Consider the two stirred tank heaters system shown in Figure 1. We would like to control...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the two stirred tank heaters system shown in Figure 1. We would like to control temperature T₂(t) by manipulating the heating medium temperature in either the first or the second heater (i.e., Ts1 (t) or Ts2 (t)). It can be considered that temperatures of the heating media remain practically constant along the respective heating coils. The inlet flow rate F remains constant, while its inlet temperature Ti(t) changes, thus creating the need for control. The recycle stream flowrate F3 is equal to half of F₁. Assume that the changes in temperature in the tanks do not affect the density p and heat capacity of the fluid Cp. Tank 1 F, T/(t) T₁1(t) F3, T₂(t) F₁, T₁(t) Tank 2 F₂ T₂(t) Tsz(t) Figure 1. Two stirred tank heaters in series with recycle system Starting from the mathematical model in the time domain of the system shown in Figure 1, use Laplace transforms to determine all transfer functions that describe this process in deviation state in the open loop. Determine initially any first order dependencies between variables and calculate their respective gains and time constants. Furthermore, combine these first order transfer functions to obtain the transfer functions describing the effect of temperatures Ti(t) and T₂(t) to changes to the temperatures T₁ (t), T2 (t) and Ti(t). Clearly show all steps taken and clearly indicate the units of all involved variables. Consider the two stirred tank heaters system shown in Figure 1. We would like to control temperature T₂(t) by manipulating the heating medium temperature in either the first or the second heater (i.e., Ts1 (t) or Ts2 (t)). It can be considered that temperatures of the heating media remain practically constant along the respective heating coils. The inlet flow rate F remains constant, while its inlet temperature Ti(t) changes, thus creating the need for control. The recycle stream flowrate F3 is equal to half of F₁. Assume that the changes in temperature in the tanks do not affect the density p and heat capacity of the fluid Cp. Tank 1 F, T/(t) T₁1(t) F3, T₂(t) F₁, T₁(t) Tank 2 F₂ T₂(t) Tsz(t) Figure 1. Two stirred tank heaters in series with recycle system Starting from the mathematical model in the time domain of the system shown in Figure 1, use Laplace transforms to determine all transfer functions that describe this process in deviation state in the open loop. Determine initially any first order dependencies between variables and calculate their respective gains and time constants. Furthermore, combine these first order transfer functions to obtain the transfer functions describing the effect of temperatures Ti(t) and T₂(t) to changes to the temperatures T₁ (t), T2 (t) and Ti(t). Clearly show all steps taken and clearly indicate the units of all involved variables.
Expert Answer:
Answer rating: 100% (QA)
System Description The system consists of two continuously stirred tank heaters connected in serie... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
-
answer all questions as instructed below. make sure you have attended all questions .Comparative Architectures (a) Describe the organisation of a two-level branch predictor that makes use of a global...
-
It is stated in Section 40.3 that a finite potential well always has at least one bound level, no matter how shallow the well. Does this mean that as U 0 0, E 1 0? Does this violate the Heisenberg...
-
Assume McGregor Consultants purchased a building for $445,000 and depreciated it on a straight-line basis over 40 years. The estimated residual value was $90,000. After using the building for 20...
-
3. We have a one-dimensional array int arr[]={0,1,1, -1, -10, 2,5,4,-6,9,0,1}; write a code to display arr, *arr and *(arr+5). (20pts) 4. We assign the values from "arr" to a two-dimensional array...
-
What discovery devices you may use to obtain facts?
-
In this problem, you will see why the Equity Premium Puzzle described in Application 4.5 really is a puzzle. Suppose that a person with $100,000 to invest believes that stocks will have a real return...
-
We create a CDO with 100 loans of $1 mill each. These loans either pay off or default (Recovery Rate = 0), and the probability of a default of each mortgage is 15%. The defaults are independent...
-
Amazon.com, Inc., headquartered in Seattle, WA, started its electronic commerce business in 1995 and expanded rapidly. The following transactions occurred during a recent year (dollars in millions):...
-
Suppose that tuition is initially $100 per credit and increases by 6% from the first year to the second year. What is the cost of tuition the second year? Now suppose that tuition decreases by 6%...
-
How do you approach financial decisions that affect large groups of people in an organization ((for example, health, and insurance)? How would you value this deal on its own? Are there any potential...
-
1. Dan is involved in three business activities. He does not materially participate in any activity. He has at-risk amounts in excess of $250,000 for each. During the year, the activities produced...
-
A company needs to raise 8M in equity from a venture capital fund to finance an expansion. The company will be worth as provided below in 5 years. If the venture capitalist wants to achieve a rate of...
-
1.17 A tension test performed on a metal specimen to fracture produced the stress-strain relationship shown in Figure P1.170. Graphically determine the following (show units and all work): 100 80...
-
During a penetration test, a security professional runs the following command during a security assessment: -(kali kali)-[~] nc -lvnp 8387 Ncat: Version 7.92 ( https://nmap.org/ncat ) Ncat: Listening...
-
1) Find the mean of the sampling distribution of sample means.If necessary, round your answer to the tenths place (one decimalplace). The mean age of employees at a large corporation is 43.6...
-
The Place-Plus real estate development firm in Problem 24 is dissatisfied with the economists estimate of the probabilities of future interest rate movement, so it is considering having a financial...
-
What concept does RTD add to our CRE algorithm and where does it fit in the algorithm (1) Mole Balance, (2) Stoichiometry, and so on?
-
Go to the LearnChemE screencast link for Chapter 18 (http://umich.edu/~elements/6e/18chap/learn-cheme-videos.html). View one or more of the screencast 5- to 6-minute videos and write a two-sentence...
-
Use Equation (3-20) to make a plot of f(E,T) as a function of E for T = 300, 500, 800, and 1200 K. a. What is the fraction of molecules that have sufficient energy to pass over a energy barrier of 25...
-
Consider the regression model with a single regressor: \(Y_{i}=\beta_{0}+\beta_{1} X_{i}+u_{i}\). Suppose the least squares assumptions in Key Concept 4.3 are satisfied. a. Show that \(X_{i}\) is a...
-
In their study of the effectiveness of cardiac catheterization, McClellan, McNeil, and Newhouse (1994) used as an instrument the difference in distances to cardiac catheterization and regular...
-
In his study of the effect of incarceration on crime rates, suppose Levitt had used the number of lawyers per capita as an instrument. Would this instrument be relevant? Would it be exogenous? Would...
Study smarter with the SolutionInn App