This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: University of Maryland at College Park Dept. of Aerospace Engineering ENAE 432: Aerospace Control Systems Problem Set #9 Issued: 23 Apr 2011 Due By: 29 Apr 2011 Question 1: Prove that:  S ( j )  = 1 2sin( / 2) Question 2: Prove that if the peak of the sensitivity diagram satisfies max  S ( j  6 dB then the feedback system is guaranteed to have gain margin in the range 0 . 5 a 1 . 5 and the phase margin is guaranteed to satisfy   > 29 . Hint: this is not so easy as applying the result in Question #1, since  S ( j )  is not generally the peak of the sensitivity diagram. We will show in class that  1 + L ( j )  is the distance from the 1 point to the polar plot of L at each frequency . The statement above is equivalent to a minimum guaranteed value of this distance. Use this fact, and the definition of phase and gain margin, to establish the claimed properties. Question 3: A tracking antenna has azimuthal pointing dynamics given by ( t ) + 2 ( t ) = 5 u ( t ) where ( t ) is the azimuth angle, and u ( t ) is the current commanded to the driving servo motor by the tracking computer. The quantity 5 u ( t ) is the actual torque developed by the servomotor in response to these commands. The system is required to perfectly track targets moving so that d ( t ) = A + A 1 t where A and A 1 can be of arbitrary sign and magnitude. The tracking bandwidth of the system should also be at least 2 rad/sec. The goal of this problem is to design a feedbacksystem should also be at least 2 rad/sec....
View
Full
Document
This note was uploaded on 04/07/2012 for the course ENAE 432 taught by Professor Dr.sanner during the Spring '09 term at Maryland.
 Spring '09
 DR.SANNER

Click to edit the document details