The paper addresses the problem of direct adaptive disturbance compensation in a linear system with known parameters and unmeasurable state. It is assumed that the amplitudes, frequencies, and phases of the external disturbance are a priori unknown, however the maximum number of harmonics is known. The solution to the problem is reduced to dynamic error model used to design an augmented error based adaptation algorithm with finite time convergence. The proposed adaptation algorithm is based on the prediction of dynamics of standard gradient-based algorithm and: preserves all properties of the gradient-based algorithm, including the convergence of the control error to zero irrespectively from the frequency properties of the regressor; ensures the finite time convergence of the parametric errors to zero under the persistent excitation condition or under the weaker condition of interval excitation; provides the alertness to slow or jumping variations of unknown parameters.

The problem of estimating the magnitude of faults in nonlinear dynamic systems in the presence of external disturbances is solved. The solution uses optimal control methods based on the transformation of the original system to a reduced linear system of a special type, sensitive to faults and insensitive to disturbances. Unlike sliding observers, traditionally used to solve this problem, the proposed approach allows avoiding high-frequency switching.

Modeling the process of thermophysical measurements is necessary when determining the thermal conductivity of the heat -protective coating of buildings, the industrial premises of the agro-industrial complex, industrial structures in real environmental conditions. The problem of choosing the structure of an intelligent measuring system of thermophysical properties of materials in accordance with the thermal conductivity of materials is solved. An intelligent procedure for converting modules of structural, mathematical, metrological and software support is implemented in accordance with the strategy of reconfiguring the system structure and taking into account the measurement situation, which allows automating the processes of managing thermophysical measurements to improve the accuracy of determining the thermal conductivity of materials. The use of the proposed mathematical model of measurements makes it possible to expand the intelligent system functionality, to implement prompt and accurate determination of the thermal conductivity of heat-protective coatings of objects under the influence of external destabilizing factors in conditions of uncertainty.

The impact-friction interaction of the left and right feet with the supporting surface is investigated. For a visual representation, the step cycle phases in bipedal walking are correlated with quad sectors, in which this interaction is presented. The work is based on experimental data on flexion-extension-rotation of the ankle joint and foot reactions when walking on a dynamometric platform. A technique for analyzing paired interaction of both feet is developed, using Hermite functions to model impact impulses of tangential reaction forces of the heel and toe of the foot. At the kinematic analysis stage, angular velocities of rotation of the ankle joint of one leg with full support and of the other in free transfer are calculated. Transmission coefficients are estimated. It is shown that at the stage of dynamic analysis in the phases of impact impulses of the foot on the supporting plane their pair is formed. The results of the study can be used both in developing protocols for ankle rehabilitation and in training athletes when assessing the quality of the foot action during a push.

The control element of the autocollimation system (reflector) is considered, which is a mirror tetrahedron, the lower face of which is replaced by a cylindrical surface, while the angle between the flat faces is not equal to 90 °. A mathematical model of this reflector is synthesized, describing the image change depended on the rotation angles. The possibility of using the model to measure characteristic image parameters is analyzed. A computer model of the autocollimation system (ACT-60 autocollimator) is created with Zemax software tool. An algorithm for measuring the rotation angles of a control element based on determining the characteristic image parameters is presented. Based on the simulation results, the consistency of mathematical and computer models is proved using the overlay method. The results obtained can be applied in systems requiring precise angular positioning of elements, for example, in the study of deflections and deformations of experimental structures, installation and assembly of large-sized parts of products, installation of aircraft and ship slipways.

Additional design stages introduced into the development process of wide-spectrum refractive lenses operating in the spectral range from ultraviolet to near infrared are considered. Such lenses are in demand in luminescent analysis tasks. Additions to the lens calculation method include: the formation of a catalog of optical materials for calculation in a given spectral range; the determination of the possibility of gluing components during the formation of the basic scheme; refinement of the nomogram method to select optimal combinations of materials that meet the requirements of achromatization and athermalization, and a wide operating spectral range. The augmented method allows the design of wide-spectrum lenses for luminescent analysis.

The problem of identifying the executive zone of the solenoid, i. e. that of its median part with a length of [L], where the field strength H is almost constant, is solved in order to conduct research in it. According to the results of the diagnostics of the multilayer solenoids used (four, differing in length L), the acceptability of solving this problem is shown by adapting the well-known fundamental expression for H in a single-layer solenoid to a multilayer one: by means of a coefficient slightly greater than unity. It was found that, based on the requirement that the H value in the center of the solenoid be very close (with an underestimation of no more than 1-2%) to the potential value (in an infinitely long solenoid), the length-to-diameter ratio should be L/D ≥ 5-7. To determine [L], the current value of H on its coordinate characteristic is estimated, which indicates a noticeable (within acceptable limits, in particular, 3%) decrease in H compared to the potential one. The distance x = [x] from the end of the solenoid is determined, where, upon the requirement of field uniformity, such a decrease in H, for example, by more than ε = 5%, is hardly acceptable. It is shown that, regardless of the length L of the solenoids, the length values [x] of their lateral parts, where the field strength is significantly underestimated, are close, and the relative values [x]/L are subject to feedback from L/D. The dependences for [L] and [L]/L on L and L/D are obtained graphically and analytically.

The results of an experimental determination of the possibility of using optical laser triangulation to measure profile characteristics and evaluate the surface quality of parts with a multi-edge structure obtained by milling are presented. An algorithm for the formation and analysis of the profile of finned products by laser triangulation is developed and corresponding software is implemented to measure the geometric parameters of products, including linear, diametrical dimensions, finned parameters, and thickness. An algorithm for estimating the roughness of products with a developed surface obtained as a result of milling using a laser triangulation sensor has been developed implemented. Presented results of experimental testing of the algorithms confirm the effectiveness of using laser triangulation in technical control systems. This makes it possible to improve the manufacturing quality of complex shaped products and reduce the level of manufacturing defects by increasing the accuracy and information content of the control.

Methods for determining the thickness of mask layers for plasma chemical etching processes are considered. A method for calculating the thickness of the mask layers during the formation of an instrument layer for the manufacture of sensitive elements of a micromechanical accelerometer is proposed. The results of the evaluation of the calculation method based on the measured values of the mask thickness before and after plasma-chemical etching of the instrument layer on a silicon substrate with sensitive elements are presented. A conclusion is formulated on the effectiveness of using the presented method in the manufacturing technology of micromechanical accelerometers and gyroscopes.