MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
2.151 Advanced System Dynamics and Control
Linear Graph Modeling: Two-Port Energy Transducing Elements1
1
Introduction
One-port model elements are used to represent energy storage,

Observability and the Separation Principle
Observability: Definition, tests, canonical/normal forms
Duality
Observer design and detectability
Separation principle
Design of stabilizing output-feedback controllers
Related Reading
[KK] 4.1-4.4 [AM]: 7.

Proceedings of the World Congress on Engineering and Computer Science 2013 Vol II
WCECS 2013, 23-25 October, 2013, San Francisco, USA
Simulation of Electrochemical Shaping of Airfoils
Using Continuous and Pulse Current
J. Kozak Member, IAENG
AbstractElect

EEME E6601
Prof. Longman
Homework 4
Problem 1
Consider a system governed by the following differential equation
d 2 y(t)
dy(t)
+2
+ 2y(t) = 1.9yD (t)
2
dt
dt
where yD (t) is the command input.
(a) Find the undamped natural frequency n

Richard Longman
Problem 2
EEME E6601
Prof. Longman
Homework 4
G1(s)=K/s, H(s)=1, G2(s)=1/[(s+3)(s+4)]
(A) Find the range of gains K that correspond to asymptotic stability of this feedback
control system. When K reaches the upper limit, what

ME E4610 Advanced Manufacturing Processes, Fall 2016
HOMEWORK #2
DUE October 5
1. a. Consider the energy levels E1 and E2 of a two-level system. Determine the population ratio
of the two levels if they are in thermal equilibrium at room temperature, 27C,

ME E4610 Advanced Manufacturing Processes, Fall 2016
HOMEWORK #4
DUE November 30
1. For vaporization cutting of stainless steel 304 with absorbed laser intensity of 6.3x1010 W/m2,
verify the penetration velocity V is about 0.946 m/s (assuming heat conduct

EEME E6601
Prof. Longman
Homework 3
Problem 1
(A) Consider the following differential equation
d2y
dy
+ 3 + 2y = u
2
dt
dt
What is the characteristic equation? What is the general solution of the
homogeneous equation? Find the transfer

Professor Longman
EEME E6601
Homework 6
Problem 1
Problem 2
Design the steady state Kalman filter for the following system
x! = Ax + Bu + w
y = Cx + v
E[w(t)] = 0
E[v(t)] = 0
E[w(t)wT ( )] = Q (t )
E[v(t)vT ( )] =

ME E4610 Advanced Manufacturing Processes, Fall 2016
HW3 (due October 26)
1. To determine the material constants A, B, and C in the Cauchys equation (Eq. 7) for
crystal quartz (Fig. 3.26) and explain why index of refraction increases with reduced
waveleng