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ps1a - University of Maryland at College Park Dept of...

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University of Maryland at College Park Dept. of Aerospace Engineering ENAE 432: Aerospace Control Systems Problem Set #1 Issued: 28 Jan. 2011 Due By: 4 Feb. 2011 Suggested Reading: Review Math 140-246 (as needed); Nise, Chapter 1, Section 2.2. Notes: These questions cover some of the prerequisite math skills you will need to succeed in this course. Review as necessary. Show all work in your solutions. Matlab may not be used for any of these problems. Question 1: The differential equations modeling the simple hovercraft example from class are ˙ y ( t ) = v ( t ) ˙ v ( t ) = Ku ( t ) Assume y (0) = y 0 = 0, v (0) = v 0 = 0, and that we desire y ( t ) = 10, v ( t ) = 0 for all t t f . There are many u ( t ) which will solve this problem. Suppose we limit the class of u ( t ) as follows: first, we will use only a single nonzero value for u ( t ), call it U 0 , but with either sign ( U 0 itself is assumed to be positive). Thus u = 0 or u = ± U 0 are the only allowable values for u ( t ). Second, we allow only three total switchings of u ( t ) between these values in the interval [0 , t f ]: one at the beginning (at t
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