Robust active vibration suppression control with constraint on the control signal: application to flexible structures

Abstract

SUMMARYA uniÿed mathematical framework, sustained by experimental results, is presented for robust controller design taking into account the constraint on the control signal. The design procedure is exempliÿed for an active vibration suppression control problem with applications to exible structures. The considered experimental set-up is a three-storey exible structure with an active mass driver placed on the last storey. First, the considered exible structure is identiÿed and the model's parametric uncertainties are deduced. Next, control constraints are presented for the robust control design problem, taking into account the restriction imposed on the control signal. Finally, the e ectiveness of the control system is tested through experiments, when the input disturbance is assumed to be a sinusoidal one as well as a historical earthquake record (1940 El Centro record).

Free Vibration Response of a Frame Structural Model Controlled by a Nonlinear Active Mass Driver System

“…Some approaches deal with preventing saturation of the control signal by designing the control system to always operate below its limits in the framework of linear control [3]. Another category of control methods accounts for system limitations directly in the control algorithm.…”

A Review on Adaptive Methods for Structural Control

“…The consequence is the application of an impulsive force that can provoke damage to the control device or to the structure. Even when damage can be prevented by brake systems and buffers that soften the impulse loads, the overall control effectiveness can be impaired or the system can operate in an anomalous way that might produce instability [98].…”

“…A proper way to handle physical limits of active control devices providing acceptable solutions from an economic viewpoint, is including them directly in the control law, allowing the system to reach its limits in a controlled way [98,99], adopting nonlinear control strategies [100]. Nonlinear controllers proposed in the last years for constrained systems can be classified in two main groups.…”

Robust structural control with system constraints

“…Indeed, most of the contributions are limited to the saturation case (e.g. [20][21][22][23][24][25]). Mongkol et al [26], for instance, proposed to handle force saturation in active mass dampers (AMDs) by coupling a 'low-gain' controller with a 'bang-bang' one.…”