### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 2pSA2. Active structural vibration control via sliding modes: Links to
Lyapunov design.

**Shawn E. Burke
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*The Charles Stark Draper Lab., 555 Technology Square, Mail Stop 53,
Cambridge, MA 02139
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**John E. Meyer
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*Failure Analysis Associates, Menlo Park, CA 94025
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A nonlinear active vibration control design method is developed based upon
an extension of variable structure control (VSC) techniques, in particular
sliding mode control, to distributed parameter systems. The temporal
compensator design utilizes a generalized wave equation representation of the
plant. The control is implemented via a series of decentralized
single-input/single-output (SISO) local loops around collocated transducers. No
a priori knowledge of the temporal plant model is assumed, hence the resulting
designs are insensitive to variations in the plant modal frequencies. The
equivalent control reduces to output velocity feedback, a known stabilizing
control. Active damping performance is enhanced through the introduction of an
additive nonlinear term which selectively increases the velocity feedback
control with a constrained nonlinear gain profile away from the zero-velocity
phase plane origin. Stability constraints are discussed. For simple structural
components such as beams and plates, the design method yields controllers
identical to those derived using Lyapunov's direct method, which extremize
total system energy. Example controllers for beams and plates are presented. In
order to demonstrate the application of the nonlinear control, closed-loop
vibration control experiments on a 56- x59-in. nine-bay aluminum grillage are
summarized.