12_BioreactorSimulator_W12 - Page 1 of 10 SCHOOL OF...

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Unformatted text preview: Page 1 of 10 SCHOOL OF CHEMICAL, BIOLOGICAL and ENVIRONMENTAL ENGINEERING OREGON STATE UNIVERSITY CHE 361 - BIOREACTOR "Simulator" DESCRIPTION OF SIMULINK BLOCKS The bioreactor block diagram, bio_reac.mdl, is a simulation of a reactor with "full" dynamic variables, not deviation variables. Because of this, several additional steps must be taken to set up the model which are not done in simple dynamic simulations involving transfer function models. Another feature is that the blocks in bio_reac have been designed so that it is very simple to do parameter estimations for a transfer function model from a step response experiment (see Chap. 7 in SEMD3) and frequency response analysis from a pulse response experiment (see Chap. 14 in SEMD3). The revised diagram shown below contains 17 "blocks" and 2 "button boxes". The button boxes are used after a simulation has been completed. The example shown here is set up for the response of the bug concentration (B = y1) as output to a step increase of 10% in the full-variable value of the nominal flow rate (F = u1) as the input. Each type of block will be described, starting at the left of the diagram and following the flow of information. "Open" a block by double clicking on it and change names by clicking on the name. Draw lines from blocks using the left mouse button held down; draw lines from lines using the right mouse button held down. Page 2 of 10 INPUT BLOCKS The first two blocks, F_step_in and Ni_step_in, are subsystem blocks for setting up the input variables F and Ni to the bioreactor. Double clicking on one of these blocks "opens" the subsystem to reveal the components shown below. You must enter your nominal steady-state values for F and Ni in the constant blocks, shown here as 1. and 5.2 in the example. The "F, + step" block is used to run a positive Step Fcn block, the "F, - step" block is used to run a negative Step Fcn block. Double clicking on either brings up a Step Fcn menu window with Step time, Initial value, and Final value. The two steps can be used together to create a rectangular pulse, as done in HW #7. The Sum2 blocks add the steady-state value of F to the deviation variable made by Sum1 to get the "full" variable which is needed by the bioreactor simulation and sent out of the subsystem F_step_in through the out_1 port block. The Mux block combines the three signals t (from Clock1), the full F and deviation F' and sends them as a vector to a workspace variable (which is an Nx3 matrix) called "tFin". If you entered tFin in the MATLAB Command Window after the simulation you would see three columns of numbers corresponding to t,F,F' values. The tUin Workspace block creates a variable which is used by the PULSE_analysis button block. If your chosen input variable is Ni, the tUin block needs to be moved to the Ni_step_in subsystem shown below (see step 7 in the "checklist" on pg 6). Page 3 of 10 Bio361 BLOCK Double click on this block to enter YOUR bioreactor parameters and Initial B and N to YOUR nominal steady-state values, as shown in the Bio_reactor(Mask) menu below on the left. Once you have done this be sure to SAVE the bio_reac.mdl file to your own account on the fileserver or your laptop so that you can use it later. PLOT BLOCKS The blocks named Fin, Nin, Bout and Nout are all plotting blocks and can be changed by double clicking on them, which brings up a Graph scope (Mask) menu as shown on the right above. You should adjust the Min y and Max y values to give you a good display and the Time range value must agree with the “Stop Time” (here = 6 hours) you set in the Configuration Parameters: option shown below which you get to from the “Simulation” pulldown menu option in the bio_reac.mdl block diagramWindow. Page 4 of 10 OUTPUT BLOCKS The blocks named Store_tBout and Store_tNout record the numerical values of the outputs to variables in the workspace. Double clicking on either opens up its subsystem shown below, where you must enter your initial steady-state values of B and N. These operate similarly to the input blocks in that the variables tBout and tNout are in columns of t,y,y' for time, full value, deviation value. The workspace variable tYout corresponding to the ORANGE block with that name must be moved to the Store_tNout block if your output is N instead of B (see step 10 of the checklist that starts on pg. 8). Page 5 of 10 "BUTTON" BLOCKS (Chapters 7 & 14 in SEMD3 textbook) STEP TEST FIT : The block named Step_Analysis is used AFTER you have run a step input simulation. Double clicking this button block starts the step2g.p program which uses the tYout.dat which is a matrix of (t,y,y’ ) columns created by the “tYout” Block. This data will be for the “Bug” concentration or “Nutrient” concentration coming out of the reactor, depending on where you connect the “tYout” Block. The step2g.p program runs in the MATLAB Command Window and first plots