ps6sol

# ps6sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 6 Solutions Problem 1 1. ⎣ ⎤ ⎦ = B AB = 1 − 1 − 1 1 There are two states, so we need two independent columns to show controllability. But the control- lability matrix has only one independent column, so the system is uncontrollable. 2. 1 1 1 ⎤ ⎦ = B AB A 2 B = 1 ⎡ 1 1 There are three states, so we need to find three independent columns to show controllability. The 1 controllability matrix includes the vectors ⎡ , 1 ⎡ , and ⎡ , which are independent and span the 1 state-space ⇒ 3 , so the system is controllable. Problem 2 1. (a) The characteristic equation of the open-loop system is: det( sI − A ) = s 3 + 9 s 2 + 23 s + 15 = ( s + 5)( s + 3)( s + 1) = So the poles of the open-loop system are at s = − 1, s = − 3, and s = − 5. (b) We are given that the closed-loop poles are at s = − 3 and s = − 4 ± 4 j , so we want the characteristic equation for the closed-loop system to be: ( s + 3)( s 2 + 8 s + 32) = s 3 + 11 s 2 + 56 s + 96 = In terms of the matrices A , B , and K , the characteristic equation is given by det( sI − ( A −...
View Full Document

## This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

### Page1 / 4

ps6sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online