Professor Longman
EEME E6601
Homework 3
(A) By manipulating these equations in the time domain (applying appropriate set of
derivatives to these equations), find a differential equation relating the input e(t) to the
output y(t) without including the inte
EEME E6601
Homework 1
Prof. Longman
Problem 1
For each of the following 9 equations:
(a) Say if the corresponding control system is asymptotically stable, unstable, or
marginally stable.
(b
Longman
Homework 5
EEME E6601
Problem 1
Given a differential equation
d n y(t)
d n 1 y ( t )
+ an 1
+ + a0 y ( t ) = f ( t )
dt n
dt n 1
Suppose you have two particular solutions, y p1 ( t) and y p 2 ( t) , so that
d n y p1 ( t )
d n 1 y p1 ( t )
+ an 1
+
Professor Longman
EEME E6601
Homework 4
Problem 1
3 1
(A) Given the matrix A =
, find the eigenvalues and eigenvectors.
2 0
(B) Find a matrix N such that N 1 AN = where is a diagonal matrix.
(C) Given a differential equation x = Ax , make a change o
Prof. Longman
EEME E6601
Homework 2
Problem 1 (Complete the Table of Particular Solutions)
The handout 6601SolveFor ParticularSol.pdf has a table of Guesses to use to find
particular solutions for various forcing functions. In class we showed how to deriv
EEME E6601
How to Find the General Solution of a Homogeneous Differential Equation
with Constant Coefficients in Terms of R eal Valued F unctions
Given an nth order homogeneous linear differential equation with constant coefficients
dny
d n 1y
d2y
dy
+ a
EEME E6601
One Method to Find a Particular Solution of a NonHomogeneous Linear
Differential Equation with Constant Coefficients
Given an nth order nonhomogeneous linear differential equation with constant coefficients
dny
d n 1y
d2y
dy
+ an 1 n 1 + L +
EEME E6601
Prof. Longman
Handout #3
Routine Control Laws
(C) The Proportional Plus Integral Controller (PI)
t
K
m(t ) = K P e(t ) + K I e( )d
M (s) = ( K P + I ) E (s)
0
s
E (s)
KI
s
KP +
M (s )
Properties:
(1) Has two control gains Kp and KI to adjust. M
Longman 9/14/05
EEME E6601
Handout Number 2
Control System Design and Differential Equations
(A) The first step in design is to characterize your physical objectives.
v (t)
y c(t)
e (t)
+

C o n tr o lle r
m (t) + +
u (t)
P la n t
y (t)
(1) Get the ordin
EEME E6601
Professor Richard Longman
Handout #1
 Laws of heat transfer govern the relationship between the heat supplied to a room per
unit time and the temperature of the room
 Newtons laws for translational motion determine how a car responds when a f
General Information
EEME E6601
Fall 2013
Professor Richard Longman
Office hours: 4:10 to 5:00PM Monday and Wednesday
Office: 232 Mudd
Phone: (212)8542959
EMail: RWL4@columbia.edu
You can try to ask me questions outside my office hours. Be sure to make i