Experiment of a noncollocated controller for wave cancellation

Abstract

Wave-absorbing control for vibration suppression of flexible space structures is demonstrated experimentally. The experimental model is a hung flexible beam with a sensor and a noncollocated torque actuator. The wave-absorbing control employs partial differential equations as the mathematical model of structural dynamics, and the controller can be designed without any use of the modal expansion. Thus, the control is free from the crucial truncation effect. The structural vibration is expressed in terms of propagating disturbances in the frequency domain. The control forces are applied to eliminate outgoing waves at the boundaries of the structure. The controller is implemented in the form of a nonrecursive digital filter. Details of the controller implementation are discussed, including the digital filter as a compensator, filter truncation, and the hardware. Experimental results show satisfactory performance of the controller and good agreement with the performance predicted analytically. ARGE space structures (LSS) will be inevitably flexible in their structure, and their structural vibration will be easily excited. Therefore, control techniques of structural vibration are necessary to satisfy performance of LSS. Most of the studies on the control problem of LSS employ the dynamic model with a discretized description for flexible structures that are inherently distributed parameter systems. The discretization is usually employed to adopt the conventional state-space method. Methods free from the discretization are natural and suitable to the control of such distributed parameter systems as the LSS. This paper treats through the experiment the wave-absorbing control for vibration suppression of flexible structures. The wave-absorbing control employs partial differential equations as the mathematical model of structural dynamics to design the controller, and the discretization method is not employed in the analyses. The controller obtained is thus free from the crucial truncation effect. The equations are Laplace transformed with respect to time to describe the structural responses in terms of propagating disturbances in the frequency domain. Boundary conditions of the system are expressed as relations between incoming waves, outgoing waves, and external control forces at the boundaries. External control forces are applied to eliminate outgoing waves at the boundaries. Resulting closed-loop behavior of the system shows drastic improvement for disturbance attenuation in comparison with open-loop behavior. The concept of the traveling wave approach is applied to the control problem of LSS by von Flotow.13 He introduces the viewpoint that the elastic response of LSS may be aptly viewed in terms of the disturbance propagation characteristics of the structure. Active vibration isolation by cancelling traveling waves based on the same concept is studied in Refs. 4-8. The technique aims to isolate one part of a structure from disturbances excited elsewhere in the structure. Actuators are located at midpoints of structural members and cancel passing disturbances so that the disturbances do not disturb downstream portions. A generic description of the traveling wave control for structural networks is given in Ref. 9. Miller et al.