MU-SYNTHESIS BASED ACTIVE ROBUST VIBRATION CONTROL OF AN MRI INLET

In this paper, a robust control technique based on μ-synthesis is employed in order to investigate the vibration control of a funnel-shaped structure that is used as the inlet of a magnetic resonance imaging (MRI) device. MRI devices are widely subjected to the vibration of the magnetic gradient coil which then propagates to acoustic noise and leads to a series of clinical and mechanical problems. In order to address this issue and as a part of noise cancellation study in MRI devices, distributed piezo-transducers are bounded on the top surface of the funnel as functional sensor/actuator modules. Then, a reduced order linear time-invariant (LTI) model of the piezolaminated structure in the state-space representation is estimated by means of a predictive error minimization (PEM) algorithm as a subspace identification method based on the trust-region-reflective technique. The reduced order model is expanded by the introduction of appropriate frequency-dependent weighting functions that address the unmodeled dynamics and the augmented multiplicative modeling uncertainties of the system. Then, the standard D-K iteration algorithm as an output-feedback control method is used based on the nominal model with the subordinate uncertainty elements from the previous step. Finally, the proposed control system implemented experimentally on the real structure is to evaluate the robust vibration attenuation performance of the closed-loop system

Modeling, identification and active vibration control of a funnel-shaped structure used in MRI throat

The purpose of this paper is designing an optimal controller for vibration suppression of a funnel-shaped smart structure with distributed piezoelectric actuators and sensors applicable in Magnetic Resonance Imaging (MRI) system. This can help sensitive human beings from vibration and acoustic noise syndrome. Also, the vibration suppression in this structure prevents the test results to be damaged, which is an important issue in medical tests. For this aim, the problem of the vibration control for the funnel-shaped inlet structure of the MRI tomography is stated and the structure is described, first. Then the task of the structure modeling is tackled applying the FEM approach. Identification of the dynamic frequency response of the desired funnel is performed using the modal-based identification method and the state space model is obtained. Then, the control design for the structure is considered using LQG control method. Complete design and control development procedure is implemented in order to reduce the vibration magnitude of a funnel-shaped shell. Finally, the performance of the designed controllers in both frequency domain and time domain are compared with the open loop systems and results are discussed

Frequency Domain Subspace Identification of Multivariable Dynamical Systems for Robust Control Design

Black-box system identification is subjected to the modelling uncertainties that are propagated from the non-parametric model of the system in time/frequency-domain. Unlike classical H1/H2 spectral analysis, in the recent robust Local Polynomial Method (LPM), the modelling variances are separated to noise contribution and nonlinear contribution while suppressing the transient noise. On the other hand, without an appropriate weighting on the objective function in the system identification methods, the acquired model is subjected to bias. Consequently, in this paper the weighted regression problem in subspace frequency-domain system identification is revisited in order to have an unbiased estimate of the frequency response matrix of a flexible manipulator as a multi-input multi-output lightly-damped system. Although the unbiased parametric model representing the best linear approximation (BLA) of the system in this combination is a reliable framework for the control design, it is limited for a specific signal-tonoise (SNR) ratio and standard deviation (STD) of the involved input excitations. As a result, in this paper, an additional step is carried out to investigate the sensitivity of the identified model w.r.t. SNR/STD in order to provide an uncertainty interval for robust control design

Optimal Input Excitation Design for Nonparametric Uncertainty Quantification of Multi-Input Multi-Output Systems

In this paper, the impact of various input excitation scenarios on two different MIMO linear non-parametric modeling schemes is investigated in the frequency-domain. It is intended to provide insight into the optimal experiment design that not only provides the best linear approximation (BLA) of the frequency response functions (FRFs), but also delivers the means for assessing the variance of the estimations. Finding the mathematical representations of the variances in terms of the estimation coherence and noise/nonlinearity contributions are of critical importance for the frequency-domain system identification where the objective function needs to be weighted in the parametrization step. The input excitation signal design is tackled in two cases, i.e., multiple single-reference experiments based on the zero-mean Gaussian and the colored noise signal, the random-phase multisine, the Schroeder multisine, and minimized crest factor multisine; and multi-reference experiments based on the Hadamard matrix, and the so-called orthogonal multisine approach, which additionally examines the coupling between the input channels. The time-domain data from both cases are taken into the classical H1 spectral analysis as well as the robust local polynomial method (LPM) to extract the BLAs. The results are applied for data-driven modeling of a flexible beam as a model of a flexible robotic arm

