Problem 1. SIR Epidemic Dynamics Control using IMC design (CMA 4). The goal of this problem...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 1. SIR Epidemic Dynamics Control using IMC design (CMA 4). The goal of this problem is to apply Internal Model Control to design a feedback control system for the SIR model derived in prior EPA exercises (and examined in CMA No. 2). The control strategy considered requires that the transmission rate constant (t) be manipulated to reduce the infected population I(t) to a desired setpoint, all while in the presence of "disturbances" arising from changes in the recovery rate constant y(t) and the vaccination rate k(t). The linearized nominal model describing the dynamics between B(t) and I(t) conforms to a second-order transfer function according to: p(s) = bs+b2 s+as+a2 (1) From the Symbolic Math Toolbox transfer function models generated in EPA 5, Prob. 3d and CMA No. 2, we learned that, over all operating conditions, 1. the steady-state gain for this transfer function will always have a positive sign (which consequently implies that lowering will reduce the infected population) and 2. the plant zero in the transfer function (1) will always lie in the Left-Half Plane (LHP). This second characteristic will greatly simplify the use of the IMC design procedure to obtain a feedback control law in this case, as the IMC controller q = p is stable and causal (but improper). Note: you may assume that the system is also open-loop stable. a) Apply the Internal Model Control design procedure to this problem using a first-order Type I filter (with A as the adjustable parameter) to obtain a feedback controller for this system. Express the controller as a ratio of polynomials (with numerator cnum and denominator cden). b) Show that the controller from part a) can be expressed as an ideal PID controller with filter, according to: c(s) = Ke (1+ 1 + TIS -TDS) (73+1) TFS (2) Generate tuning rules for Ke, TI, TD, and TF for this control system, which will be in terms of the model coefficients in (1) and an adjustable parameter A. Note: this problem is conceptually similar to Example 1c that is discussed in the IMC class presentation, and the EOLSS chapter as well. Problem 1. SIR Epidemic Dynamics Control using IMC design (CMA 4). The goal of this problem is to apply Internal Model Control to design a feedback control system for the SIR model derived in prior EPA exercises (and examined in CMA No. 2). The control strategy considered requires that the transmission rate constant (t) be manipulated to reduce the infected population I(t) to a desired setpoint, all while in the presence of "disturbances" arising from changes in the recovery rate constant y(t) and the vaccination rate k(t). The linearized nominal model describing the dynamics between B(t) and I(t) conforms to a second-order transfer function according to: p(s) = bs+b2 s+as+a2 (1) From the Symbolic Math Toolbox transfer function models generated in EPA 5, Prob. 3d and CMA No. 2, we learned that, over all operating conditions, 1. the steady-state gain for this transfer function will always have a positive sign (which consequently implies that lowering will reduce the infected population) and 2. the plant zero in the transfer function (1) will always lie in the Left-Half Plane (LHP). This second characteristic will greatly simplify the use of the IMC design procedure to obtain a feedback control law in this case, as the IMC controller q = p is stable and causal (but improper). Note: you may assume that the system is also open-loop stable. a) Apply the Internal Model Control design procedure to this problem using a first-order Type I filter (with A as the adjustable parameter) to obtain a feedback controller for this system. Express the controller as a ratio of polynomials (with numerator cnum and denominator cden). b) Show that the controller from part a) can be expressed as an ideal PID controller with filter, according to: c(s) = Ke (1+ 1 + TIS -TDS) (73+1) TFS (2) Generate tuning rules for Ke, TI, TD, and TF for this control system, which will be in terms of the model coefficients in (1) and an adjustable parameter A. Note: this problem is conceptually similar to Example 1c that is discussed in the IMC class presentation, and the EOLSS chapter as well.
Expert Answer:
Related Book For
Numerical Methods With Chemical Engineering Applications
ISBN: 9781107135116
1st Edition
Authors: Kevin D. Dorfman, Prodromos Daoutidis
Posted Date:
Students also viewed these chemical engineering questions
-
Q.3 A vibratory system performs the motions as expressed by the following equations: f *+800x+900 = 0 +8000+ 90x = 0 If the system is turned through 1.5 radiance and released, find the two natural...
-
Data set Theory Assume an informational record with one association parent including matches (a, b) where a can't try not to be a parent of b. (a) Write a Datalog demand which gives the graph of...
-
"I'm not sure we should lay out $300,000 for that automated welding machine," said Jim Alder, president of the Superior Equipment Company. "That's a lot of money, and it would cost us $84,000 for...
-
The objective of this problem is to design and develop a program for Huffman coding algorithm. The discrete source has an alphabet X = {x1, x2, x3, x4, x5, x6, x7, x8, x9} with corresponding...
-
Use MATLAB to plot the following sinusoids for 0 < t < 5: (a) 5 cos 3t - 2 cos(3t- /3) (b) 8 sin( t + /4) + 10 cos( t- /8)
-
Different management levels in Bates Inc. require varying degrees of cost accounting information. Because of the need to comply with the managers requests, three ways of variances analysis for...
-
Label each of the following characteristics of a corporation as either an (A) advantage or a (D) disadvantage: a. Organizational costs b. Continuity of existence c. Capital raising capability d....
-
The Thompson Toy Company manufactures toy building block sets for children. Thompson is planning for 2017 by developing a master budget by quarters. Thompsons balance sheet for December 31, 2016,...
-
19. Shila Nathan, the hospital administrator for a hospital in Chennai, India, has to devise for the coming week a workforce schedule for nurses in the orthopedic department of the hospital. The...
-
Fix the code so it can output the correct information #include #include #include #include #include using namespace std; struct menu { double sushi = 4.99; double fries = 2.50; double nuggets = 4.20;...
-
What is the interest earned on $350 invested 4 years at a 5% simple interest?If I put $1500 into my savings account and earned $180 of interest at 4% simple interest, how long was my money in the...
-
The following information is available for Market, Incorporated and Supply, Incorporated at December 31: Accounts Accounts receivable Allowance for doubtful accounts Sales revenue Market,...
-
Develop a simulation of a Light Detector using Tinkercad. The LCD will display the INPUT 10- bit Value received from Photo resistor and OUTPUT 8-bit converted from Input 10-bit value. Red LED will be...
-
What happens when you change the data in a worksheet associated with a chart?
-
Find the solutions of the equation a cosh x b sinh x = c, assuming that a, b, and c are constants. [Hint: The result should have the form x = f(a,b,c), where f(a, b, c) is a specific function.] =
-
Jeremy, a woodcarver, wants to create a carving, to scale, of an eagle. He has a block of wood that is 1.50 m long and 1.25 m high. Jeremy finds out that an eagle has a body length of about 90 cm and...
-
Read the Forecasting Supply Chain Demand Starbucks Corporation case in your text Operations and Supply Chain Management on pages 484-485, then address the four questions associated with the...
-
An increase in the demand for land will a. increase the price of land and increase the quantity of land supplied. b. increase the price of land but not change the quantity of land supplied. c....
-
At low levels of interest, borrowers will want to borrow ___ and suppliers of funds will want to supply ___. a. more; less b. less; more c. more; more d. less; less
-
How is the price of capital determined?
Study smarter with the SolutionInn App