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

The Charles Stark Draper Lab., 555 Technology Square, Mail Stop 53, Cambridge, MA 02139

John E. Meyer

Failure Analysis Associates, Menlo Park, CA 94025

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.