System identification and model-based robust nonlinear disturbance rejection control

Der robuste Stör- oder Führungsregler war aufgrund der unbestreitbaren Wichtigkeit für die Automatisierung Gegenstand intensiver Forschung. Die moderne Regelungstheorie tendiert dazu, modelbasierte Ansätze gegenüber modelfreien zu verwenden, insbesondere wenn es um hoch-moderne Anwendungen geht. Das Backbone der Dissertation ist auf der systematischen Modellierung dynamischer Systeme sowie der Entwicklung fortgeschritter Regelungsmethoden basiert. Dementsprechend beginnt die Dissertation mit der Untersuchung von Nichtlinearitäten in dynamischen Systemen. Dementsprechend wird die Erweiterung klassischer Subspacealgorithmen für lineare Systeme im Frequenzbereich unter Verwendung des neuartigen lokalen Polynomansatzes angegangen. Als nächstes wird das Problem der Störungsregelung zerlegt, nämlich werden Modelierungsunsicherheit und nicht modelierte Dynamik hoher Ordnung, Fragilität des Regler- und Beobachter-Systeme, die Nichtlinearitäten von seperat analysiert

ROBUST MIXED H2/H8 ACTIVE VIBRATION CONTROLLER IN ATTENUATION OF SMART BEAM

The lack of robustness of the mechanical systems due to the unmodeled dynamics and the external disturbances withholds the performance and optimality of the structures. In this paper, this deficiency is obviated in order to reach the desired robust stability and performance on smart structures. For this purpose a multi-objective robust control strategy is proposed for vibration suppression of a clamped-free smart beam with piezoelectric actuator and vibrometer sensor in an LMI framework which is capable of handling weighted exogenous input signals and provides desired pole placement and robust performance at the same time. An accurate model of a homogeneous beam is derived by means of the finite element modal analysis. Then a low order modal system is considered as the nominal model and remaining modes are left as the multiplicative unstructured uncertainty. Next, a robust controller with a regional pole placement constraint is designed based on the augmented plant composed of the nominal model and its accompanied uncertainty by solving a convex optimization problem. Finally, the robustness of the uncertain closed-loop model and the effect of performance index weights on the system output are investigated both in simulation and practice

Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution

One of the interesting fields that attracted many researchers in recent years is the smart structures. The piezomaterials, because of their ability in converting both mechanical stress and electricity to each other, are very applicable in this field. However, most of the works available used various inexact two-dimensional theories with certain types of simplification, which are inaccurate in some applications such as thick shells while, in some applications due to request of large displacement/stress, thick piezoelectric panel is needed and two-dimensional theories have not enough accuracy. This study investigates the dynamic steady state response and natural frequency of a piezoelectric circular cylindrical panel using exact three-dimensional solutions based on this decomposition technique. In addition, the formulation is written for both simply supported and clamped boundary conditions. Then the natural frequencies, mode shapes, and dynamic steady state response of the piezoelectric circular cylindrical panel in frequency domain are validated with commercial finite element software (ABAQUS) to show the validity of the mathematical formulation and the results will be compared, finally

Liquid Sloshing in a Horizontal Circular Container with Eccentric Tube under External Excitation

Appropriate conformal mapping transformation in combination with the linear potential theory is employed to develop mathematical model for two-dimensional sloshing in horizontal circular cylindrical containers with overall eccentric hole. The tube-type tank is filled with inviscid incompressible fluid up to its half depth and subjected to lateral accelerations. A ramp-step excitation encountered in a road turning maneuver as well as real seismic event is used to simulate the lateral acceleration excitation. The resulting linear sets of ordinary differential equations are truncated and then solved numerically by employing Laplace transform technique followed by Durbin’s numerical inversion pattern. The effects of excitation input time, eccentricity, and radii ratio on the hydrodynamic responses and suppression of the induced destabilizing lateral forces are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as the simulations performed by using a commercial FEM software package are obtained