The dynamic model for a process is given by where u(t) is the input function and y(0) and dy dt (0) are both zero What are the functions of the time (e g , e t Iuml ) in the solution for each of the following cases (a) u(t) be 2t (b) u(t) ct b and c are constants You do not have to find y(t) in the...

a Laplace transform on the ODE gives Thus Regardless of the numerical values ...

The dynamic model for a process is given by where u(t) is the input function and y(0)

Question:

The dynamic model for a process is given by + 8y = 3u(t) +6 dt? dt

where u(t) is the input function and y(0) and dy/dt (0) are both zero.

What are the functions of the time (e.g., e^ˆ’t/Ï„) in the solution for each of the following cases?

(a) u(t) = be^ˆ’2t
(b) u(t) = ct

b and c are constants.
You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Process Dynamics and Control

ISBN: 978-1119385561

4th edition

Authors: Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp, Francis J. Doyle

See More Books

Question Posted: Jul 30, 2018 01:39 PM

See More Questions

The figure shows a simple model of the loading of a square thread of a power screw transmitting an axial load F with an application of torque T. The torque is balanced by the frictional force Ff...
Given that F[ f (t)] = ( j /)(ej - 1), find the Fourier transforms of: (a) x(t) = f ( t) + 3 (b) y(t) = f ( t - 2) (c) h(t) = f ' ( t) (d) +10f 3 g() = 4ft 10f
The discrete transfer function of a process is given by (a) Calculate the response y(k?t) to a unit step change in u using simulation of the difference equation.(b) Check your answer in (a) by using...
The time it takes a cell to divide (called mitosis) is normally distributed with an average time of one hour and a standard deviation of 5 minutes. (a) What is the probability that a cell divides in...
Review the following real-world Hewlett Packard Statement of Cash flows and address the two questions below: Required: 1) Please calculate the percentage increase or decrease in cash for the total...
Assume that as of January 1, 2013, Sylvester Consulting has total assets of $500,000 and total liabilities of $150,000. As of December 31, 2013, Sylvester has total liabilities of $200,000 and total...
Effects of an Unusual Point. You are analyzing a data set of size $n=100$. You have just performed a regression analysis using one predictor variable and notice that the residual for the 10th...
Tolo Co. plans the following repurchases: $10 million in one year, nothing in two years, and $20 million in three years. After that, it will stop repurchasing and will issue dividends totaling $25...
21 In the following we consider vectors x = 22 in R3. Determine (with 23 justification) whether the following sets are subspaces of R3. 1. (5pts) V = {x R | x1 = x2 = x3}
Create a new mission statement for Google/Alphabet that will take it through the rest of this century?
Figure E3.3 shows a pulse function,u(t). (a) From the information shown in Fig. 3.3, calculate the pulse width, t w . (b) Express u(t) as the sum of simpler functions (some perhaps translated in...
The dynamic model between an output variable y and an input variable u can be expressed by (a) Does this system exhibit an oscillatory response after an arbitrary change in u? (b) What is the...
Match each equation in Column I with the best first step for solving it in Column II. e 2x-1 = 24 A. Use the product rule for exponents. B. Take the common logarithm on each side. C. Write the sum of...
"Retirement Financing: Pensions and Savings" Young adults typically do not think about retirement financing. Retirement planning can be challenging, when living on an already tight-budget. Imagine...
Jaquar advertises a 48 month lease for the E-Type with monthly payments of only $869.11. The price of the car is $61100. Jaquar Financial Services charges 4.40% (APR) on the lease. How much of the...
Walmart Financial Statement: https://finance.yahoo.com/quote/WMT/financialsLinks to an external site. Target Financial Statement: https://finance.yahoo.com/quote/TGT/financialsLinks to an external...
Selling home 160,000, down payment 20,000, rate interest 3 1/2%, in 30 years loan, what is monthly payment, and what is payment per 1,000
Explain why MNCs such as Coca Cola and PepsiCo, Inc., still have numerous opportunities for international expansion. Explain briefly
__________ reduce costs and maintain low prices by buying opportunistically from manufacturers with excess inventory, offering limited assortments of household goods and groceries, as well as health...
The tractor is used to lift the 150-kg load B with the 24-mlong rope, boom, and pulley system. If the tractor travels to the right at a constant speed of 4 m/s, determine the tension in the rope when...
Which solutions of the following equations will exhibit convergent behavior? Which are oscillatory? All of the above differential equations have one common factor in their characteristic equations....
The differential equation model for a particular chemical process has been found by testing to be as follows: where ? 1 and ? 2 are constant parameters and u(t) is the input function of time. What...
Find the complete time-domain solutions for the following differential equations using Laplace transforms: (d) A process is described by two differential equations If x 1 = e ?t and x 2 = 0, what can...
1. Raman purchases a motor car from Bharathan whose cash price is Rs. 56,000 on 11.93. Rs. 15,000 is paid on signing the contract and the balance is to be paid in three equal annual instalments of...
Write a function that takes in a value x, a value el, and a list and adds as many el's to the end of the list as there are x's in the list. Make sure to modify the original list using list mutation...
Our office building has a total square footage of 120,000 square feet.We have 9 tenants in the building and no vacancies.The total square footage of the tenant spaces is 105,000.A) What is the Load...

The dynamic model for a process is given by where u(t) is the input function and y(0)

Question:

+ 8y = 3u(t) +6 dt? dt

Step by Step Answer:

a Laplace transform on the ODE gives Thus Regardless of the numerical values ...View the full answer

Process Dynamics and Control

Students also viewed these Physics questions