Robert T. Bupp

A BENCHMARK PROBLEM FOR NONLINEAR CONTROL DESIGN

This paper describes a nonlinear control design problem involving the nonlinear interaction of a translational oscillator and an eccentric rotational proof mass. This problem provides a benchmark for examining nonlinear control design techniques within the framework of a nonlinear fourth-order dynamical system. The problem is posed in the spirit of the linear benchmark problem described in Reference 1. This system was originally studied as a simplified model of a dual-spin spacecraft to investigate the resonance capture phenomenon.2 More recently, it has been studied to investigate the utility of a rotational proof-mass actuator for stabilizing translational motion.3~5 Viewed in this way, the rotational/translational proof-mass actuator (RTAC) has the feature that the nonlinearities associated with the actuator stroke limitation are implicit in the system dynamics. In contrast, the stroke limitation constraint must be considered separately in linear translational proof-mass actuators.6 A similar system has been studied as a rotating unbalanced mass (RUM) actuator in References 7 and 8.

Resetting virtual absorbers for vibration control

A novel class of controllers, called resetting virtual absorbers, is proposed as a means for achieving energy dissipation. A general framework for analyzing resetting virtual absorbers is given, and stability of the closed-loop system is analyzed. Special cases of resetting virtual absorbers, called the virtual trap-door absorber and the virtual one-way absorber, are described, and some illustrative examples are given.

Vibration suppression of multi-modal translational motion using a rotational actuator

In recent the work of Wan et al. it was shown that a rotational torque actuator with attached eccentric mass can be used to globally stabilize a one-mode translational oscillator. A family of globally stabilizing nonlinear feedback control laws was derived by using partial feedback linearization and integrator backstepping. These control laws accounted for the strongly nonlinear coupling between the rotational motion of the eccentric mass and the translational motion of the oscillator. In the present paper, we extend these results to address the problem of stabilizing the translational motion of multi-mode systems with a rotational actuator. The controller synthesis methodology extends the previous work to address a system involving six state variables. Detailed numerical simulation of the closed-loop system illustrates the angular position of the eccentric mass and the harmonic content of its motion in suppressing both modal frequencies.<<ETX>>

Finite settling time control of the double integrator using a virtual trap-door absorber

Finite settling time control of the double integrator is considered. The approach taken is to design a compensator based on a virtual lossless absorber which is tuned so that, at some predetermined time, the virtual subsystem possesses all of the systems energy. At this time the controller is turned off, and the double integrator remains at rest at the origin. This strategy gives the appearance of instantaneously removing all of the systems energy as if a trap door had been sprung. A practically useful feature of the virtual trap-door absorber is that only position measurement is required. Controller parameters for the virtual trap-door absorber controller are chosen, and the resulting controller is compared to the classical minimal-time and minimal-energy controllers, which require measurements of both position and velocity.