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Q1: Consider a weight held in place by a spring. Initially suspended at rest, the height ofThe spring constant is kThis represents how "stiff" the spring is and is constant. The frictional losses areisthe weight is x=0The mass of the weight ismcharacterized by the constant b . The force applied to the weight after t=0 f(t) . This leads to the ODE m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=f(t) 2. (65 points) Imagine the spring is vertical. The weight is held by a platform atx=0 initially. If m=0.1kg , b=0.1 kg/ s , and k=1.0 kg/s . The platformis removed at t=0 O What are the initial conditions for this system? b. (15 points) What is the new steady-state position? That is, where willt - o ? Show this using the final-value theorem.the mass settle as c. (15 points) What is the maximum distance the mass will move from itsinitial position? (Hint: what is the force applied to the weight?)(15 peints) Whatvalue vwill recuultming d. (15 points) What spring constant value will result in the system comingto (and remaining within) 1% of its new steady-state position withoutovershooting that value as quickly as possible? e. (15 points) Imagine the spring system is now horizontal.represents how far the spring is from its resting position. If 1 N of forceis instantaneously transferred to the weight (in thedirection)described above att=0 ,what is the response? That is, what isx(t) when the weight is flicked with 1 N of force? Assume the weightis only free to move in one direction.See Answer
Q2: Complete the following quiz using only materials distributed in this class. You mayuse any material in the class Google Drive and your textbook, but no othermaterials or people. You must do your work on your own. Enter your answers intothis document and convert it to a PDF prior to submission on eCampus. If your workinvolves long, handwritten solutions then you may attach those as an image eitherin this document or as a separate document. Final answers, however, MUST be inthis document. 1. (20 points) What is the input function and the Laplace transform of the following figure?See Answer
Q3: 3. (15 points) Prove that a second-order system that results from two first-ordersystems in series can never be underdamped.See Answer
Q4: In the process presented in Figure Q1, tomato pulp is heated as it passes through a steam heat exchanger and then enters an evaporator where the water boils off. The purpose of this process is to produce tomato paste, which has a lower water content than the pulp. As a chemical engineer, you are tasked to control the liquid level and temperature in the evaporator.Considering this information, answer the following: (a) Define the process variables and the manipulated variables, as well as possible disturbances. (b)Propose feedback control loops by sketching a schematic diagram. (c) Propose any additional features in order to assure the safe operation of the process. Illustrate these features using a schematic diagram.See Answer
Q5:Question 1 An engineer uses a temperature sensor mounted in a thermowell to measure the temperature in a CSTR. The temperature sensor behaves as a first-order process with a time constant of 3 seconds, and the thermowell behaves as a first order process with a time constant of 9 seconds. Using Matlab: (a) Plot the open-loop response of the system to a step-change in the CSTR temperature. Comment on whether the response in under or over damped (b) Plot the closed-loop response of the system for proportional only control with a controller gain of unity. (c) The engineer notes that the measured temperature has been varying sinusoidally between 180 and 186°C with a period of 20 seconds for at least 10 minutes. Determine the likely temperature fluctuation in the CSTR contents to the nearest degree.See Answer
Q6:I Preamble Noise Disturbance in Control Systems Control engineering, as one of the cornerstones of automation, has contributed enormously to the development of modern industrial society; and a control system is useful for regulating the behaviour of industrial systems. In this assignment, you are required to analyze the following control system in Figure 1 where X(s) is the signal input, N(s) the noise input and Y(s) the system output. G₁(s) = K G₂ (s) = G3(s) = G₁(s) = H₂(s) = 1 s+2 X(s) Figure 1 The gain values for the respective forward and feedback paths are given: 2 s+4 4 S H₁(s) = 1 10 s + 10 H3(s) = 2 G₁ G₂ H₂ H₂ N(s) G3 H3 G4 Y(s) Task 1: Analytically determine the signal and noise transfer function of the control system in Figure 1. If x(t) is a unit step input then how do the signal and noise vary at the output for any change in the value of K as t → ∞o. Task 2: Using Matlab determine the signal and noise transfer function of the control system in Figure 1 assuming K = 1. Indicate clearly the Matlab code applicable to appropriate block reduction. Plot the step response using Matlab to verify the final steady-state value obtained in Task 1 y(t) as t→∞o for signal and noise.See Answer
