This preview shows pages 1–2. Sign up to view the full content.
MEEN 651
Control System Design
Homework 12: LQR, LQG, and LTR
Assigned:
Tuesday, 18 Nov. 2008
Due:
Tuesday, 25 Nov. 2008, 5:00 pm
Textbook Problems
Do the following problem from “
Feedback Control of Dynamic Systems
” 5
th
ed., Franklin and Powell.
Problem 1)
Problem 7.57
Exam Problems from 2007 (actual and potential exam problems)
Problem 2)
Consider the diagrams provided below, where
G
1
(s)
and
G
2
(s)
are stable, completely
controllable, and completely observable.
For each configuration, determine if the
composite system is always:
a)
Stable
b)
Completely Controllable
c)
Stabilizeable
Please provide a proof or counterexample to justify your answer.
Parallel Connection
Series Connection
Feedback Connection
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentDesign Problems
Problems 3) – 5) are concerned with the linearized and normalized dynamics of the magnetically
suspended ball, described by:
ݔሶ
ଵ
ሺݐሻൌݔ
ଶ
ሺݐሻ
ଶ
ଵ
ሺݐሻ ݑሺݐሻ
Problem 3)
Assume a quadratic performance index of:
ܬൌන
ሾݔ
ଵ
ଶ
2ݔ
ଵ
ݔ
ଶ
ݔ
ଶ
ଶ
ݑ
ଶ
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Staff

Click to edit the document details