I need this project to be completed. I'm more focused on completely understanding steps 1 to 4. I need you to explain how you went about creating the matlab file so I can understand everything. Not to be shared on this site or anywhere else please.
ChE 489 Dr. Basuray Process Control Project Due: May 1, 2023, 11:59PM A process that involves two electrically heated tanks in series is shown in the diagram below. The inlet temperature to the first tank To varies with time while the inlet flow rate wo is constant. The objective is to control the outlet temperature T by keeping it at a desired set point Tsp using the feedback control system shown in the diagram. In the feedback control scheme, the outlet temperature T is measured and the heater input Q2 is manipulated through the regulator R to keep the temperature at the set point. Figure 1. Tank-temperature process schematic, with feedback control loop. Parameter Units Value V1 m 3 30 V2 m 3 40 wO kg/s 10 θ s 8 CP J/kg/°C 2000 ρ kg/m3 1000 ChE 489 Dr. Basuray Process Control Project Several simplifying assumptions may be made about the system: ● Both tanks operate at constant volume and are perfectly mixed. ● The physical properties of the process fluid are constant. ● There is negligible heat loss to the surroundings. ● The first heater does not deviate from its steady state value. ● The temperature to the inlet of the second tank is approximated by a constant time delay , i.e. = .θ (t )T 2 = T 1 − θ ● The temperature transmitter TT, the regulator R and the controller calibration have negligible dynamics, hence their transfer functions & gains are GM = 1.0, GR = 1.0 and KM = 1.0 respectively. ● Any time delay appearing in a transfer function should be approximated by a Taylor expansion: se−θs = 1 − θ Tasks: 1.) Derive the transient energy balances on Tank 1 and Tank 2, in terms of deviation variables, starting from Eqn. 2-11 in the book. 2.) Take the Laplace Transforms of your transient energy balances and solve for T1’(s) and T’(s). Along the way, derive and explain the Laplace relationship between T1’(s) and T2’(s), using the concept of time delay. 3.) Derive the process (GP) and disturbance (GD) transfer functions, defined as: . Note here that the inputs are the temperature(s) G (s)Q (s) (s)T (s)T ′ = P 2′ + GD 0′ deviation in the FIRST tank, and the heater in the SECOND tank. 4.) Create a Simulink block diagram for this system (process with a feedback loop). Be sure to appropriately label all blocks and streams! For tasks 5-8, assume that the controller is a proportional controller (i.e. GC = KC). 5.) Derive the closed-loop transfer function relating the deviation in outlet temperature to a deviation in set-point temperature, (servo problem)(s)/T (s)T ′ SP ′ 6.) This system requires that a step-change in the temperature set-point should produce no more than a 5% offset in outlet temperature. Determine the limiting value of the controller gain KC that meets this requirement (hint: it’s very large). 7.) Using the KC you found in part 6, determine the response and steady-state offset(t)T ′ for a unit-step increase in setpoint , if . Plot this response using(s) /sT ′sp = 1 (s)T ′0 = 0 your Simulink model. What range of values must KC be to ensure a stable system? 8.) Using the KC you found in part 6 and setting , observe the effect of a unit-step(s)T ′sp = 0 increase in using your Simulink model. How well does your feedback loop control forT ′0 this disturbance? Hint: Your stop time will need to be at least twice as long as your ofτ GP in order to fully visualize the dynamics. ChE 489 Dr. Basuray Process Control Project Project Milestones: There will be several milestones in this project that will require submission. The preliminary dates for those submissions are listed on Canvas. Project Report Guidelines: This project will be completed in groups, and a final typewritten report will be submitted on Canvas. Your report should conform to the style outlined in the CME Style Guide, available https://chemicaleng.njit.edu/student-resources. This report is a “Technical Report” and so you’ll want to look at Appendix B in particular for writing and organizational tips. Note: Your original work (handwritten derivations and Simulink Model file) must be uploaded alongside the report. If you do not include your work you will lose a significant amount of credit. Teamwork Guidelines: You will split up into teams of maximum 4 individuals for this project. The teams will be formed using self-sign up on Canvas. You are required to sign up to a team before the first Milestone is due. You will also be evaluating your and your team-mate’s participation on the project, using CATME. https://catme.org/login/index . This information will be used to differentiate individual project scores. Please see the Project Rubric for details. If at any time you cannot log in to CATME (this happens especially the first time) follow the password reset instructions. Your email address is your NJIT email. Organization and Communication: ● You can carry out all group meetings remotely. You are allowed to meet in person unless ● To facilitate such communication, you are encouraged to use any telecommunication available to you, including WebEx, Zoom, Google Hangouts, phone calls, Google Drive etc… Tips for Effective Teamwork: ● Agree on a common meeting time and what each member should do before the meeting. It often helps to have regular weekly meetings, or alternatively, to have “milestone” meetings each time a task is completed. https://chemicaleng.njit.edu/student-resources https://catme.org/login/index ChE 489 Dr. Basuray Process Control Project ● Do any required individual preparation. Read through the section you plan to work on, try working it out yourself before coming together. ● Meet and work. Review the work that was completed, and decide what the next steps will be. ● If you’re splitting up the tasks, check each other's work. This is perhaps the single most important thing you’ll do - your team goal should be to make sure everyone is on the same page at all times. What to do if a conflict arises: ● Consult with your instructor immediately if a conflict arises that cannot be worked through by the team. ● Firing: If a team member refuses to cooperate with the team, their name should not be included on the project report. If the non-cooperation continues, the team should meet with the instructor so that the problem can be resolved, if possible. If no resolution is achieved the cooperating team members may notify the uncooperative team member in writing (by email, cc the instructor) that they are in danger of being fired. If there is no subsequent improvement on the next assignment, the team should notify the uncooperative team member in writing (by email, cc the instructor) that they are no longer with the team. ● Quitting: Students who are consistently doing all the work for their team may issue a warning (by email, cc the instructor) that they will quit unless they start getting cooperation and a second memo (by email, cc the instructor) quitting the team if things do not improve. Students who are fired or quit must meet with the instructor immediately, or they will get zeros for the remaining assignments. Students who quit will be allowed to join another team (cannot exceed 4 members) or to work alone, by their own choice. If a student decides to work alone, they may not later ask to join a team. Students who are fired may work together (if there is more than one at any time). Otherwise, they must work alone. Modelling non-isothermal CSTR using MATLAB and Simulink Sreerag Kaaliveetil
[email protected] Problem Statement Consider a CSTR with an overflow outlet. Solutions of sodium hydroxide and ethyl acetate (reactants A and B), of equimolar concentrations and at the same feed temperature, are fed at equal flow rates into the reactor. The product of this second order reaction are ethyl alcohol and sodium acetate (product C and D). All the stoichiometric coefficients are 1. The rate of reaction is given by The following are three possible approaches for starting up the reactor 1. Add both reactants simultaneously into the empty reactor. 2. Start with a certain volume of reactant A, then add both reactants simultaneously. 3. Fill the reactor with A, then add both reactants simultaneously. 2 Overflow outlet Inlet A B Startup Type 1 Overflow outlet Inlet A B Startup Type 2 Overflow outlet Inlet A B Startup Type 3 Three ways to startup the reactor 3 Partially filled with reactant A Completely filled with reactant A Reactor initially empty Assumptions 1. Negligible variations of heat capacity and heat of reaction with temperature. 2. No change in volume due to mixing or reaction. 3. Constant density. 4. No side reactions. 5. Since we have a liquid mixture under atmospheric pressure, we can safely equate the internal energy to the enthalpy of the system. 6. Resistance to heat transfer inside the reactor and through its walls, and the shaft work due to mixing, are negligible. 4 Startup Type 1 • Add both reactants simultaneously into the empty reactor. • Mass balance ? ?? ??! = ??!" + ??!? V is the volume, Ci is the concentration of reactant/product, F is the flow rate of reactants, Cif is the initial feed concentration, ?! = -1 for reactants and +1 for products ??? ?? = 1 ? [??!" − ??! + ?!??] Overflow outlet Inlet A B 5 Startup Type 1 • Energy balance ? ?? ? Σ?!?! = ? Σ?!"?!" − ?∗ • After some manipulations, this equation takes the form Cpi is the specific heat capacity of reactants and products, Cif is the initial feed concentration of reactants, Tf is the temperatures of the feed. 6 Startup Type 1 Mass balance for products and reactants • The aim is come up with the concentration and temperature profile. • But solving these equations analytically is very hard and might involve lot of approximations. • The solution – Use MATLAB! Energy Balance 7 Note: Since the initial conditions and the differential equation are same for reactants A and B (also for products C and D) , the concentration profile will also be same for both. Constants 8 Integration in Simulink • Integrator block in Simulink can be used to perform complex integrations. • Simulink uses numerical approximation methods to evaluate the integral. Define RHS ??? ?? Ca ??? ?? Integrator 9 Integration in Simulink 10 Mass Balance for reactants 11 Rate of the reaction. Since both CA and CB have same differential equation and initial conditions, both of their profiles will be same at every point in time. Hence we can say CA = CB 12 Mass Balance for the products 13 Energy Balance 14 Energy Balance 15 Defining Volume 16 • For startup type 1 and 2 the volume keeps on changing until it reaches the overflow volume (2.8 L). • For startup 1, volume can be defined as shown below Data store memory Data store write Data store read 17 • This is an important step to do before running the model. • The start time shouldn’t be 0. This will produce an error. 180 2 4 6 8 10 12 14 16 18 Time(min) 0 0.02 0.04 0.06 0.08 0.1 C on ce nt ra tio n( M ) Concentration profile of reactants and products Reactants Products Offset=0 190 2 4 6 8 10 12 14 16 18 Time(min) 24 25 26 27 28 29 Te m pe ra tu re (° C ) Temperature Profile Offset=0 Other start up types • Your task is to model startup types 2 and 3. • You can modify this program to model startup types 2 and 3 and come up with their concentration and temperature profile. • Startup 2 still have 3 stages – filling up of the reactor, approaches steady state and then operates steadily. • Startup type 3 only have 2 stages since it is initially completely filled. 20 21 Solution 1 Start up: Type 1 This type of start up will have three stages. Stage 1 - reactor is filling up, so volume is varying. Stage 2 - Reactor is filled up, so the volume is constant. Stage 3 - Reactor reaches steady state. Mass balance dCi dt = 1 V [FCif − FCi + σiV r] σi = −1 for the reactants and σi = +1 for the products. Energy balance dT dt = 1 V ∑ cpiCi [ (−F ∑ cpiCif )(T − Tf ) − rV∆H0r − 4hairV D (T − Tamb) ] Initial conditions and other parameters Initial feed concentration, Cif = { 0.1 M, For reactants 0 M, For products V = { Ft, In stage 1 2.8, In stage 2 and 3