Vincent T. Coppola

Adaptive autocentering control for an active magnetic bearing supporting a rotor with unknown mass imbalance

This paper presents a new approach, called adaptive autocentering, that compensates for transmitted force due to imbalance in an active magnetic bearing system. Under the proposed control law, a rigid rotor achieves rotation about the mass center and principal axis of inertia. The basic principle of this approach is to perform on-line identification of the physical characteristics of rotor imbalance and to use the identification results to tune a stabilizing controller. This approach differs from the usual strategy of adaptive feedforward compensation, which models the effect of imbalance as an external disturbance or measurement noise, and then cancels this effect by generating a synchronous reference signal. Unlike adaptive feedforward compensation, adaptive autocentering control is frequency independent and works under varying rotor speed. Performance of the control algorithm is demonstrated in simulation examples for the case of rigid rotors with static or dynamic imbalance.

Global stabilization of the oscillating eccentric rotor

The oscillating eccentric rotor has been widely studied to model resonance capture phenomena occurring in dual-spin spacecraft and rotating machinery. This phenomenon arises during spin-up as a resonance condition is encountered. We consider the related problem of rotor despin. Specifically, we determine nonlinear feedback control laws that not only despin the rotor but also bring its translational motion to rest. These globally asymptotically stabilizing control laws are derived using partial feedback linearization and integrator backstepping schemes. For the case in which the oscillating eccentric rotor is excited by a translational sinusoidal forcing function, the control law is shown to attenuate the amplitude of the translational oscillation.

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.

Adaptive Virtual Autobalancing for a Rigid Rotor With Unknown Mass Imbalance Supported by Magnetic Bearings

The objective of this paper is to describe an imbalance compensation scheme for a rigid rotor supported by magnetic bearings that performs on-line identification of rotor imbalance and allows imbalance cancellation under varying speed of rotation. The proposed approach supplements existing magnetic bearing controls which are assumed to achieve elastic suspension of the rotor. By adopting a physical model of imbalance and utilizing measurements of the spin rate, the proposed algorithm allows the computation of the necessary corrective forces regardless of variations in the spin rate. Convergence of the algorithm is analyzed for single-plane balancing, and is supported by simulation in single- and two-plane balancing, as well as by experimental results in single-plane implementation.

NEW RESULTS ON CONTROL OF MULTIBODY SYSTEMS WHICH CONSERVE ANGULAR MOMENTUM

A planar system of rigid bodies interconnected by one degree of freedom rotational joints is considered. This multibody system is referred to as a multilink, and the rigid bodies are referred to as links. The angular momentum of the multilink is conserved but is not necessarily zero. We show that if the number of links is at least four, then periodic joint motions can make the absolute orientation of a specified base link track exactly a specified function of time whose time derivative is periodic. This result on the use of periodic joint motions for orientation tracking extends previous work [15], [20], [22] on using periodic joint motions for rest-to-rest reorientation. It has interesting physical consequences. Specifically, in the case of non-zero angular momentum periodic joint motions can maintain the orientation of the base link constant. In the case of zero angular momentum periodic joint motions can change the orientation of the base link at a specified angular rate. We also demonstrate that if the multilink consists of at least three links, then for any value of the angular momentum joint motions can reorient the multilink arbitrarily over anarbitrary time interval. This result extends similar results in [15] for zero angular momentum and in [20] that apply for nonzero angular momentum but not for an arbitrary time interval. In terms of their control-theoretic aspects, the problems treated in the paper can be viewed as controllability problems for a class of nonlinear control system with time-dependent drift.

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>>

Asymptotic tracking of spacecraft attitude motion with inertia matrix identification

The problem of a spacecraft tracking a desired trajectory is defined and addressed using adaptive feedback control. The control law, which has the form of a sixth-order dynamic compensator, does not require knowledge of the inertia of the spacecraft. A Lyapunov argument is used to show that tracking is achieved globally. A simple spin about the intermediate principal axis and a coning motion are commanded to illustrate the control algorithm. Finally, periodic commands are used to identify the inertia matrix of the spacecraft.

Global asymptotic stabilization of a spinning top with torque actuators using stereographic projection

The dynamical equations for a spinning top are derived in which theorientation is specified by a complex variable using stereographic projectionof Poissons equations. Necessary and sufficient conditions for Lyapunovstability of the uncontrolled motion of the spinning top are derived usingthe Energy-Casimir method. Control laws that globally asymptoticallystabilize the spinning top to the sleeping motion using two torque actuatorsare synthesized by employing techniques from the theory of systems in cascadeform and generalized using Hamilton-Jacobi-Bellman theory with zero dynamics.In short, this paper provides a nice example where the interplay betweendynamics and control leads to elegant and powerful results.

An actively controlled control moment gyro/gyropendulum testbed

An experimental testbed for investigating control algorithms for reducing or eliminating the effects of mass imbalance in rotating bodies has been designed and constructed. This control moment gyro/gyropendulum testbed allows researchers to experimentally demonstrate control algorithms for reorientation, stabilization and vibration suppression.

A Lyapunov function for the Energy-Casimir method

Provides a tutorial exposition for the Energy-Casimir method and constructs a Lyapunov function to prove stability for systems having at least two integrals of motion. Stabilization of the intermediate axis rotation of an asymmetric rigid spacecraft by applying input torque along the minor or major axis is reconsidered. For the axially symmetric spacecraft, the authors construct a linear torque applied at the symmetry axis which Lyapunov stabilizes rotation about a transverse principal axis.<<ETX>>