Q7:1 Preamble The aim of this coursework is to enhance your understanding of the dynamics of multi-degree of freedom systems to compliment what you have learnt in the EG5027 Dynamics and Control module. 2 Assignment Tasks (1) Derive the mass and stiffness matrices for the vibrating system shown in Figure 1. (2) Show that the natural frequencies and mode shapes of the coupled system are: f₁ = 1.24 Hz, f₂ = 2.59 Hz -0.89 = { 056 )}. {21 = {-000} {y} = 150 N m-1 www 80 Nm-1 2 kg (3) Write a Matlab program to compute the natural frequencies and mode shapes of the coupled system and compare the results obtained with the values given in Part (2). [20%] U/1 140 Nm wwww 1 kg Figure 1: A 2DOF vibrating system. [10%] U₂ [40%] [30%]/n3 Assignment Submission Format You are required to a PDF file of no more than four A4 pages showing: (a) The derivation of the mass and stiffness matrices of the system. (b) The derivation of the natural frequencies and mode shapes of the system. (c) The listing of your Matlab® script for calculating the natural frequencies and mode shapes of the system (Note: you should list the code within the PDF file as plain text, you are not required to submit your M-file.) (d) Comment(s) on the results obtained in (b) and (c). The page layout should be portrait, single column and margins should not be less than 20 mm. The file should be typeset with a minimum font size and linespacing of 12pt and 1.5, respectively. Equations prepared using technical typesetting software, such as LATEX or Math Type, are preferred, but if you are not able to do so, high-quality scanned clear and legible hand-prepared equations are acceptable. No title page is required for the PDF file. Pages of the file should be numbered consecutively and shown on the centre footer of each page. Your student number must be clearly shown on the right header of all pages. The PDF file should have the module code, your student number, assignment identifier as the filename; and 'pdf' as the extension, in the form of EG5027_u1234567_CW1R.pdf.¹See Answer
Q8:Use a trial-and-error approach in Matlab to determine the ultimate controller gain Kcu and the ultimate period Pu for control of a FOPDT process with a deadtime of 30 seconds and a process time constant of 50 s. Use the Ziegler-Nichols rules to tune a PI controller, providing Kc and reset time. Plot (a) the open loop response to a step-change in setpoint without control (b) the closed loop response to a step-change in setpoint without control, and (c) plot the closed-loop response to a step-change in setpoint with the ZN tuned controller.See Answer
Q9:The process described by the transfer function GP(S) Kp (T₁S+1) e-TDS (T₂S + 1)(T3S + 1) Gp(s) = is controlled by a P controller with an arbitrary gain of Kc. a) If Kc = 2; Kp = 5; T₁ = 2; Td = 1; T₂ = 2; T3 = 3 determine whether the closed-loop response will be stable using frequency response techniques. What is the limiting value of the controller gain to ensure stability? b) For the following scenarios, generate the Bode plots for the open- loop behavior using Excel. Comment on the effect of the parameter changes on plots 2, 3 and 4 using plot 1 as the reference. 1. 2. 3. 4. Kc = 2; Kp = 5; t₁ = 0; TD = 0; T₂ = 2; T3 = 3 Kc = 2; Kp = 5; t₁ = 0; TD = 5; T2 = 2; T3 = 3 Kc = 4; Kp = 5; T₁ = 0; TD = 0; T₂ = 2; T3 = 3 Kc = 2; Kp = 5; T₁ = 0; TD = 10; T₂ = 2; T3 = 3 c) Using the same general transfer function, plot the Nyquist plots using Excel for the following parameters. Comment on the behavior. 1. Kc = 2; Kp = 5; T₁ = 1; TD = 0; T₂ = 2; T3 = 3 2. Kc = 2; Kp = 5; T₁ = 3; TD = 0; T2 = 2; T3 = 3See Answer
Q10:Question 4 Two thermocouples are placed in an air stream whose temperature is varying sinusoidally. The temperature responses of each thermocouple are recorded for a range of frequencies, with the phase angle between the two measurements tabulated below. The standard thermocouple is known to have first-order dynamics with a time constant of 0.15 minutes when operating in air. Show the unknown thermocouple also displays first order behavior and determine its time constant. After approximately 30 seconds the standard themocouple shows a sinusoidal variation in air temperature between 96 and 104 degrees Celcius, at a rate of two cycles per minute. What error will the standard thermocouple report in this instance if left to measure the air temperature indefinitely? CHEM ENG 4050: Advanced Chemical Engineering Advanced Control Table 1. Thermocouple phase difference for Question 4. Frequency (cycles/min) 0.05 0.1 0.2 0.4 0.8 1.0 2.0 4.0 Phase Difference (deg) 4.5 8.7 16.0 24.5 26.5 25.0 16.7 9.2See Answer
Q11:Question 5 Determine the controller gain (Kc) for a proportional-only feedback controller for the system comprising the following elements that ensures a gain margin of at least 2 and a phase margin of at least 30°. Plot the controlled and uncontrolled closed-loop response of the system to a unit-step change in set- point. Gc= Kc; Gp = 50 30s +1' G₂ = 0.016 3s +1' Gm = 1 10s + 1See Answer
Q12:Question #1 The mass fraction of product A leaving a reactor (Y(s)) can be related to the reactor temperature (U(s)) by the transfer function G₁(s): Y(s) 12(s + 4) = G₁(s) = U(s) (s + x)(s + 3)(s+8) Where x = 4 a. If a step change is made to the reactor temperature will the mass fraction of A in the product reach a steady value? Clearly justify your answer. [3 marks] b. The relationship between the reactor temperature and the coolant flow rate (Z(s)) is given by the transfer function G₂(s). What is the transfer function that gives the relationship between the coolant flow and the mass fraction of product A leaving the reactor? [2 marks] c. G₂(s) can be represented by a first-order transfer function. Provide an example of such a function that will result in a stable system and an example that will result in an unstable system. Here stability is defined as the mass fraction of A reaching a steady value if a unit step change is made to the coolant flow rate. Include x in your functions. Clearly justify your choices. [5 marks]See Answer
