreading services which helps in identifying & rectifying errors present in assignments like grammar mistakes, spelling mistakes, punctuation problems etc., thereby ensuring top-notch quality work, before submission takes place! We understand how important accuracy & consistency are when it comes to grading systems used at universities nowadays, so taking extra care during this phase becomes absolutely essential if good grades are desired afterward!

See also  Write a report on: MMA (MANUAL METAL ARC ) WELDING TECHNOLOGY

Coursework Help
For those who find coursework difficult due to complications of being quite technical in nature; CustomPaperHelp extends its support here too, by providing quality solutions every single time – starting from understanding concepts properly up until composing flawless answers following university guidelines closely enough making sure no loopholes remain whatsoever! Whether it’s related math problem-solving algorithms or lengthy home assignments – our expert panel has got you covered from head-to-toe leaving no stone unturned during this very crucial stage since final grades depend largely upon the success rate achieved here successfully!

Assignment Help
Assignments form an integral part of getting better scores & ultimately, a degree itself (in case pursuing a masters/PhD) – something only possible if precision is made a priority right away; otherwise, chances of failure increase exponentially over a time period detrimentally affecting performance evaluation systems later down road drastically hence stressing timely importance completion prior commencement other operations associated same project altogether consistently meeting high standards expected each situation respectively! Here too, CustomPaperHelp presents comprehensive solution package exceeding expectations beyond point offering optimal values therein ensuring maximum satisfaction reached under circumstances prevailing accordingly without fail…proving once more why people trust us implicitly without second thought whatsoever!!

Calculate your paper price
Pages (550 words)
Approximate price: -

Why Choose Us

Quality Papers

We value our clients. For this reason, we ensure that each paper is written carefully as per the instructions provided by the client. Our editing team also checks all the papers to ensure that they have been completed as per the expectations.

Professional Academic Writers

Over the years, our Acme Homework has managed to secure the most qualified, reliable and experienced team of writers. The company has also ensured continued training and development of the team members to ensure that it keep up with the rising Academic Trends.

Affordable Prices

Our prices are fairly priced in such a way that ensures affordability. Additionally, you can get a free price quotation by clicking on the "Place Order" button.

On-Time delivery

We pay strict attention on deadlines. For this reason, we ensure that all papers are submitted earlier, even before the deadline indicated by the customer. For this reason, the client can go through the work and review everything.

100% Originality

At Custom Paper Help, all papers are plagiarism-free as they are written from scratch. We have taken strict measures to ensure that there is no similarity on all papers and that citations are included as per the standards set.

Customer Support 24/7

Our support team is readily available to provide any guidance/help on our platform at any time of the day/night. Feel free to contact us via the Chat window or support email: support@acmehomework.com.

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

Custom Paper Help has stood as the world’s leading custom essay writing services providers. Once you enter all the details in the order form under the place order button, the rest is up to us.

Essays

Essay Writing Services

At Custom Paper Help, we prioritize on all aspects that bring about a good grade such as impeccable grammar, proper structure, zero-plagiarism and conformance to guidelines. Our experienced team of writers will help you completed your essays and other assignments.

Admissions

Admission and Business Papers

Be assured that you’ll definitely get accepted to the Master’s level program at any university once you enter all the details in the order form. We won’t leave you here; we will also help you secure a good position in your aspired workplace by creating an outstanding resume or portfolio once you place an order.

Editing

Editing and Proofreading

Our skilled editing and writing team will help you restructure you paper, paraphrase, correct grammar and replace plagiarized sections on your paper just on time. The service is geared toward eliminating any mistakes and rather enhancing better quality.

Coursework

Technical papers

We have writers in almost all fields including the most technical fields. You don’t have to worry about the complexity of your paper. Simply enter as much details as possible in the place order section.

See all services