Modal control based on direct modal parameters estimation

Modal active control is based on a state model that requires the identification of modal parameters. This identification can typically be done through a rational fraction polynomial algorithm applied in the frequency domain. This method generates numerical problems when estimating high-order models, particularly when moving from the basis of orthogonal polynomials for the modal basis. This algorithm must therefore be applied independently on multiple frequency ranges with a low order for each range. In this case, the controller design cannot be automated and requires a lot of human intervention, especially to build the state space model. To address this issue, this paper presents the application of the direct modal parameters estimation (DMPE) algorithm for active modal control design. The identification algorithm is presented in a simplified version with only positive frequencies. Unlike other classical identification methods in the frequency domain, the DMPE algorithm provides a solution with a great numerical stability and allows estimating models with a higher order. Using this method, the design of the controller can be largely automated and requires a minimum of human intervention. After a theoretical presentation, the proposed method is experimentally validated by controlling the vibration modes of a suspended plate.

Comparison of Different Estimation Algorithms Used in the Experimental Determination of Modal Parameters

The paper deals with the estimation of modal parameters and its main purpose is to compare differences in the values of natural frequencies and damping ratios, which were estimated using three different extraction methods: Rational Fraction Polynomial method, Complex Mode Indicator Function and Polyreference Time Domain Technique. These methods are well suited to the more general application to multi-FRF data, both of the SIMO and the MIMO types. The object of measurement was a freely suspended steel rod of circular cross section. The responses of the analyzed structure were measured by accelerometer and laser vibrometer. The results of these measurements are also discussed in the paper.

Study on Global-Piecewise Fitting for Modal Parameter Identification

Based on the global orthogonal polynomial algorithm, a global-piecewise fitting method for eliminating affections of modes outside of fitting bands is proposed. Both lower and higher modes outside of the fitting band are analyzed and processed. The frequency response data are revised by means of modes in two frequency bands close to the fitting band, and a curve fitting model is derived. Simulation results indicate that the proposed method possesses higher precision than the general rational fraction polynomial algorithm.

Cracks Detection Using Active Modal Damping and Piezoelectric Components

The dynamics of a system and its safety can be considerably affected by the presence of cracks. Health monitoring strategies attract so a great deal of interest from industry. Cracks detection methods based on modal parameters variation are particularly efficient in the case of large cracks but are difficult to implement in the case of small cracks due to measurement difficulties in the case of small parameters variation. Therefore the present study proposes a new method to detect small cracks based on active modal damping and piezoelectric components. This method uses the active damping variation identificated with the Rational Fraction Polynomial algorithm as an indicator of cracks detection. The efficiency of the proposed method is demonstrated through numerical simulations corresponding to different crack depth and locations in the case of a finite element model of a clamped-clamped beam including four piezoelectric transducers.

Crack detection based on optimal control

Techniques for optimal control to increase system security attract a great deal of interest from industry. The presence of transversal cracks can considerably modify the dynamics of a system. In the case of closed-loop systems, i.e. controlled systems, these faults can cause the destabilization and variation of control performance. Consequently, such variations can be used to detect transversal cracks. Therefore, the present study proposes an investigation into the possibility of detecting structure modification based on estimated control performance by using the Rational Fraction Polynomial algorithm. This method is applied numerically to a multi-cracked controlled truss. Both the optimal control of the cracked structure and the possibility of detecting the presence of cracks by monitoring the evolution of control performance are studied. The efficiency of the proposed method is demonstrated through numerical simulations corresponding to different crack orientations and locations.