MIT 2 004 - Modeling the System (10 pages)

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Modeling the System



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Modeling the System

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Pages:
10
School:
Massachusetts Institute of Technology
Course:
2 004 - Dynamics and Control II
Dynamics and Control II Documents

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MIT OpenCourseWare http ocw mit edu 2 004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use visit http ocw mit edu terms Massachusetts Institute of Technology Department of Mechanical Engineering 2 004 Dynamics and Control II Spring 2008 Laboratory Project Active Damping of Tall Building Vibrations1 Week 1 Modeling the System Overview The high rise building is a modern miracle miles of steel beams and welds thousands of fasteners allowing graceful structures of one hundred or more stories in height Like any highaspect ratio structure the skyscraper is exible You might not notice this until a strong wind storm sets up large scale vibrations in the rst bending mode Then the motions will make you ill or at a minimum cause fatigue The motions certainly cause damage to the building notably in the loss of windows which can crack or fall and in long term fatigue life reduction Among potential remedies for building sway the most common today is the passive or active mass concept In fact our own Hancock Tower in Boston has two 300 ton masses near the top oor that damp out vibrations caused by wind In these nal three lab sessions you will study in detail a physical structure with a similar dynamic response creating a linear model from rst principles and using Simulink to characterize it synthesizing an active control system design based on the model and testing your controller on the actual device The teaching sta will act as consultants The Experimental Plant Figure 1 shows the experimental system that you will work with The building consists of a block of metal atop a pair of steel side plates with low lateral sti nes so that the mass can sway from side to side The passive damping elements along with the actuator and motion sensors are mounted on the steel plate The moving mass is a steel shaft mounted in frictionless air bearings A wire spring couples the moving mass to the building At each end of the sliding shaft is a



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