The problem of nonstationary wave radiation in an infinitely long thick-wall piezoelectric cylinder in fluid medium is considered. The influence of an oscillating circuit with lumped parameters on characteristics of transient process is taken into consideration. Problem formulation is executed within the forced electrostatic theory, acoustic approximations, and quasistatic theory for electric circuit. The solution method is based on the integral Laplace transform in time. This allows analytically reducing the problem to solving a system of Volterra integral equations with retarded arguments. The numerical results of calculations are presented and analyzed.
The behavior of a double-layer (metal-piezoceramics) rectangular plate under nonstationary electromechanical loading is studied. It is assumed that the mechanical load versus time law and the area of its application are specified. The electric signal applied to solid electrode coatings of the piezolayer reduces the amplitudes of mechanically induced vibrations of the plate. Two approaches to determining the profile of the electric signal are considered – the first is focused on minimizing the plate strained state, and the second approach deals with suppressing forced vibrations with an account of minimizing power input for forming a control action. The Kirchhoff-Love generalized hypotheses are used for simulating electromechanical vibrations. The boundary problem solution was derived using the Laplace integral transform in time and separation of variables. To assess the effectiveness of the approaches suggested, the plate vibrations were investigated when the piezolayer was in the direct piezoelectric effect mode. The numerical and analytical results were validated by comparison with finite element solutions. The paper also describes the method of solving the problem of restoring the time dependence of the mechanical load based on known values of the difference of potentials between open piezolayer electrodes, which occur due to bending vibrations of the bimorph plate.
Д-р физ.-мат. наук, доцент, профессор кафедры теории машин и механизмов, Харьковский национальный автомобильно-дорожный университет, Украина ГАРАНТИРОВАННОЕ УПРАВЛЕНИЕ ДВИЖЕНИЕМ МАНИПУЛЯЦИОННОГО РОБОТА Рассматривается задача управления движением манипуляционного робота при наличии в его модели параметрической неопределенности и действии неконтролируемых возмущений. Предложен робастный регулятор, основанный на методе вычисляемого момента, в котором для вычисления дополнительного управления, обеспечивающего компенсацию действия неопределенных факторов, используется гарантированный подход, согласно которому значения этих факторов известны лишь с точностью до принадлежности некоторым множествам. Для оптимизации управления использован квадратичный критерий качества. Эффективность предложенного решения подтверждено результатами численного моделирования. Ключевые слова: манипуляционный робот, регулятор с вычисляемым моментом, гарантированное управление, множество возможных состояний.
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