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Unformatted text preview: EE 428 PROBLEM SET 7 DUE: 12 NOV 2007 Reading assignment: Reading assignment: Ch 5, sections 5.1 through 5.5 Problem 29: (20 points) A control engineer is designing an attitude control system for a rocket. Figure 1 shows a block diagram of the attitude control system. The engineer finds that the inputoutput transfer function G p ( s ) of the dynamics of the rocket, from the input thrust U ( s ) to the output attitude ( s ), is G p ( s ) = ( s ) U ( s ) = K Js 2 where K [meters] is the aerodynamic gain of the rocket and J [kilogrammeter 2 ] is the moment of inertia of the rocket about its center of gravity. The control engineer specifies the use of a proportionalplusderivative (PD) controller G c ( s ) = U ( s ) E ( s ) = K o + K d s, where the closedloop error signal E ( s ) = R ( s ) ( s ) is the difference between the desired attitude R ( s ) and the actual attitude ( s ). Figure 1: Rocket attitude control system. The control engineer subcontracts the following tasks to you: 1. (3 points) Assume K d is fixed and sketch the root locus of the closedloop attitude control system as the proportional gain K o is increased from zero to infinity. 2. (3 points) Assume K o is fixed and sketch the root locus of the closedloop attitude control system as the derivative gain K d is increased from zero to infinity. Construct the PD controller gain plane of K o versus K d (with K p on the ordinate and K d on the abscissa) and show the following regions in the plane: 3. (2 points) Stable region. 4. (2 points) Unstable region. 5. (2 points) Trajectory on which the closedloop attitude control system is critically damped (that is, the trajec tory on which the dimensionless damping ratio of the closedloop attitude control system is unity). 6. (2 points) Region in which the closedloop attitude control system is overdamped (that is, the region in which > 1). 7. (2 points) Region in which the closedloop attitude control system is underdamped (that is, the region in which < < 1)....
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This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Pennsylvania State University, University Park.
 Fall '07
 SCHIANO

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