A benchmark problem for nonlinear control design: problem statement, experimental testbed, and passive nonlinear compensation

Abstract

This paper serves three distinct purposes. First, it provides the problem statement for the benchmark problem for nonlinear control design, an invited session which is the basis for six related papers at the conference. The problem considers a translational oscillator with an attached eccentric rotational proof mass actuator, where the nonlinear coupling between the rotational motion of the actuator and the translational motion of the oscillator provides the mechanism for control. Secondly, the paper describes an experimental testbed that has been constructed by the authors to experimentally investigate this problem. Finally, the paper presents the authors' approach to the benchmark problem, which is based on emulation of passive nonlinear mechanical absorbers with single and multiple modes. These controllers are shown to provide asymptotic stability and disturbance rejection with a bounded input signal. Both numerical and experimental results are presented.