Q13:Question #2 Dodecane is pumped into a well-insulated 2 m diameter cylindrical tank where it is heated to a temperature of 150 °C. The tank is 10 m tall, and the steady state liquid height is 6.5 m. The inlet temperature of the dodecane is 10 °C. In answering this question you can assume that the density and specific heat capacity of dodecane are constant, and that they have values of 750 kg m³ and 2200 J kg-¹ K¹, respectively. a. Draw a clear diagram of the system, and referring to this diagram derive suitable mass and energy balances for the system. Clearly state any assumptions that you have made. [5 marks] b. The outlet flow rate (Four) is proportional to the liquid height and the resistance of the outlet valve (R): h Fout R The inlet flow rate to the system is 120 L min¹¹. What is the value of R? [2 marks] c. If the inlet flow rate is 120 L min¹ how much energy needs to be supplied by the heater such that the outlet temperature is 150 °C? Here you can assume that the system is at steady state. [2 marks] d. The inlet flow-rate is increased stepwise from 120 to 180 L min-¹ and at the same time the energy supplied to the system is increased from the value calculated in part (c) to 550 kW. Plot the response of the system to these changes. Determine: • The steady-state value of the liquid height. • The steady-state value of the liquid temperature. • The values of the gain and time constant for the liquid height. 16 markslSee Answer
Q14:Question #3 A second system for heating dodecane is going to be built, this system is the same as the one from the previous question. In order to save money it is being proposed that the system is not insulated. Your manager would like to know how removing the insulation would affect the dynamics of the system. In performing this analysis you can assume that the air temperature is 10 °C and that the heat transfer coefficient between the tank and the air is 20 W m² K¹¹. In answering this question: • Clearly show how the changes to the design affect the mass and energy balances for the system. • Determine how much energy needs to be supplied by the heater to keep the uninsulated tank at a temperature of 150 °C for an inlet flow rate of 120 L min¹¹. • Compare how the insulated and uninsulated systems respond to a stepwise increase in the inlet flowrate from 120 to 180 L min¹. Use a value of 500 kW for the heater power, and an initial temperature of 150 °C for both cases. State whether or not you think building the system without insulation is a good idea. Make sure you justify your decisions. [10 marks] 3See Answer
Q15:Question #4 A system of three cylindrical tanks holding liquid is arranged as shown in Figure 1. Fint Fina Tank #1 R₁ F₁ h₁ h3 h₂ h₁ F₁ = R₁ Tank #2 R₂ F₂ Tank #3 Figure 1- Schematic showing layout of tanks. For all three tanks you can assume that the outlet flow rate is equal to the height in the tank divided by the valve resistance, i.e.: h3 hz F₂= F3: R₂ R3 a. Clearly derive the transfer function that relates the height in tank #1 (hi) to the inlet flow to the tank (Fin). [4 marks] b. Tank #1 is 0.5 m in diameter and the value of R₁ is 200 s m². At steady state the liquid height is 1 m. What is the flow rate of liquid entering the tank (i.c. what is Fin,1)? [1 mark] c. Calculate the gain and time constants for tank #1. [2 marks] d. Derive the transfer function that relates the height in tank # 3 (ha) to the flow entering the system (i.e. to Flis and F2.in). [5 marks] c. Tank #2 has the same diameter as Tank #1, but R₂ = 0.5R₁. Tank #3 has double the diameter of Tank #1 (i.e. it is 1 m in diameter), and R3= R₁. Fin1 = Fin2 = 0.01 m³ s¹. If the system is at steady state what is the liquid level in each of the tanks? [3 marks]See Answer
Q16: ACS219 Process Control Group assignment Payam Soulatiantork October 2023 1 Introduction The assignment is linked to chemical engineering applications related to control scheme design, instru- mentation, control strategies and looking at the control of selected systems. Students work in groups of four students to produce a number of separate posters, one for each case study. The main purpose of each poster is to demonstrate the importance of a given control strategy or design in the context of chemical engineering. The poster should include context and numerical illustrations and, for high marks, should also include evidence of analysis and independent systematic design. A typical case study could either: (i) focus on the efficacy of different strategies for controlling a given system, or (ii) the efficacy of a given strategy for tackling particular scenarios, perhaps using several systems to illustrate. Most likely numerical evidence will be produced using Matlab or TSC although other software tools may be used. This is 45hr work per student and thus to achieve good marks, the submissions must not be superficial. Typical marking guidance is provided at the end for information. As this is a group work assignment, each group will also need to submit, as a group, an agreed