Design of a control system using linear matrix inequalities for the active vibration control of a plate

The study of algorithms for active vibration control in smart structures is an area of interest, mainly due to the demand for better performance of mechanical systems, such as aircraft and aerospace structures. Smart structures, formed using actuators and sensors, can improve the dynamic performance with the application of several kinds of controllers. This article describes the application of a technique based on linear matrix inequalities (LMI) to design an active control system. The positioning of the actuators, the design of a robust state feedback controller and the design of an observer are all achieved using LMI. The following are considered in the controller design: limited actuator input, bounded output (energy) and robustness to parametric uncertainties. Active vibration control of a flat plate is chosen as an application example. The model is identified using experimental data by an eigensystem realization algorithm (ERA) and the placement of the two piezoelectric actuators and single sensor is determined using a finite element model (FEM) and an optimization procedure. A robust controller for active damping is designed using an LMI framework, and a reduced model with observation and control spillover effects is implemented using a computer. The simulation results demonstrate the efficacy of the approach, and show that the control system increases the damping in some of the modes.

Landau and Kolmogoroff type polynomial inequalities

Let 0inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained.

Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Characterization of generalized Bessel polynomials in terms of polynomial inequalities

Generalized Bessel polynomials (GBPs) are characterized as the extremal polynomials in certain inequalities in L-2 norm of Markov type. (C) 1998 Academic Press.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Is the equivalence for the response of static scalar sources in the Schwarzschild and Rindler spacetimes valid only in four dimensions?

It was shown recently that in four dimensions scalar sources with fixed proper acceleration minimally coupled to a massless Klein-Gordon field lead to the same responses when they are (i) uniformly accelerated in Minkowski spacetime (in the inertial vacuum) and (ii) static in the Schwarzschild spacetime (in the Unruh vacuum). Here we show that this equivalence is broken if the spacetime dimension is more than four.

Influence of detector motion in Bell inequalities with entangled fermions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

The Lactate Minimum Test protocol provides valid measures of cycle ergometer VO2 peak

Aim. The aim of the present study was to investigate the validity of the Lactate Minimum Test (LMT) for the determination of peak VO2 on a cycle ergometer and to determine the submaximal oxygen uptake (VO2) and pulmonary ventilation (VE) responses in an incremental exercise test when it is preceded by high intensity exercise (i.e., during a LMT).Methods. Ten trained male athletes (triathletes and cyclists) performed 2 exercise tests in random order on an electromagnetic cycle ergometer: 1) Control Test (CT): an incremental test with an initial work rate of 100 W, and with 25 W increments at 3-min intervals, until voluntary exhaustion; 2) LMT: an incremental test identical to the CT, except that it was preceded by 2 supramaximal bouts of 30-sec (similar to120% VO(2)peak) with a 30-sec rest to induce lactic acidosis. This test started 8 min after the induction of acidosis.Results. There was no significant difference in peak VO2 (65.6+/-7.4 ml.kg(-1).min(-1); 63.8+/-7.5 ml.kg(-1).min(-1) to CT and LMT, respectively). However, the maximal power output (POmax) reached was significantly higher in CT (300.6+/-15.7 W) than in the LMT (283.2+/-16.0 W).VO2 and VE were significantly increased at initial power outputs in LMT.Conclusion. Although the LMT alters the submaximal physiological responses during the incremental phase (greater initial metabolic cost), this protocol is valid to evaluate peak VO2, although the POmax reached is also reduced.

Inequalities in access to education and healthcare

The burden of disease is borne by those who suffer as patients but also by society at large, including health service providers. That burden is felt most severely in parts of the world where there is no infrastructure, or foreseeable prospects of any, to change the status quo without external support. Poverty, disease and inequality pervade all the activities of daily living in low-income regions and are inextricably linked. External interventions may not be the most appropriate way to impact on this positively in all circumstances, but targeted programmes to build social capital, within and by countries, are more likely to be sustainable. By these means, basic oral healthcare, underpinned by the primary healthcare approach, can be delivered to more equitably address needs and demands. Education is fundamental to building knowledge-based economies but is often lacking in such regions even at primary and secondary level. Provision of private education at tertiary level may also introduce its own inequities. Access to distance learning and community-based practice opens opportunities and is more likely to encourage graduates to work in similar areas. Recruitment of faculty from minority groups provides role models for students from similar backgrounds but all faculty staff must be involved in supporting and mentoring students from marginalized groups to ensure their retention. The developed world has to act responsibly in two crucial areas: first, not to exacerbate the shortage of skilled educators and healthcare workers in emerging economies by recruiting their staff; second, they must offer educational opportunities at an economic rate. Governments need to lead on developing initiatives to attract, support and retain a competent workforce.

Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Bell inequalities for entangled pairs of neutral kaons

We extend the use of Bell inequalities to Φ → K0K̄0 decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a CP-violating Hamiltonian. © 1999 The American Physical Society.

Bound constrained smooth optimization for solving variational inequalities and related problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

Robust control to parametric uncertainties in smart structures using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft and aerospace structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. This article shows some steps that should be followed in the design of a smart structure. It is discussed: the optimal placement of actuators, the model reduction and the controller design through techniques involving linear matrix inequalities (LMI). It is considered as constraints in LMI: the decay rate, voltage input limitation in the actuators and bounded output peak (output energy). Two controllers robust to parametric variation are designed: the first one considers the actuator in non-optimal location and the second one the actuator is put in an optimal placement. The performance are compared and discussed. The simulations to illustrate the methodology are made with a cantilever beam with bonded piezoelectric actuators.