the data and then asks what kind of transfer function you want to use. Then it asks if you want a fixed KM value for use with the response. If you respond that you do, it asks you for the fixed value, which should correspond to your final output value at the new steady state. Remember for the Bioreactor you must calculate the correct new final steady state of your bioreactor output from the steady state equations (6) of the Bioreactor project handout and use the deviation value of your y’ for your KM value. Obviously when you use different step inputs, you are using different M values and will use different calculated final y’ values. The step2g.p program next asks if you want a fixed time delay. For the bioreactor project, you would normally respond that you do, and that the fixed value is 0. Then the program asks for reasonable initial estimates of parameters for the particular type of G(s) you chose. One you might try your local G(s) values. The program then draws a plot of the data as circles and begins a search for the best variable parameters, in the sense that the norm of the error vector is minimized by using a simplex type search of those variable parameters. After you watch the program converge, the final parameters are reported to the MATLAB Command Window, along with the location of any zero and the pole(s). The sum of the squared errors and the sum divided by the number of data points are also reported and can be used for comparison of the goodness of fit of two kinds of transfer functions, e.g. first over second versus simple first order when the more complex transfer function may have pole-zero "near cancellation". The button Re-opt on the plotting window allows you to watch the optimization again, however it will take just as long to redo. Here is an example of what could appear in the Command Window with user inputs in bold: step2g.m not found. (Don’t worry – we’re using step2g.p) ......... loading the response data file. This file must have 3 columns containing ascii data (t,yfull,ydev) --- it MUST be named tYout.dat First look at the shape of the data response. Then make your choice of the kind of transfer function. You may now EXIT (pick 0) in order to EDIT & PRINT this plot of only the data, or you can go on to the fitting step .... Page 6 of 10 Specify general type of G(s) |--------------------------------------| | Enter: | | | | 0 to EXIT | | 1 for 1st order model | | 2 for 2nd order model | | 3 for 1st/2nd order model | | 4 for 1st/2nd with zero at origin | |--------------------------------------| Enter choice 1,2,3 or 4 : 1 --------------------------------------HOW to treat KM Enter 0 for computer adjusted Enter 1 for fixed KM : 1 For standard G(s) form Fixed KM = -0.09764 --------------------------------------HOW to treat time delay Enter 0 for computer adjusted Enter 1 for fixed time delay : 1 For standard G(s) form Fixed time delay = 0 --------------------------------------Enter estimate of tau : 1 End --------- Final Parameters -----------Final KM = -0.0976 Final time delay = 0.0000 Final tau = 0.4827 --------- Poles and zeros ------------One pole at s = -2.0716 --------------------------------------How GOOD was your fit ?? The sum of the squares of your model errors = 0.005687 but the more data points you have, the bigger the number will be. Thus you need to divide by the number of points to get the per_data_pt contribution to the sum of the squared errors. Your value for this model and data set was = 9.1726e-005 for a total of 62 data points. Page 7 of 10 PULSE TEST - Bode diagram. The PULSE_Analysis button box runs the program pulsec.p, which does a number of operations to enable you to easily find the frequency response of your bioreactor from a pulse response experiment: Saves values of t,u,u’ in a matrix named tUin and a file uin.dat Saves values of t,y,y’ in a matrix named tYout and a file yout.dat Calculates the frequency response based on the rectangular pulse time response Makes a Bode plot, then a separate Amplitude ratio and Phase angle plot. The pulsec.p program runs in the MATLAB Command window. The following are appropriate for the Base Case example of a bioreactor. You may need to use different values. After double clicking the RUN pulsec block you should see in the MATLAB Command Window: pulsec.m not found. (Don’t worry, we use pulsec.p instead) Use the Help browser Search tab to search the documentation, or type "help help" for help command options, such as help for methods. Enter min frequency to calculate : 0.01 Enter max frequency to calculate : 10 Enter number of freqencies to calculate : 200 The Figure above contains a BODE plot. Two additional Figures are made, one of the Amplitude vs. Frequency, the other the Phase Angle in degrees vs. Frequency. These extra plots are sometimes easier to analyze than the combined plot shown here – see Chap. 14 in SEMD3. Page 8 of 10 Checklist for Bioreactor Simulink Simulator Use (1) Copy files in the folder named “Bioreactor” on the class webpage to your network or