MIT16_30F10_assn05

# MIT16_30F10_assn05 - 16.30/31 Prof J P How and Prof E...

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: 16.30/31 October 22, 2010 Prof. J. P. How and Prof. E. Frazzoli Due: October 29, 2010 T.A. B. Luders 16.30/31 Homework Assignment #5 Goals: Controllability and observability (part 2), full-state feedback, LQR, system zeros 1. For each state-space model, identify whether the system is observable , controllable , detectable , and/or stabilizable . Conclude whether each model is a minimal realization. (a) A = − 1 3 , B = 1 1 , C = 2 − 1 , D = 1 1 6 ⎡ ⎤ ⎡ ⎤ 1 2 1 (b) A = ⎣ 1 − 3 ⎦ , B = ⎣ 1 ⎦ , C = 1 , D = − 1 − 1 − 3 1 2. Consider the state-space model x ˙ = − 5 1 x + 1 u, 14 1 y = 1 x . Suppose we want to apply full-state feedback to the system, of the form u = − K x . (a) Without computing the transfer function, identify the open-loop system poles and zeros. (b) Select K such that the closed-loop system poles are placed at the roots of s 2 + 2 ζω n s + ω n 2 = 0 ....
View Full Document

## This note was uploaded on 02/03/2012 for the course AERO 16.30 taught by Professor Ericferon during the Fall '04 term at MIT.

### Page1 / 3

MIT16_30F10_assn05 - 16.30/31 Prof J P How and Prof E...

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

View Full Document
Ask a homework question - tutors are online