PROCESS CONTROL - EXAMPLE 6.3 : The differential equation is 3 dy / dt + 2y = 1 with y(0) = 1. (a) The Laplace transformation, L for given terms are : L (dy / dt) = sY(s) - y(0), L(y) = Y(s), L(1) = 1 / s. Use such transformation to find Y(s). (b) The initial value theorem states that : When t approaches 0 for a function of y(t), it is equal to a function of sY(s) when s approaches infinity. Use the initial value theorem as a check to the answer found in part (a).
Answer Posted / kangchuentat
PROCESS CONTROL - ANSWER 6.3 : (a) For the equation 3 dy / dt + 2y = 1, its Laplace transformation is 3 [ sY(s) - y(0) ] + 2Y(s) = 1 / s, 3 (sY - 1) + 2Y = 1 / s, 3sY - 3 + 2Y = 1 / s, 3sY + 2Y = 1 / s + 3, Y (3s + 2) = (1 + 3s) / s. Y = Y(s) = (1 + 3s) / [ s (3s + 2) ]. (b) Initial value theorem states that y(0) = sY(infinity), then 1 = s (1 + 3s) / [ s (3s + 2) ] = (1 + 3s) / (3s + 2) approaches 1 when the value of s approaches infinity. The checking is correct. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
Is This Answer Correct ? | 0 Yes | 0 No |
Post New Answer View All Answers
could any one plzz give me the placement tech papers taken by iocl,and bpcl in chemical stream..... my id is.... mishra.gaurang@gmail.com
Are there any alternatives to scraping a shell and tube if a capacity increase will make the pressure drop across the exchanger too large?
Explain what is the best way to configure a bypass line in slurry services?
Are there any methods of preventing cracking of carbon steel welds in refining environments?
Name some common causes of control valve noise?
What are some guidelines for sizing a psv for a fire scenario on a vessel in a refinery service?
sir,please give me some exam paper for referance. Thanks & Regards,
Explain the reasons of removal of particles from effluent gas?
sir i am appearing in railway exam of section engineer and my branch is chemical engineering i want previous question paper of section engineer of chemical branch please tell me as soon as possible my email id is surendrasaroj18@gmail.com THANKYOU
How does a tank-blanketing valve operate?
What are the reasons of removal of particles from effluent gas?
What is the wet bulb globe temperature (wbgt)?
could anyone send me model question papers or outline of graduate trainee(chemical engg) post?
How can one determine if a particular solid can be fluidized as in a fluidized bed?
What are the factors involved in designing kettle type reboiler?