quiz2_practice

quiz2_practice - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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± ² ± ² ± ² MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 Quiz 2 Practice Problems State-Space 1. For the state model: 0 1 0 1 0 x ˙ = 2 3 x + 1 u ; y = 0 1 x (a) What are the poles of the system? Is the system stable? (b) Calculate the transfer function G ( s ) (c) Calculate the state transition matrix Φ( t ) (d) Use the convolution integral to find the output response of the system to a unit step input and the initial conditions x o =[11 ] . 2. Check the controllability of the following system: ⎡ ⎤ 010 0 x ˙= 001 ± ± x + 0 u abc 1 Does the answer depend on the values of a , b ,and c ? 3. Full state feedback controller design: Problem 12.9 in Van de Vegte. 1
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Root Locus 1. Sketch root locus patterns for the following, for positive and negative gain: (1) (2) (3) (4) 2. Sketch by hand the loci of the closed loop system poles for varying K> 0 for systems with the following open loop transfer
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quiz2_practice - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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