Polynomial method for the synthesis of regulators for the special case of multichannel objects with one input variable and several output values

Currently, an urgent task in control theory is the synthesis of regulators for objects with a smaller number of input values compared to output ones, such objects are described by matrix transfer functions of a non-square shape. A particular case of a multichannel object with one input variable and two / three / four output variables is considered; the matrix transfer function of such an object has not a square shape, but one column and two / three / four rows. To calculate the controllers, a polynomial synthesis technique is used, which consists in using a polynomial matrix description of a closed-loop control system. A feature of this approach is the ability to write the characteristic matrix of a closed multichannel system through the polynomial matrices of the object and the controller in the form of a matrix Diophantine equation. By solving the Diophantine equation, the desired poles of the matrix characteristic polynomial of the closed system are set. There are many options for solving the Diophantine equation and one of them is to represent the polynomial matrix Diophantine equation as a system of linear algebraic equations in matrix form, where the matrix of the system is the Sylvester matrix. The choice of the order of the polynomial matrix controller and the order of the characteristic matrix is carried out on the basis of the theorem given in the works of Chi-Tsong Chen, which always holds for controlled objects. If the minimum order of the controller is chosen in accordance with this theorem, and the Sylvester matrix has not full rank, then this means that there are more unknown elements in the system of linear algebraic equations than there are equations. In this case, the solution corresponding to the selected basic minor has free parameters, which are the parameters of the regulators. Free parameters of regulators can be set arbitrarily, which is used to set or exclude some zeros in a closed system. Thus, using various examples of objects with a non-square matrix transfer function, a polynomial synthesis technique is illustrated, which allows not only specifying the poles of a closed system, but also some zeros, which is a significant advantage, especially when synthesizing controllers for multichannel objects.

Electromagnetoelastic Actuator for Nano Physics and Optics Sciences

The regulation and mechanical characteristics of the electromagnetoelastic actuator are obtained for control systems in nano physics and optics sciences for scanning microscopy, adaptive optics and nano biomedicine. The piezo actuator is used for nano manipulators. The matrix transfer function of the electromagnetoelastic actuator is received for nano physics and optics sciences

Multilayer Electro Magneto Elastic Actuator for Nano Science and Engineering

We obtained the structural diagram of the multilayer electromagnetoelastic actuator for nano science and engineering in contrast to electrical equivalent circuits of the piezotransmitter and piezoreceiver, the vibration piezomotor. In this work the structuralparametric model, the structural diagram and the matrix transfer function of the multilayer electromagnetoelastic actuator for nano science and engineering are determined.

Structural-Parametric Model and Diagram of a Multilayer Electromagnetoelastic Actuator for Nanomechanics

In this work, the parametric structural schematic diagrams of a multilayer electromagnetoelastic actuator and a multilayer piezoactuator for nanomechanics were determined in contrast to the electrical equivalent circuits of a piezotransmitter and piezoreceiver, the vibration piezomotor. The decision matrix equation of the equivalent quadripole of the multilayer electromagnetoelastic actuator was used. The structural-parametric model, the parametric structural schematic diagram, and the matrix transfer function of the multilayer electromagnetoelastic actuator for nanomechanics were obtained.

Electro Magneto Elastic Actuator for Nanoscience

The mathematical model, the structural scheme, the matrix transfer function, the characteristics of the electro magneto elastic actuator is obtained. The transfer functions of the magneto elastic actuator are described the characteristics of the actuator with regard to its physical parameters and external load.

Random Response Relationships to Transfer Function and State-Space Properties

Output variables of dynamic systems subject to random inputs are often quantified by mean-square calculations. Computationally for linear systems, these typically involve integration of the output spectral density over frequency. Numerically, this is a straightforward task and, analytically, methods exist to find mean-square values as functions of transfer function (frequency response) coefficients. These formulations offer analytical relationships between system parameters and mean-square response. This paper develops further analytical relationships in calculating mean-square values as functions of transfer function and state-space properties. Specifically, mean-square response is formulated from (i) system pole-zero locations, (ii) as a spectral decomposition, and (iii) in terms of a system matrix transfer function. Direct, closed-form relationships between response and these properties are afforded. These new analytical representations of the mean-square calculation can provide significant insight into dynamic system response and optimal design/tuning of dynamic systems.

A New Way of Solving Transient Radiative-Conductive Heat Transfer Problems

One-dimensional transient energy transfer by conduction and radiation is solved for a finite medium. The semitransparent layer emits, absorbs, and scatters radiation (participating medium). The coupled transfer is solved analytically by considering the well-known two-flux approximation, assuming linear transfer and using the Laplace transform. The semitransparent layer can then be modeled by a matrix transfer function. The accuracy of the solution is verified in the case of sharp thermal excitation by a heat pulse on the front face. It is shown that this general model is very accurate for simulating both the limiting cases of purely scattering and purely absorbing media. In the latter case, the same modeling is derived using the kernel substitution technique, and very good agreement is achieved compared with numerical simulations. The resulting computation times are very small, and suggest that such a model can be used in the inverse approach of thermal problems involving semitransparent materials.