peer assessment of the contribution of each group member with some explanation and evidence where the marks are not awarded equally. In order to ensure no group member is disadvantaged or excluded, groups will have a private discussion board on Blackboard they can use to communicate dates, locations and summaries of core meetings as well as to share interim documentation. The groups are self-enrolled so you can choose the students you want to work with on your project. Some possible scenarios are listed over the page, but students should feel free to explore other areas they find interesting which fall within the remit. Some good resources including some Matlab files are also available on the BB page -> Group assignment for ACS219 -> Coursework useful material. • Students are reminded that the substantive work submitted should be their own. Where resources have been used from elsewhere, these must be clearly and explicitly referenced. • Students are reminded of University policy on unfair means and moreover should ensure that any resource they use is fully cited. http://www.shef.ac.uk/ssid/exams/plagiarism. • Groups can meet with staff during the tutorials and lectures to discuss any queries. Please see staff immediately if special circumstances are affecting your performance http://www.shef.ac.uk/ ssid/forms/special. Group feedback will appear on Blackboard after marking is complete for the whole class. 2 Submission details Posters are submitted in soft copy onto Blackboard through the group assignment link. The deadline is the Friday of week 12 of semester 1, 15 December 2023 at 5pm. 3 Feedback Group feedback will appear on Blackboard after marking is complete for the whole class. Also, in a single hour lecture on Friday of week 11, the students will get a chance to bring their posters along and get some interim feedback. 1 4 A table of potential themes Case study scenario Low order systems for use in the case studies Systems in series and higher order dynamics Multi-input-multi- output systems Impact of constraints and actuation choices Impact of measurement and delays Advanced control strate- Develop an awareness of some alternative control strategies and why these gies are deployed in industry such as: cascade, feedforward, selective control, split-range control, ratio control, model predictive control, smith predictors and time delays, anti-windup strategies, inferential control, fault-tolerant control, optimal control, robust control, sequence control, on-off control. Discrete control Fault tolerant con- trol/safety Impact of design on con- trol performance Impact of uncertainty PID tuning Possible content 1st order in series, distillation column, multi-tank system, thermocouple delay, power generation, stirred tank with cascade. Valve sizing Higher order systems are less easy to control with PI. Students can explore through several case studies the consequences of more involved dynamics such as multi-1st-order in series, non-min phase. (Multi CSTR, multi-tank, distillation column, etc.) Discuss the challenges of controlling systems with interacting dynamics. Illustrate with case studies such as distillation columns and oil fired power generation. Use case study examples to demonstrate how constraints limit performance and impact on safety. Brief discussion of how these might be handled in practice (say with PID and predictive control). Use case studies to analysis the impact of actuator choices on controllability, constraint handling and performance. Consider the consequences on control performance (and safety) of poor measurement such as accuracy, repeatability, lag/delay, reliability. Use a few case studies illustrating different sensor choices to show how these impact on control loop performance. Include inferential control. What is the impact of discretising a control law that is implementing via a computer and thus involving sampling? Use some case studies to demonstrate the impact of actuator/sensor failure and discuss possible mitigation. Show through case studies how poor design effects control, e.g. Vaporizer, reboiler, knockout drums, ball mills, cooling towers, simple distillation tower, etc. How would you undertake control design when the system/model parame- ters are continually changing, or unknown? What is the impact on control of significant sensor noise or large input/output disturbances? Compare and contrast different tuning methods for PID, e.g.: Zeigler- Nichols, Cohen-Coon, Modified Ziegler-Nichols method, Tyreus-Luyben method, Damped oscillation method, C-H-R method, Fertik method, Ciancone-Marline method, Minimum error criteria (IAE, ISE, ITAE), etc. Identify, select and position different instruments appropriately within a control loop. 2 5 Marking criteria and Grade Descriptors for ACS219 group assignment 7-10 • Extensive knowledge of the subject area and the engineering context. A perceptive and focused use of the relevant material. Widespread evidence of independent sourcing and original thought. 5-6 6-7 • A sound knowledge of the subject area and engineering context. A comprehensive use of the relevant material with some evidence of independent sourcing and original thought. 4-5 • Shows an insight and depth of understanding, including an awareness of the complexities and subtleties. 