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
which materials can l use if l want to use length wave 680 to 900 in hplc
Name some common problems associated with dilute phase pneumatic conveying?
Corenuts technology interview questions
What particle sizes are electrostatic precipitators used to remove?
Please colleagues I need to choice a proper hopper shape for a Fertilizer bulk blender flowing throut a high humidity raw material like zeolite, so we are in doubt whether use squard or rectangular hopper shape to avoid the so call voul effect that can create obstruction
How does hollow shaft impeller works? Does it based on principle of pitot tube?
Explain what are the affinity laws associated with dynamics pumps?
What is the best way to control an oversized, horizontally oriented shell and tube steam heater?
Explain global warming from a common man's and an engineer's perspective?
What are some common causes of gas pipeline vibration 20 carbon steel line?
Are some heat transfer services more prone to tube vibration that others for a shell and tube exchanger?
Is there a quick rule-of-thumb to estimate a gas side heat-transfer rate inside the tubes of a shell and tube heat exchanger?
What is minimum flow required of NG having BTU value of 920 btu/scf for flame stability of LBTU gas of BTU value 220 BTU/SCF against the flow 80KPPH.
What is a good way to get started in doing a plant-wide steam consumption analysis?
What is the wet bulb globe temperature (wbgt)?