Kai Yew Lum

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.

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.

Generalized Serret-Andoyer transformation and applications for the controlled rigid body

AbstractThe Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2-dimensional Hamiltonian flow. First, we show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction associated with the lifted left-action of SO(3) on T*SO(3)—a generalization and extension of Noethers theorem for Hamiltonian systems with symmetry. In fact, we go on to generalize the Serret-Andoyer transformation to the case of Hamiltonian systems on T*SO(3) with left-invariant, hyperregular Hamiltonian functions. Interpretations of the Serret-Andoyer variables, both as Eulerian coordinates and as canonical coordinates of the co-adjoint orbit, are given. Next, we apply the result obtained to thencontrolled rigid body with momentum wheels. For the class of Hamiltonian controls that preserve the symmetry on T*SO(3), the closed-loop motion of the main body can again be reduced to canonical form. This simplifies the stability proof for relative equilibria , which then amounts to verifying the classical Lagrange-Dirichlet criterion. Additionally, issues regarding numerical integration of closed-loop dynamics are also discussed. Part of this work has been presented in LumBloch:97a.

Global stabilization of the spinning top with mass imbalance

We define the sleeping motion and show that it is a solution of the equations of motion of a balanced top. In the general case of a top with known mass imbalance, we derive two families of globally asymptotically stabilizing control laws for the sleeping motion based on Hamilton-Jacobi-Bellman theory with zero dynamics. Two actuation schemes using torque actuators are considered.

Adaptive virtual autobalancing for a magnetic rotor with unknown dynamic imbalance

This paper presents an extension of the adaptive virtual autobalancing controller for a rigid, statically unbalanced rotor, previously proposed by the authors (1995), to the case of a rigid, dynamically unbalanced rotor. The state equations of the controller are based on the equations of motion of a multiple-plane autobalancer, and the interaction between rotor and autobalancer is emulated using a pair of magnetic actuators. It is shown in simulation that the adaptive virtual autobalancing controller can achieve stabilization of rotor motion as well as adaptation to changes in imbalance.

Adaptive Autocentering Control for an Active Magnetic Bearing Supporting a Rotor with Unknown Mass Imbalance

Abstract This paper presents a new approach, called adaptive autocentering, that attenuates synchronous transmitted force due to imbalance in an active magnetic bearing system. The basic principle is to perform on-line identification of rotor imbalance and adaptively tune a controller that stabilizes the motion of the rotors mass center and principal axis of inertia. Unlike the usual strategy of adaptive feedforward compensation, which adaptively cancels the effects of rotor imbalance modeled as synchronous disturbance or measurement noise, adaptive autocentering control is frequency independent and can achieve the control objective under varying rotor speed.

Adaptive virtual autobalancing for a magnetic rotor with unknown mass imbalance

An adaptive control scheme is proposed for stabilizing a planar statically unbalanced rotor mounted on a magnetic bearing. The control strategy involves the concept of virtual autobalancing, where the control algorithm emulates the dynamics of a mechanical autobalancer by applying forces that are equivalent to the action of the autobalancer on the rotor. Equations of motion for a planar, torque-free, elastically suspended rotor equipped with an autobalancer are derived. Based on these equations, an adaptive controller for the magnetic rotor is formulated. The results are demonstrated in simulation.

A Serret-Andoyer transformation analysis for the controlled rigid body

The Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2D Hamiltonian flow. First, we generalize the Serret-Andoyer transformation to the case of Hamiltonian systems on T*SO(3) with left-invariant, hyperregular Hamiltonian functions, and show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction. Interpretations of the Serret-Andoyer variables, both as Eulerian coordinates and as canonical coordinates of the co-adjoint orbit, are given. Next, we apply the result obtained to the controlled rigid body with momentum wheels. For the class of Hamiltonian controls that preserve the symmetry on T*SO(3), the closed-loop motion of the main body can again be reduced to canonical form. This allows a simple stability proof for relative equilibria by verifying the classical Lagrange-Dirichlet criterion.