3-4 ● Very high standard of critical analysis and evaluation. • Clearly structured presentation, showing logical development of arguments and properly referenced data and examples. • Shows an understanding of arguments, contribution and context, including some awareness of the complexities and subtleties. ● High standard of critical analysis of the source material. Evidence of some evaluation and synthesis. • Clearly structured presentation, showing logical development of arguments and properly referenced data and examples. • Some knowledge of the subject area and engineering context. Makes some use of the relevant material with little or no evidence of independent sourcing, or original thought. • Shows some understanding of arguments, contribution and context. • Attempts analysis of the source material but may include some errors/omissions. Little evidence of evaluation and synthesis. • Presentation reasonably clear with arguments not fully developed and data and examples not fully referenced. • Some knowledge and appreciation of the engineering context. Superficial use of the material provided. No evidence of independent sourcing, or original thought. • Some areas of understanding of the arguments, contribution and context. • Confused analysis including errors and omissions. No evidence of evaluation and synthesis. • Descriptive presentation based on confused arguments. Includes poorly referenced data and examples provided during lectures. • Limited and patchy knowledge and appreciation of the engineering context. Poor use of the material provided. No evidence of independent sourcing, or original thought. • Limited understanding of the arguments. No understanding of the contribution and context. • Confused analysis including a number errors and omissions. No evidence of evaluation and synthesis. • Descriptive presentation based on confused arguments. Poor use of data and examples provided during the lecture. No references 0-3 ● Inadequate knowledge and no appreciation of the engineering context. Poor use of the material provided. No evidence of independent sourcing, or original thought. 3 ● Inadequate understanding of the arguments, contribution and context. • Inadequate grasp of the analysis including many errors and omissions. No evidence of evaluation and synthesis. • Presentation that contains no data, examples or even class notes. 4See Answer
Q17:Please study the process described in the attached file. Your task is to: 1. Specify instrumentation at key process locations and 2. Draw feedback control loops to control the process./n 112 DESIGN AND CONTROL OF THE BUTYL ACETATE PROCESS which has a reboiler temperature of about 344 K). The use of heat integration is not included in this study but would obviously reduce energy consumption. The butanol/butyl acetate separation is somewhat difficult and therefore requires a distil- lation column with a modest reflux ratio (RR = 1.92) and a modest number of stages (47). 8.3 PROCESS FLOWSHEET Figure 8.4 gives the flowsheet of the process after economic optimization, to be discussed in Section 8.4. Flowsheet stream conditions, equipment sizes, and heat exchanger heat duties are provided. 8.3.1 Reactor Fresh feed with composition 60 mol% methyl acetate and 40 mol% methanol and flowrate 100 kmol/h is fed into a 4 m³ reactor, which operates at 350 K and 5 atm. The residence time in the reactor is about 6 min since the kinetics are fast and chemical equilibrium is quickly attained. Fresh butanol (59.4 kmol/h) is added to a butanol recycle stream (120.6 kmol/h, 90 mol% butanol, 10 mol % butyl acetate) to give a total butanol stream (Bo) of 180 kmol/h, which is fed into the reactor. A methyl acetate/methanol recycle (171.2 kmol/h, 64 mol% methyl acetate, 36 mol % methanol) is combined with the feed stream (100 kmol/h), giving a total methyl acetate/methanol stream (Mo) of 271.2 kmol/h, which is fed to the reactor. These two total streams (Btot and Mot) will be the major design optimization variables. The Feed 100 kmol/h 0.60 MeAc 0.40 MeOH 305 K Reactor 4 m³ 350 K 5 atm -89 kw Bot 180.0 kmol/h 0.067 BuAc 0.933 BUOH 399 K 15 atm Mtot 271.2 kmol/h 0.6254 MeAc 0.3746 MeOH 399 K 15 atm RR-0.317 ID=1.72 m 3.64 MW BuOH Feed 59.4 kmol/h 305 K; 15 atm 401 K MeAc Recycle; 171.2 kmol/h; 0.64 MeAc; 0.36 MeOH C1 20 BuOH Recycle; 120.6 kmol/h; 0.90 BuOH; 0.10 BuAc 36 333 K 1.2 atm 3.75 MW D1 271.27 kmol/h 0.4075 MeAc 0.5915 MeOH 10-6 BUOH 0.0010 BuAc A B1 179.9 kmol/h 0.0010 MeAc 10-11 MeOH 0.6066 BUOH 0.3924 BuAc C2 18 26 329 K 1.1 alm 3.02 MW AR=0.996 ID=1.38 m 3.01 MW 344 K MeOH Product 100.1 kmol/h 0.0100 MeAc 0.9872 MeOH 0.0027 BuAc Figure 8.4. Proposed flowsheet. 459 K C3 27 46 437 K 4 atm 3.50 MW RR=1.92 ID=1.78 m 4.05 MW BuAc Product 59.32 kmol/h 0.003 MeAc 0.010 BUOH 0.987 BuAc icluded a distil- es (47). ussed in at duties flowrate nce time ; quickly kmol/h, kmol/h, 54 mol% 1), giving e reactor. bles. The 7K tm 0 MW BuAc Product 59.32 kmol/h 0.003 MeAc 0.010 BUOH 0.987 BuAc 8.3 PROCESS FLOWSHEET 113 per-pass conversion of methyl acetate is about 34%. A small amount of heat (89 kW) must be removed from the reactor. 