Consider the level dynamics of a spherical reboiler with 1.0 ft radius, Jin h Jout The...
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Consider the level dynamics of a spherical reboiler with 1.0 ft radius, Jin h Jout The differential equation describing how level (h) responds to changes in the inlet and outlet volumetric flowrates (in and out, respectively) in the tank is dh dt = Jin-Yout h (2r-h) h is both the system state and output variable, 9in is the disturbance variable, and out is the manipulated variable. Task 1: Use MATLAB with Simulink to develop a computer program that numerically integrates the system models (both nonlinear and linearized approximation). First, linearize the given ODE above, assuming that the system is initially at a steady state. (No numerical values) Then, consider the following scenario. Initially, the spherical reboiler is filled at 25% capacity by volume (hint: use this information to calculate the initial value of h) and is at a steady state with inlet and outlet flow rates equal to 1 gallon/minute. When t = 5 min, the inlet flow rate suddenly increases by 1 gallon/minute, while the output flow rate remains unchanged. Enter the input values in MATLAB scripts. Complete the Simulink file by specifying each block's parameters and connecting them to solve linearized and nonlinear ODEs. Use your MATLAB with Simulink simulation to determine how long it takes before the tank is filled to 75% capacity by volume for both linearized and nonlinear cases. Plot the responses for both models. A "clean" .mlx file and .slx file have been posted on the course Canvas webpage to assist you. Task 2: Use your MATLAB with Simulink code to consider another scenario. Consider the settings in Task 1, except that you now have the opportunity to make a step change in the outlet flow rate at the same time (t=5 min) that the inlet flow rate changes. Calculate the magnitude of change required in the outlet flow rate such that the reboiler reaches 75% capacity by volume at t=30 min (25 minutes after the change in the inlet flow rate). Hint: derive the analytical solution by integration of separation of variables. Show your work to receive full credits. Input the calculated magnitude of change required in the outlet flow rate to both linearized and nonlinear models in Simulink. Simulate the resulted transient responses and estimate the time needed to reach 75% capacity from plots for both models. Your submission (due on 9/28) should be one combined pdf file that includes the following parts in sequence: 1. Linearize ODE. 2. Calculate the liquid level at 25% and 75% capacity by volume. Show all steps to receive full credits. 3. In task 2, calculate the magnitude of change required in the outlet flow rate such that the reboiler reaches 75% capacity by volume at t=30 min. Show all steps to receive full credits. 4. Complete MATLAB scripts (exported as pdf format) and Simulink block diagrams for both linearized and nonlinear cases (screenshots, saved as pdf format). Your name should appear in both scripts and the Simulink window. 5. Generate figures for Task 1 and Task 2 (saved as pdf format). Make sure that your name appears in the title of each generated figure. Consider the level dynamics of a spherical reboiler with 1.0 ft radius, Jin h Jout The differential equation describing how level (h) responds to changes in the inlet and outlet volumetric flowrates (in and out, respectively) in the tank is dh dt = Jin-Yout h (2r-h) h is both the system state and output variable, 9in is the disturbance variable, and out is the manipulated variable. Task 1: Use MATLAB with Simulink to develop a computer program that numerically integrates the system models (both nonlinear and linearized approximation). First, linearize the given ODE above, assuming that the system is initially at a steady state. (No numerical values) Then, consider the following scenario. Initially, the spherical reboiler is filled at 25% capacity by volume (hint: use this information to calculate the initial value of h) and is at a steady state with inlet and outlet flow rates equal to 1 gallon/minute. When t = 5 min, the inlet flow rate suddenly increases by 1 gallon/minute, while the output flow rate remains unchanged. Enter the input values in MATLAB scripts. Complete the Simulink file by specifying each block's parameters and connecting them to solve linearized and nonlinear ODEs. Use your MATLAB with Simulink simulation to determine how long it takes before the tank is filled to 75% capacity by volume for both linearized and nonlinear cases. Plot the responses for both models. A "clean" .mlx file and .slx file have been posted on the course Canvas webpage to assist you. Task 2: Use your MATLAB with Simulink code to consider another scenario. Consider the settings in Task 1, except that you now have the opportunity to make a step change in the outlet flow rate at the same time (t=5 min) that the inlet flow rate changes. Calculate the magnitude of change required in the outlet flow rate such that the reboiler reaches 75% capacity by volume at t=30 min (25 minutes after the change in the inlet flow rate). Hint: derive the analytical solution by integration of separation of variables. Show your work to receive full credits. Input the calculated magnitude of change required in the outlet flow rate to both linearized and nonlinear models in Simulink. Simulate the resulted transient responses and estimate the time needed to reach 75% capacity from plots for both models. Your submission (due on 9/28) should be one combined pdf file that includes the following parts in sequence: 1. Linearize ODE. 2. Calculate the liquid level at 25% and 75% capacity by volume. Show all steps to receive full credits. 3. In task 2, calculate the magnitude of change required in the outlet flow rate such that the reboiler reaches 75% capacity by volume at t=30 min. Show all steps to receive full credits. 4. Complete MATLAB scripts (exported as pdf format) and Simulink block diagrams for both linearized and nonlinear cases (screenshots, saved as pdf format). Your name should appear in both scripts and the Simulink window. 5. Generate figures for Task 1 and Task 2 (saved as pdf format). Make sure that your name appears in the title of each generated figure.
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Related Book For
Process Dynamics and Control
ISBN: 978-1119385561
4th edition
Authors: Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp, Francis J. Doyle
Posted Date:
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