The article formulates the task of synthesizing closed-circuit control systems for electric resistance furnaces (ERF) according to a complex criterion for minimizing energy costs and transient time in these systems. This quality criterion relatively fully takes into account the basic requirements for the functioning of ERF, which form a fairly wide class of control object (their number reaches up to 90 % of all electrothermal installations in the country), characterized by high energy consumption and inertia of processes. The optimal control problem uses a generally accepted mathematical model of ERF dynamics in the form of a transfer function describing the dependence of the temperature in the furnace (adjustable value) on the control action, which is the electric power released on the heating element. А method for solving it is proposed, which provides a significant reduction in energy costs when controlling the furnace in comparison with known methods, high accuracy of temperature control, as well as the possibility of taking into account restrictions on the values of the controlled value and control action. The method is based on the transformation of this quality criterion into a kind of generalized functional and the application of the theory of analytical design of optimal regulators by А. A. Krasovsky using the predictive model of free movement of ERF. The proposed energy-saving positional control algorithms allow for a relatively simple implementation using modern microprocessor control devices. An example of the synthesis of energy-saving feedback algorithms for a specific object is considered.

The study is devoted to the development of a methodology for the synthesis of a control system for the transportation of a long, deformable, elastic material that is subject to external disturbances and variations in internal parameters. To achieve this, the features of flow lines as control objects have been identified, which significantly complicate the achievement of high-quality technological processes. А set of methods for the synthesis of controllers for linear and nonlinear dynamic systems has been determined, as well as the sequence of their application, which allows for the most effective overcoming of the complexity factors of the controlled object while meeting the specified technical requirements. The developed complex four-stage methodology for the synthesis of a two-channel nonlinear control system is based on the joint use of the principles of separating the rates of motion of the " fast" and "slow" subsystems, as well as robust modal control of the specified accuracy, to form the dynamics and ensure the specified static accuracy of the local channels, followed by the use of the method of analytical design of aggregated controllers for the linearization of nonlinear material deformation by feedback and the adaptation of the system to multiple changes in the elastic properties of the moving web. To illustrate the effectiveness of the proposed approach, a step-by-step example of applying the developed methodology for the synthesis of an automatic control system for a real technological object is considered. In the first step, a mathematical model of a section of a production line consisting of a two-channel DC electric drive and a transporting zone for a deformable material with second-order elasticity as a control object is created. Next, a control subsystem for the local channel is synthesized, which has the desired dynamic, static, and robust properties. In the next step, a subsystem is developed to ensure the linearity of the dynamic properties of the transporting process for the processed material. And, finally, an option for adapting the system to changes in the elastic properties of the moving web is proposed. During the study of the ACS, the reduction of mathematical models was applied twice: in the first case, to achieve robust properties, and in the second case, to simplify the procedure for synthesizing the controller. The effectiveness of the proposed approach has been confirmed by the results of digital simulation modeling at each stage of the automatic control system synthesis.

An analytical method for the step-by-step modeling of "one-versus-all" combat operations based on the "mean-field dynamics" model is proposed. It is shown that finding the functions describing the change in the number of groups on each side does not require solving the general eigenvalue problem for the lethality matrix, which is necessary in the classical operator method. Instead, the images of the group sizes are formed based on an algorithm for expanding the characteristic determinant, enabling a selective search for the necessary transfer functions of the system based on computational efficiency. The original functions describing the change in the number of groups on each side are found using residues for images of a repeating standard form, invariant to the model order. The pole values required for the calculations are found using elementary operations. The modeling takes into account the objective necessity of dividing the confrontation process into stages as the participating groups of the "all" side are eliminated, in contrast to the situation where the "one" side is destroyed first. Calculation formulas are provided for conditional time points that characterize either the end of the battle or the moment of transition to a new stage with model reduction upon the destruction of one of the components of the "all" side. The conjugation of the functions describing the change in the number of groups, calculated step-by-step, is performed with a shift in conditional time. The proposed analysis procedures are illustrated by a modeling example in Mathcad 14.0, including a comparison with known numerical methods. It is shown that the built-in numerical integration functions in Mathcad 14.0 are "incapable" of solving the problem and lead to rough results. At the same time, the approximation of the matrix exponential using the method of functionally transformed matrices leads to estimates that practically coincide with those obtained analytically.

This paper proposes a synthesis procedure for a two-degree-of-freedom (2DOF) robust loop-shaping controller using the Particle Swarm Optimization (PSO) algorithm. The controller is designed to satisfy predefined performance constraints in both time and frequency domains. А key idea is the use of a generalized weighting function instead of a simple first-order one. This provides a more flexible framework for controller design. Coefficients of this generalized function are treated as decision variables in a constrained optimization problem. By integrating strengths of 2DOF robust loop shaping with computational capabilities of PSO in a closed-loop design, the synthesized controller demonstrates high robustness to significant system parameter variations. In addition, it helps reduce overshoot, shorten settling time, and improve disturbance rejection. Simulation results from a quadrotor attitude control system indicate that the proposed controller can provide robust performance under complex flight conditions. Moreover, its performance and robustness are validated through comparison with a controller designed using the NOMAD (Nonlinear Optimization with Mesh Adaptive Direct search)

This paper proposes a method for estimation of surface accommodation coefficient for a small spacecraft with a complex shape. The method combines modeling of gas-surface interaction of a free molecular flow (computational experiment) and analyzing orbital motion (ballistic experiment). The computational experiment includes determining attitude dependence of the drag coefficient. Direct simulation Monte Carlo is used for aerodynamic calculations. The accommodation coefficient is varied. The ballistic experiment is performed under the assumption of a known atmospheric density model and considered both angular and orbital motion. Spacecraft attitude is determined and it’s averaged projection area is estimated. Processing trajectory information is used for estimation of the ballistic coefficient. Accommodation coefficient is the agreement factor and it is selected by comparing the drag coefficient estimated from the computational experiment with the results of the ballistic experiment. The averaged projection area is used for estimating the drag coefficient, which can lead to results ambiguity. The method illustrated for SamSat-Ion and SamSat-Ionosphere small spacecraft, which have complex geometry. However, the small spacecraft attitude has low sensitivity to aerodynamic disturbances due to large residual magnetic moment, so orbital motion information was used. The proposed method requires a priori information on the averaged projection area of the small spacecraft, so the angular motion of the small spacecraft should correspond to the steady-state mode. The proposed method may provide more reliable estimate of the drag coefficient. Further estimation of the atmospheric density can be made by the already determined drag coefficient.