8.3.2 Column C1 Reactor effluent is fed to column C1, which splits the two light components from the two heavy components. Methyl acetate and methanol are taken overhead while butanol and butyl acetate leave in the bottoms. The column has 37 stages and is fed on Stage 20. We use the Aspen tray-numbering convention of counting trays from the top with the condenser as Stage 1. The specifications for this column are somewhat unusual. The key components are not adjacent in terms of boiling points. The normal boiling points of methyl acetate, methanol, butanol, and butyl acetate are 330.1, 337.8, 390.8, and 399.3 K, respectively. So the separ- ation in this column should be to keep butanol from going overhead and methanol from going out the bottom. But as the stream data given in Figure 8.4 show, the concentration of butanol in the distillate is much lower than the concentration of butyl acetate. In the bot- toms, the concentration of methanol is much lower than the concentration of methyl acetate. This odd behavior may be the result of the azeotropes. The specification for the distillate is 0.1 mol % butyl acetate. The specification for the bottoms is that the sum of the methanol and the methyl acetate is 0.1 mol %. For some values of parameters, the dominant impurity in the bottoms is methanol, but for other values of parameters, the dominant impurity in the bottoms is methyl acetate. The sum of the compositions is obtained in the Radfrac model in Aspen Plus by selecting both components as the Selected component in the Design spec feature. The required RR in column C1 is 0.317 and reboiler heat duty is 3.64 MW. Low-pressure steam is used in the reboiler (433 K at 6 atm) since the base temperature is 401K, The column operates with a condenser pressure of 1.2 atm, which gives a reflux-drum tempera- ture of 333 K and permits the use of cooling water in the condenser. 8.3.3 Column C2 The distillate stream from column C1 is fed to column C2, which produces high-purity (98.72 mol %) methanol out the bottom and a distillate stream with a composition (64 mol % methyl acetate) near the azeotrope. The distillate is recycled back to the reactor at a rate of 171.2 kmol/h. The column has 27 stages and is fed on Stage 18. The specifications are 64 mol % methyl acetate in the distillate and 0.1 mol % methyl acet- ate in the bottoms. To achieve these specifications, the RR is 0.996 and reboiler heat duty is 3.01 MW. Low-pressure steam is used in the reboiler since the base temperature is 344 K. The column operates with a condenser pressure of 1.1 atm, which gives a reflux-drum temperature of 329 K and permits the use of cooling water in the condenser. 8.3.4 Column C3 The bottoms from C1 is fed to column C3, which produces high-purity (98.7 mol %) butyl acetate out the bottom and a butanol-rich distillate (90 mol %) that is recycled back to the reactor at a rate of 120.6 kmol/h. The column has 47 stages and is fed on Stage 27. The specifications are 0.1 mol % butanol in the bottoms and 10 mol % butyl acetate in the distillate. To achieve the specifications, the RR is 1.92 and reboiler heat duty is 4.05 MW. 114 DESIGN AND CONTROL OF THE BUTYL ACETATE PROCESS Since the base temperature is 459 K, high-pressure steam (527 K at 42 atm) must be used in the reboiler. The column operates with a condenser pressure of 4 atm, which gives a reflux-drum temperature of 437 K. As noted earlier, this temperature is high enough to permit heat inte- gration with the low-temperature reboiler (344 K) in column C2. The total energy consumption of the three columns in this flowsheet is 10.7 MW, not con- sidering any heat integration. Using a price of $7.78/GJ for low-pressure steam (columns Cl and C2) and $9.83/GJ for high-pressure steam (column C3), the total energy cost of the process is $2,888,000/yr. Figures 8.5 through 8.7 give temperature and composition profiles for the three distilla- tion columns. The control system developed later in Section 8.5 will use these temperature profiles to select appropriate trays for temperature control. (a) Temperature K 340.0 350.0 360.0 370.0 380.0 390.0 400.0 410.0 (b) 1.0 0.8 0.7 0.6 0.5 X (mole frac) 0.4 0.3 0.2 0.1 6.0 1.0 11.0 6.0 11.0 Temperature K 16.0 16.0 21.0 Stage 26.0 26.0 31.0 MEAC MEOH BUAC BUOH 31.0 36.0 36.0 21.0 Stage Figure 8.5. Column C1 (a) temperature profile, and (b) composition profiles. 41.0 41.0 e used in lux-drum heat inte- ', not con- lumns Cl ost of the e distilla- mperature -1.0 41.0 1. (b) Temperature K X (mole frac) 345.0 340.0 335.0 330.0 0.75 0.5 0.25 1.0 1.0 6.0 1.0 11.0 6.0 16.0 Stage 11.0 8.3 PROCESS FLOWSHEET Temperature K 21.0 16.0 Stage Figure 8.6. Column C2 (a) temperature profile, and (b) composition profiles. 21.0 26.0 MEAC MEOH 26.0 31.0 31.0 115 8.3.5 Flowsheet Convergence Convergence of steady-state simulators when recycle streams are present can be very diffi- cult. The butyl acetate process has two recycle streams, which can present problems. However, successful and robust convergence was achieved by using the strategy of fixing the total butanol flowrate Bot entering the reactor (see Figure 8.4) by varying the fresh feed of butanol. A Flowsheet design spec in Aspen Plus is used for this objective. The fresh feed stream, which is a mixture of methyl acetate and methanol, is fixed at 100 kmol/h. A value of Bot is specified, and the flowsheet is converged. There is aSee Answer