laptop directory for CHE361 (or a USB jump drive). Each member of the team should do this in their own directory ! DO NOT depend on your teammates to do all the MATLAB related tasks. (2) START the MATLAB program, change the Current Directory to your directory for CHE361. Then type >>bio_reac in the MATLAB Command Window after the >> MATLAB prompt to open your block diagram. (4) Double click on the Bio361 block and change the 4 kinetic parameters to agree with your values. (Volume should always be 1.0 liters) Then enter 2 values for your nominal steady-state B and N concentrations in the reactor. (5) Double click on F_step_in and set your nominal steady-state value in the F initial ss block. Set the F,+ step and F,- step initial and final values to 0. (6) Double click on Ni_step_in and set your nominal steady-state value in the Ni initial ss block. Set the Ni, + step and Ni, - step initial and final values to 0. (7) IF your input variable is to be Ni, you need to change the input which gets recorded by the tUin block. First select and then delete the input arrows to the ORANGE tUin block and the White Alt_input block. Then switch the positions of those two blocks by clicking and dragging them around. Then click on the output of the F_step_in box and connect it to the Alt_input box. Finally similarly click on the output of the Ni_step_in box and connect it to the ORANGE tUin box = now you are recording Ni as the input. (8) Outputs: Double click on the Store_tBout block and set your nominal steadystate value of B in the B initial ss block. (9) Double click on Store_tNout and set your nominal steady-state value of N in the N initial ss block. Page 9 of 10 (10) IF your output variable is N instead of B, move the ORANGE tYout block from the Store_tBout block to the Store_tNout block and connect the White Alt_ouput block to the Store_tBout block in a similar manner to that described in step (7) above for moving the Alt_input block. (11) Now setup the appropriate "Simulation" parameters and simulate the nominal steady-state of your bioreactor (you must get straight lines on all plots). Since all variables would be at their steady-state values, you should observe horizontal lines on your four plot figures. If not, something is incorrectly setup and you need to correct it before going any further. Be careful with “round off” ! __________________________________________________________________________________ (12) Make a “calibration” plot of steady-state values of your output vs. your input for the feasible input range, showing your nominal steady state as a point on this graph and the slope of the curve at that point as the gain of your local transfer function model. (13) Run appropriate "small" and "large" STEP response experiments, possibly in both + and - directions and use the Step_Analysis “button block” for identification of appropriate G(s) models. (14) Run appropriate "small" and "large" PULSE response experiments, possibly in both + and - directions and use the PULSE_Analysis “button block” to make Bode diagrams which you then can use to identify (by "hand" graphical methods) appropriate G(s) models. NOTE: If you have a process with a negative gain, you must change the signs of the SUM block in your output ( Store_tBout or Store_tNout) to -+ instead of +- to get “normal” phase angle behavior for analysis. (15) Analyze your results for the degree of nonlinear behavior your bioreactor exhibits and show the plot for Class A, B, C or D and declare what Class your bioreactor is in. This may require additional step tests to be performed. Include comparisons of “experimental” transfer function models with your correct “local” G(s). (16) Write up your report in a clear and concise manner, using tables to report parameter values for your various models and clearly identify all plots included in the report. Each team member must edit and be satisfied with the final version of the writing, since this is a team project and grade. Page 10 of 10 Tasks for CHE 361 Bioreactor Project Analysis Pick nominal inputs and parameter values to obtain feasible nominal steadystate outputs. Derive G(s)local Make changes to bio-reac.mdl Setup input and output subsystems. Not yet ! Straight-line simulation ? Perform Step Tests using tYout.dat, step2g.p and fitmodel.p files via Button Box Gstep1, Gstep2 , etc. Perform Pulse Tests using uin.dat, yout.dat and pulsec.p files to create freq.dat and plot a Bode plot using chebode.p via Button Box Gpulse1, Gpulse2 , etc. Run freqg.p to specify a transfer function, generate it’s frequency response via the short cut method and store in a frequency data file like freqg2.dat Use chebode2i.p to make Bode plots with freqg.dat from pulse experiment versus Glocal frequency response file calculated by freqg.p ...
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This note was uploaded on 03/01/2012 for the course CHE 361 taught by Professor Staff during the Winter '08 term at Oregon State.

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