lecture24 - Today's goals So far Feedback as a means for...

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Lecture 24 – Friday, Nov. 2 2.004 Fall ’07 Today’s goals So far – Feedback as a means for specifying the dynamic response of a system – Root Locus: from the open-loop poles/zeros to the closed-loop poles – “Moving the closed-loop poles around” • Proportional control: moving on the original Root Locus • Proportional-Derivative control: adding a zero/ speeding up the response/ maintaining constant overshoot • Proportional-Integral control: adding a free integrator ([email protected]) and a zero/ fixing steady-state error/ maintaining the speed and overshoot Today – The 2.004 Lab Tower plant – Impulse response and how it relates to the step response and the transfer function – State space: monitoring more than one dynamical variables at the same time
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Lecture 24 – Friday, Nov. 2 2.004 Fall ’07 The need for sway compensation in buildings Taipei 101; 101 floors; 448m tall (roof); 508m (spire) Distributed active compensation system www.atcouncil.org WIND SWAY Image from Wikimedia Commons, http://commons.wikimedia.org
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Lecture 24 – Friday, Nov. 2 2.004 Fall ’07 The 2.004 Tower Actuator: Voice Coil Air Bearings Spring MEMS Accelerometer Relative Velocity Velocity Sensor: Voice Coil Wind Force: impulse Goals: • Model • Control •Des ign • Implement •Test
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Lecture 24 – Friday, Nov. 2 2.004 Fall ’07 Modeling the 2.004 Tower slider mass spring, damper wind force actuator sensors controller actuator force w a k 1 b 1 b 2 k 2 m 2 m 1 x 1 w ( t ) a ( t ) x 2 m 1 tower mass, k 1 tower compliance, b 1 tower damping (viscous), m 2 slider mass, k 2 spring on slider, b 2 (viscous) damping on slider; w ( t ) wind force (impulse) on tower, a ( t ) actuator force on slider. sliding direction tower slider displacement building sway
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2.004 Fall ’07 Lecture 24 – Friday, Nov. 2 Reminder from Lecture 3: the delta (impulse) function Impulse function ( aka Dirac function) t δ ( t ) t =0 It represents a pulse of in nitessimally small duration; and nite energy. athematically, it is de ned by the properties Z + δ ( t )=1; (unitenergy)and −∞ Z + δ ( t ) f ( t )= f (0) (sifting.) −∞ M f(t) F(s) δ (t) u(t) tu(t) t n u(t) e -at u(t) sin ω tu(t) s cos ω tu(t) s 2 + ω 2 ω s 2 + ω 2 1 s + a n !
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.004 taught by Professor Derekrowell during the Fall '08 term at MIT.

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lecture24 - Today's goals So far Feedback as a means for...

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