An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

A multiple error LMS algorithm and its application to the active control of sound and vibration

Unbalance of magnetically levitated rotors causes undesirable synchronous vibrations which may lead to saturation of the magnetic actuator. To avoid this problem we propose a generalized narrow-band notch filter which is inserted into the multivariable feedback without destabilizing the closed loop. The parameters of the generalized notch filter strongly depend on the inverse sensitivity matrix evaluated at rotational speed. This matrix is easily measured a priori and stored in a look-up table. It is shown that a decentralized notch is feasible for weakly gyroscopic rotors. The proposed notch filter approach has advantages in terms of run-time complexity and analytical verification of closed-loop stability. Results from the implementation of the proposed unbalance compensation in industrial magnetic bearing systems are included.

Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings

The active minimization of harmonic enclosed sound fields, part I: Theory

A consistent framework is presented for the calculation of the optimal performance of feedforward and feedback control systems in attenuating random disturbances. In both cases, the optimization problem is transformed into a quadratic form using an internal model of one part of the physical system under control. The resulting architecture for the feedback controller is known as internal model control (IMC) and is widely used in the H/sub /spl infin// control literature. With this controller architecture, the optimum performance of a multichannel feedback system can be readily calculated using the quadratic optimization techniques already developed in the sampled time domain for multichannel feedforward control. The robustness of the stability of such a feedback controller to changes in the plant response can be separately assessed using a generalization of the complementary sensitivity function, which has a particularly simple form when IMC is used. The stability robustness can be improved by incorporating various forms of effort weighting into the cost function being minimized, some of which are already used for adaptive feedforward controllers. By way of example, the performance is calculated of both feedforward and feedback controllers for the active attenuation of road noise in cars. The variation of performance with loop delay is calculated for both types of control, and it is found that in this example, the potential attenuation is greatest using feedback control but only if the loop delay is less than 1.5 ms.

Performance of feedforward and feedback systems for active control

In this paper, we present a review of the experimental identification of dynamic parameters of bearings in a rotating machine. Major emphasis is given to vibration-based identification methods and the review encompasses descriptions of experimental measurement techniques, mathematical modeling, parameter extraction algorithms and uncertainty in the estimates applied to a variety of bearings. The parameter extraction algorithms include the descriptions of governing equations of the rotor-bearing system and identification methods in both time and frequency domains. The identification techniques have been classified based on methods used to excite the system. The review includes a variety of bearings and similar components, which play an active link between the rotating and stationary parts of a machine. Based on the state of the art in bearing identification, conclusions are made and future directions are suggested.

Identification of Dynamic Bearing Parameters: A Review

This paper presents a computationally fast and efficient least-squares method to minimize the vibration of any general rotor-bearing system by the application of external control forces. The D-optimality concept is used to optimize the force locations. The proposed method provides a wide range of statistical information, and the sensitivity of the optimum response to changes in the control forces. Magnetic bearings can be applied to implement the open-loop adaptive vibration control strategies outlined in the paper. These components can also be used to inject a multi-frequency test signal as required for identi­fication studies.

Vibration control of multi-mode rotor-bearing systems

Frequency-Domain Estimation of Linearized Oil-Film Coefficients

A comparison of multifrequency techniques for measuring the dynamics of squeeze-film bearings

A Comparison of Multifrequency Techniques for Measuring the Dynamics of Squeeze-Film Bearings

This paper presents an analytical investigation of the problem of estimating the linearized inertia, damping and stiffness coefficients of a bearing oil film. The principle of structural identifiability has been used to define and compare the conditions to be fulfilled in order to estimate the coefficients when using various types of test signal. The analysis demonstrates the limitations of many standard methods for determining the coefficients and shows how these restrictions can be overcome by using pseudo-random binary sequence forcing. The necessity is stressed for parameter estimation to be performed without any prejudgement of the significance of particular coefficients. It is shown that this basic requirement can be satisfied by using modern parameter estimation techniques.

C. R. Burrows

Papers

Vibration control of multi-mode rotor-bearing systems

Frequency-Domain Estimation of Linearized Oil-Film Coefficients

A comparison of multifrequency techniques for measuring the dynamics of squeeze-film bearings

A Comparison of Multifrequency Techniques for Measuring the Dynamics of Squeeze-Film Bearings

A coherent strategy for estimating linearized oil-film coefficients