EL6243: System Theory and
Feedback Control
Zhong Ping
ZhongPing Jiang
ECE Dept, NYU Poly, 5MTC, LC214
eeweb.poly.edu/faculty/jiang
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Fall 2012
Z.P. Jiang, NYU POLY
1
Course Goals
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Week IV: Linear Systems
y
Today s
Todays discussion topics:
What is a linear system?
Solutions and stability of linear timeinvariant
( ) y
(LTI) systems
Linearization of nonlinear systems
Connections
Week V: Controllability and State
Feedback
Todays discussion topics:
Controllability: Definition and tests
Implications of controllability in state
feedback design
Application examples
Fall 2011
Z.P.
Feedback Systems: Solutions Manual  v1.3b
207
Exercise 8.8 Using block diagram algebra, show that the transfer functions from d to y and n to y in
Figure 8.7 are given by
P
1
G yd =
G yd =
.
1 + PC
1
294
Feedback Systems: Solutions Manual  v1.3b
Exercise 11.4 Consider the springmass system given by (2.14), which has the transfer function
1
.
+ cs + k
Design a feedforward compensator that gives a
250
Feedback Systems: Solutions Manual  v1.3b
Exercise 10.1 (Ideal PID controllers) Consider the systems represented by the block diagrams in Figure 10.1.
Assume that the process has the transfer fun
Feedback Systems: Solutions Manual  v1.3b
62
Exercise 4.1 (Timeinvariant systems) Show that if we have a solution of the differential equation (4.1) given
by x(t) with initial condition x(t0 ) = x0
Week IX  Frequency Domain
Analysis
Review of Bode plot and Nyquist
diagram
Stability margins
Bodes relation
Fall 2011
Z.P. Jiang, NYU POLY
220
Response to exponential signals
p
p
g
u (t ) e
st
LTI
y
Week X: FrequencyDomain Design
Topics Under Discussion:
What i
Wh t is PID?
Lead and Lag Compensators
Fall 2011
Z.P. Jiang, NYU POLY
283
What is PID?
r
e
C(s)
u
y
P(s)

ki
Frequencydomain: C(s) k p
Week XII: Youla Parameterization
and Robustness Analysis
Todays k
T d key points:
i t
D.C. Youla
Parameterization
Robust Stability
Robust Performance
Fall 2011
Z.P. Jiang, NYU POLY
373
What is Youla P
Week XI:
Sensitivity and Performance
Key points in today s lecture:
todays
Sensitivity and S
S
iti it
d Sensitivity F
iti it Functions
ti
Performance Limitations
Feedforward and Feedback Designs
Fall
Week VIII  Tools for Frequency
Domain Analysis
Transfer function: a frequency domain
frequencydomain
approach for LTI systems
Poles, zeros, polezero cancellations
Bode l t
B d plot
Application exam
Week VI: Observability, Observer
and Output Feedback
Todays di
T d discussion topics:
i t i
Observability: Definition and tests
Implications of observability in observers
and output feedback design
Ap
Week III
Stability and Performance
Today s
Todays discussion topics:
Existence and uniqueness of solutions of
dynamic systems
Stability: Notions and basic properties
y
p p
Tests for stability
Performa
Week II: Modeling
g
Today s
Todays Lecture:
Introduce modeling techniques and the
concepts of state inputs outputs through
state, inputs, outputs,
some examples in engineering and biology.
Overhead C