Robust multivariable control of a double beam cantilever smart structure

Abstract

The uncertain surrounding environment in which smart structures are employed means that a fixed reference base with which to operate sensing/actuation devices cannot be assumed. The distributed placement of piezoceramic devices has made them the most popular choice for such an application. The limited available output force makes it essential to consider the problems of control signal saturation on the robustness of resulting controllers. Much previous work has considered smart structural control in a single dimension. The current work looks at the vibration control of a two-dimensional smart structure. Actuation is applied by means of two pairs of piezoactuators capable of applying moments with a controllable phase and amplitude difference allowing a controllable ratio of bending and torsion motion. The design process of a multivariable (multi-input multi-output) generalized minimum variance control system is discussed. Application to an experimental double cantilever beam system is shown to result in robust closed-loop control. Comparisons to the benchmark of multi-loop control demonstrate numerous advantages of the multivariable system. Results are further supported with the use of sensitivity functions showing the response of the closed-loop systems to frequencies of interest, particularly the important vibrational modes.

Reduced-order Robust Multivariable Control of a Double-beam Cantilever Structure

“…The chosen order of the polynomials P and Q balances possible controller variation and the number of variables necessary for specification. The method described above requires only three values to be specified to obtain an experimental controller and has been shown experimentally to result in satisfactory control performance (Brown et al, 2002;Scott et al, 2003).…”

“…The matrix commutativity issues are discussed and lead to a pseudo commutativity transform (Wolovich, 1974) version of the control method, a novel application to smart structures. Building on a previous paper by Scott et al (2003) a reduced-order multivariable identification scheme is used, which both reduces the complexity of the resulting controllers and also investigates the robustness to the uncertainty arising from unmodeled dynamics/modes.…”