Assignment 1-Questions

# Assignment 1-Questions - liquid , the height of the liquid...

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ECE3085 - Homework #1 Due: Jan. 21, 2009 Problem 1. (5 pts) What is the inverse Laplace transform of F ( s ) = 3 s 2 + 2 s - 3 Problem 2. (5 pts) What is the inverse Laplace transform of F ( s ) = 10 s ( s + 1)( s + 10) Problem 3. (5 pts) What is the inverse Laplace transform of F ( s ) = 3 s + 2 s 2 + 4 s + 20 Problem 4. (5 pts) What is the inverse Laplace transform of F ( s ) = 2 s 3 + 6 s 2 + 11 s + 6 Problem 5. (10 pts) Consider the tank system of Figure 1. In what follows, you are asked to perform a procedure that will be quite frequent for you in this controls class. In particular, the end result will be to derive the transfer function associated to the tank system. Figure 1 also desribes the mathematics of the tank system. The mass flux of the tank, ˙ m , is the difference between the flow in, q in , and the flow out q out (all have units of mass per time). The tank itself has a small valve that resists the flow out based on the current tank height. The total mass of water in the tank is related to the mass density of the
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Unformatted text preview: liquid , the height of the liquid in the tank h , and surface area of the tank A by (4). For simplicity, you may want to define the constant C A . (a) Use equations (2)-(4) together with the mass rate equation (1) to determine a differential equation for h in terms of h and u . (b) Given that ( h,H ) and ( u,U ) are Laplace transform pairs, what is the Laplace transform of the differential equation. This should give you an equation in the Laplace domain (ignore any evaluations of the initial time if you have any). (c) Using the Laplace domain equation, solve for H as a function of s and U . q out q in h (a) Depiction of tank system. m = q in-q out (1) q in = u ( t ) (2) q out = 1 R h (3) m = Ah (4) (b) Equations associated to tank system. Figure 1: Tank system description....
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## This note was uploaded on 05/26/2010 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.

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