MECH 466 - Lecture5-DCMotors-2009W

# 4 5 2 sec4 negative feedback system negative ea

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Unformatted text preview: stem Negative Ea Encoder (Sec.4-5-3) (Sec.4- Fact: Ki=Kb. 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). R(s) 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&lt;&lt;Ra. Then, an approximated TF is obtained by setting La=0. Analysis Laplace transform Transfer function Models for systems • electrical • mechanical • electromechanical 2nd order system 1st order system Linearization Time response • Transient • Steady state Frequency response • Bode plot Stability • Routh-Hurwitz Routh• Nyquist Design Design specs Root locus Frequency domain PID &amp; Lead-lag LeadDesign examples Matlab simulations &amp; laboratories 2008/09 MECH466 : Automatic Control 13 2008/09 What is a linear system? Real systems are inherently nonlinear. (Linear Real 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, TF timesee next slide) systems. Many control analysis/design techniques are Many available for linear systems. Nonlinear systems are difficult to deal with Nonlinear mathematically. Often we linearize nonlinear systems before Often 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 system Principle 2008/09 MECH466 : Automatic Control 15 2008/09 MECH466 : Automatic Control 16 4 Time-invariant &amp; time-varying A system is called time-invariant (time-varying) system time(timeif system parameters do not (do) change in time. if Example: Mx’’(t)=f(t) &amp; M(t)...
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