Q18:Consider the chemical reactor/separator systems shown below, one with a recycle stream and one without a recycle stream. Without Recycle Fo, Xi (A and C only) Fs, XS Fo, Xi (A and C only) F1, X1 With Recycle F1, X1 CSTR A→B Fs, X3 CSTR A→B (A and C only) F1, X2 F3, X3 (A and C only) F1, X2 F3, X3 SEPARATOR SEPARATOR (B only) F6, X3 (B only)/nFO= 1.0 F1 2.7 F3 = 1.8 F5 = 1.7 Xi A0 = 0.95 T = 1/2.7 KO = 2.7 #moles/time # moles/time # moles/time # moles/time # moles fraction #time # 1/time X1_A0 = 2/3 #moles fraction X2_A0 1/3 #moles fraction X3_A0 1/2 #moles fraction X5_A0 = 1/2 #moles fraction Assumptions Constant molar hold-up for CSTR. All molar flowrates are constant. Perfect separation unit with infinitely fast dynamics. • No transportation delay between separator and fast dynamics. • Isothermal process. Mixing Point Subsystem F₁ = F₁+F₂ F₁x₁₁A= Fox₁.A + F5X3,A (1)/nReactor Subsystem d(MX2,A) = F₁X₁,A - F₁X2₂‚A¬K₁X2,AM dt or dx2,A 1 dt -=-—- (X1₁,4 – X2,A) — K₁X2,A (2) M F₁ Separator Subsystem F₁X2,4 = F3X3,A (3)/nWithout Recycle Case X'iA X'S,A G4 G3 X'LA G₁ X'3,A G₂ X'2A 1. Develop the transfer function in the block diagram representation of the system without recycle. In this block diagram, the variables are deviation variables (for example, x'i,A = xi,A-xi,A_steady_state). 2. Using Python, simulate the dynamic system by using a step change in xi,A from 0.95 to 0.96 at t=2. Plot the response results of each variable in this order xi,A, x1,A, x2,A, x3,A, in a 4-by-1 subplot. 3. Using Python, fit a transfer function to the step response of x3,A and compare the key parameters with the theoretical parameters obtained in step-1.See Answer
Q19:Consider the chemical reactor/separator systems shown below, one with a recycle stream and one without a recycle stream. Without Recycle Fo, Xi (A and C only) Fs, XS Fo, Xi (A and C only) F1, X1 With Recycle F1, X1 CSTR A→B FS, X3 CSTR A→B (A and C only) F1, X2 F3, X3 (A and C only) F1, X2 F3, X3 SEPARATOR SEPARATOR (B only) F6, X3 (B only)/nFO= 1.0 F1 = 2.7 F3 = 1.8 F5 1.7 # moles/time Xi_A0 = 0.95 # moles fraction T = 1/2.7 #time k0 = 2.7 # 1/time X1 A0 = 2/3 X2 A0 = 1/3 X3 A0 = 1/2 X5_A0 = 1/2 Assumptions • • Mixing Point Subsystem F₁ = F₁+F₂ F₁x₁₁A=F₁x₁₁A+F5X3,A d(Mx2,4) dt or # moles/time #moles/time #moles/time Constant molar hold-up for CSTR. All molar flowrates are constant. Perfect separation unit with infinitely fast dynamics. No transportation delay between separator and fast dynamics. Isothermal process. Reactor Subsystem dx 2.4 dt T= #moles fraction #moles fraction #moles fraction #moles fraction M = F₁X₁,4-F₁X₂₁4-kox2, AM = - - - (X₁.A - X₂,₁A) - K₁X2₂,A (2) T (1) Separator Subsystem F1X2,4 =F3X3,A (3)/nWith Recycle Case X'iA G4 G3 X'LA X'JA G₁ G₂ X'2A 4. Similarly, develop the transfer function in the block diagram representation of the system with recycle. In this block diagram, the variables are deviation variables (for example, x'i,A = xi,A - xi,A_steady_state). 5. Using Python, simulate the dynamic system by using a step change in xi,A from 0.95 to 0.96 at t=2. Plot the results in the same plot produced in step-2 using different line types (or colors) representing each of the two cases and include a legend. 6. Using Python, fit a transfer function to the step response of x3,A and compare the key parameters with the theoretical parameters obtained in step-4. Analysis 7. By examining the results from part 5 and based on your chemical engineering knowledge, explain the behavior observed in the plot for the two cases and state any differences observed in their behavior. 8. Derive the overall transfer function from x'i,A(s) to x'3,A(s) for the two cases. How do the overall transfer functions differ? Are these results consistent with your answer for part 7?See Answer
Q20: 56.6°C PH1112 PreHeater 66.4°C Process Dynamics. and Control 60.0°C Additives M Reactor 11 Set Point 19.0m3/h Production R11 Reactor Walt 19.6m3/h 1225.01 4.5ba 4th Edition Process Area Preheating and reaction temperatures wwwwwww 698 "C 60.9%C 53.2°C PreHeater IN PreHeater OUT Reactor 11 Reactor 12 75.5°C Reactor 12 Set Point 21.4m3/h Production 21.6m3/h Additives M R12 Reactor Discharge 2660.01 5.0bar Seborg | Edgar | Mellichamp | Doyle Process Dynamics and Control Fourth Edition WILEY Dale E. Seborg University of California, Santa Barbara Thomas F. Edgar University of Texas at Austin Duncan A. Mellichamp University of California, Santa Barbara Francis J. Doyle III Harvard University VICE PRESIDENT & DIRECTOR SENIOR DIRECTOR EXECUTIVE EDITOR SENIOR MARKET SOLUTIONS ASSISTANT PROJECT MANAGER PROJECT EDITOR PROJECT ASSISTANT SENIOR MARKETING MANAGER DIRECTOR, PRODUCTION SENIOR CONTENT SPECIALIST PRODUCTION EDITOR COVER PHOTO CREDIT Laurie Rosatone Don Fowley Linda Ratts Courtney Jordan Gladys Soto Nichole Urban Wauntao Matthews Daniel Sayre Lisa Wojcik Nicole Repasky This book was set in 10/12 TimesTenLTStd by SPi Global, Chennai, India and printed and bound by Strategic Content Imaging. The cover was printed by Strategic Content Imaging. This book is printed on acid free paper. ISBN: 978-1-119-28591-5 (PBK) ISBN: 978-1-119-00052-5 (EVALC) Loganathan Kandan Courtesy of ABB Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work. In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business. Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support. For more information, ple visit our website: www.wiley.com/go/citizenship. Copyright © 2017, 2011, 2004, 1990 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923 (Web site: www.copyright.com). Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, or online at: www.wiley.com/go/permissions. Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instructions and a free of charge return shipping label are available at: www.wiley.com/go/returnlabel. If you have chosen to adopt this textbook for use in your course, please accept this book as your complimentary desk copy. Outside of the United States, please contact your local sales representative. Printed in the United States America Library of Congress Cataloging-in-Publication Data Names: Seborg, Dale E., author. Title: Process dynamics and control / Dale E. Seborg, University of California, Santa Barbara, Thomas F. Edgar, University of Texas at Austin, Duncan A. Mellichamp, University of California, Santa Barbara, Francis J. Doyle III, Harvard University. Description: Fourth edition. | Hoboken, NJ: John Wiley & Sons, Inc., [2016] | Includes bibliographical references and index. Identifiers: LCCN 2016019965 (print) | LCCN 2016020936 (ebook) | ISBN 9781119285915 (pbk.: acid-free paper) | ISBN 9781119298489 (pdf) | ISBN 9781119285953 (epub) Subjects: LCSH: Chemical process control - Data processing. Classification: LCC TP155 .S35 2016 (print) | LCC TP155 (ebook) | DDC 660/.2815-dc23 LC record available at https://lccn.loc.gov/2016019965 Printing identification and country of origin will either be included on this page and/or the end of the book. In addition, if the ISBN on this page and the back cover do not match, the ISBN on the back cover should be considered the correct ISBN. About the Authors To our families Dale E. Seborg is a Professor Emeritus and Research Professor in the Department of Chemical Engineering at the University of California, Santa Barbara. He received his B.S. degree from the University of Wis- consin and his Ph.D. degree from Princeton University. Before joining UCSB, he taught at the University of Alberta for nine years. Dr. Seborg has published over 230 articles and co-edited three books on process con- trol and related topics. He has received the American Statistical Association's Statistics in Chemistry Award, the American Automatic Control Council's Education Award, and the ASEE Meriam-Wiley Award. He was elected to the Process Automation Hall of Fame in 2008. Dr. Seborg has served on the Editorial Advisory Boards for several journals and a book series. He has also been a co-organizer of several major national and international control engineering conferences. Thomas F. Edgar holds the Abell Chair in chemical engineering at the University of Texas at Austin and is Director of the UT Energy Institute. He earned a B.S. degree in chemical engineering from the University of Kansas and his Ph.D. from Princeton University. Before receiving his doctorate, he was employed by Continental Oil Company. His professional honors include the AICHE Colburn and Lewis Awards, ASEE Meriam-Wiley and Chemical Engineering Division Awards, ISA and AACC Education Awards, AACC Bellman Control Heritage Award, and AICHE Comput- ing in Chemical Engineering Award. He has published over 500 papers in the field of process control, optimiza- tion, and mathematical modeling of processes such as separations, combustion, microelectronics processing, and energy systems. He is a co-author of Optimization of Chemical Processes, published by McGraw-Hill in 2001. Dr. Edgar was the president of AIChE in 1997, President of the American Automatic Control Council in 1989-1991 and is a member of the National Academy of Engineering. Duncan A. Mellichamp is a founding faculty member of the Department of Chemical Engineering of the University of California, Santa Barbara. He is edi- tor of an early book on data acquisition and control computing and has published more than 100 papers on process modeling, large scale/plantwide systems analysis, and computer control. He earned a B.S. degree from Georgia Tech and a Ph.D. from Purdue University with intermediate studies at the Technische Universität Stuttgart (Germany). He worked for four years with the Textile Fibers Department of the DuPont Company before joining UCSB. Dr. Mellichamp has headed sev- eral organizations, including the CACHE Corporation (1977), the UCSB Academic Senate (1990-1992), and the University of California Systemwide Academic Senate (1995-1997), where he served on the UC Board of Regents. He presently serves on the governing boards of several nonprofit organizations and as president of Opera Santa Barbara. Emeritus Professor since 2003, he still guest lectures and publishes in the areas of process profitability and plantwide control. Francis J. Doyle III is the Dean of the Harvard Paulson School of Engineering and Applied Sciences. He is also the John A. & Elizabeth S. Armstrong Professor of Engi- neering & Applied Sciences at Harvard University. He received his B.S.E. from Princeton, C.P.G.S. from Cam- bridge, and Ph.D. from Caltech, all in Chemical Engi- neering. Prior to his appointment at Harvard, Dr. Doyle held faculty appointments at Purdue University, the University of Delaware, and UCSB. He also held vis- iting positions at DuPont, Weyerhaeuser, and Stuttgart University. He is a Fellow of IEEE, IFAC, AAAS, and AIMBE; he is also the recipient of multiple research awards (including the AIChE Computing in Chemical Engineering Award) as well as teaching awards (includ- ing the ASEE Ray Fahien Award). He is the Vice President of the Technical Board of IFAC and is the President of the IEEE Control Systems Society in 2016.See Answer

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