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(Sec.4- Fact: Ki=Kb.
2008/09 Feedback system
MECH466 : Automatic Control 9 Ex: Derivation of transfer functions 2008/09 MECH466 : Automatic Control 10 DC motor: Transfer functions (TF) Compute transfer functions from R(s) to Y(s).
Ea Ea 2nd order system
Ea 2008/09 Ea MECH466 : Automatic Control 11 2008/09 MECH466 : Automatic Control 12 3 Course roadmap DC motor: Transfer functions (cont’d)
Modeling Note: In many cases La<<Ra. Then, an
approximated TF is obtained by setting La=0. Analysis Laplace transform
Models for systems
• electromechanical 2nd order system 1st order system Linearization Time response
• Steady state
• Bode plot
Routh• Nyquist Design
PID & Lead-lag
LeadDesign examples Matlab simulations & laboratories
2008/09 MECH466 : Automatic Control 13 2008/09 What is a linear system? Real systems are inherently nonlinear. (Linear
systems do not exist!) Ex. f(t)=Kx(t), v(t)=Ri(t)
Ex. f(t)=Kx(t), v(t)=Ri(t)
TF models are only for linear time-invariant (LTI,
timesee next slide) systems.
Many control analysis/design techniques are
available for linear systems.
Nonlinear systems are difficult to deal with
Often we linearize nonlinear systems before
analysis and design. How? System A nonlinear system does not satisfy
the principle of superposition.
MECH466 : Automatic Control 14 Why linearization? A system having Principle of Superposition
Principle 2008/09 MECH466 : Automatic Control 15 2008/09 MECH466 : Automatic Control 16 4 Time-invariant & time-varying
A system is called time-invariant (time-varying)
time(timeif system parameters do not (do) change in time.
Example: Mx’’(t)=f(t) & M(t)...
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- Winter '09