Section 8: Frequency Domain Techniques
Transfer Functions: A Quick Review
_ Consider a transfer function G(s) = KQQi (s + zi )j (s + pj )
_ Zeros: zi ; Poles: pj
_ Note that s + zi = s (zi ),
_ This is the vector from zi to s
_ Magnitude: jG(s)j = jKjQi j
Section 2: System Models
Differential equation models
_ Most of the systems that we will deal with are dynamic
_ Differential equations provide a powerful way to describe dynamic systems
_ Will form the basis of our models
_ We saw differential equations
Introduction to Linear Control Systems
Section 3: Fundamentals of Feedback
Transfer function
_ Y(s) = G(s)U(s)
_ Stability (more details later): the output y(t) is bounded for all bounded inputs u(t) if
and only if the poles of G(s) are in the open left h
Introduction to Linear Control Systems
Section 9: Design of Lead and Lag Compensators using Frequency Domain
Techniques
Frequency domain analysis
_ Analyze closed loop using open loop transfer function L(s) = Gc(s)G(s)H(s).
_ Nyquists stability criterion
Introduction to Linear Control Systems
Section 8: Frequency Domain Techniques
Transfer Functions: A Quick Review
_ Consider a transfer function G(s) = KQQi (s + zi )j (s + pj )
_ Zeros: zi ; Poles: pj
_ Note that s + zi = s (zi ),
_ This is the vector fro
EE 3CL4: Mid-Term Test, 2 March 2011
Dr. Davidson (davidson@mcmaster.ca)
Examination Conditions
This test is conducted under standard examination conditions. In particular:
You are not to communicate in any manner with any other student unless given expl
Section 4: Stability and Routh-Hurwitz Condition
Stability
A systems is said to be stable if all bounded inputs r (t) give rise to bounded outputs y(t)
Counterexamples
_ Albert Collins, Jeff Beck (Yardbirds), Pete Townshend (The Who), Jimi Hendrix, Tom
Mo