We study the solution of the so-called maximum speed problem of a linear control system, in which, unlike the classical optimal speed problem with a relay-type control, a linear control algorithm is determined for a linear object that provides the maximum speed of the system. It is of practical importance due to the widespread practical application of linear control laws. The problem is formulated in relation to continuous, one-dimensional high-order control objects described by the corresponding transfer function or an equivalent system of ordinary differential equations in a certain phase space. The time of the transition process t_tp of the designed system is understood in the sense of the classical theory of automatic control and is determined using the zone  D = spr   4,321 %, equal to the given (desired) value of the overshoot of the synthesized system. This overshoot corresponds to an oscillatory link with a damping coefficient   √2/2  — the Butterworth filter of the second order. Accordingly, the maximum performance problem is put in the following formulation: it is required to find a linear feedback algorithm that provides the closed control system with a given astatism order na and transferring the control object from the initial state to the final one, determined by the constant signal of the regulator’s task, with the minimum value of transient time t_tp and set value overshoot s = s _pr when performing a constraint on the control signal |u(t)| m u_max. At present, this problem has been solved by an approximately algebraic method of synthesizing linear control systems in determining the desired transfer function of a projected closed system based on typical (reference) normalized transfer functions (NTF). The approximate nature of the decision is determined by the fact that the NTF used in the synthesis of high-speed systems are established empirically. This paper proposes a mathematically sound solution to the problem of maximum speed using the theory of analytical design of optimal controllers (ADOC). The maximum speed and set limits on the overshoot and the value of the control signal in the synthesized system are provided by the proposed method for selecting the weights of the quadratic quality functional. We emphasize that the proposed method for the synthesis of high-speed systems, in contrast to the algebraic method, is applicable to a wider class of control objects: both minimal-phase and non-minimal-phase, as containing zeroes, and not. The method is illustrated by an example of the synthesis of a high-speed fourth-order control system containing the results of its simulation.

The article is devoted to the analysis of methods for solving systems of multivalued logical equations by iteration methods. Iterative methods for solving such systems of equations are a mathematical description of the main process of functional-logical simulation, which is used at the stage of designing digital systems for objects control to verify the correctness of the design. Consideration of multi-valued values of logical signals at the outputs of blocks and elements of digital systems is explained by the fact that in some cases, to analyze the correctness of time relationships when simulating the hardware of digital systems, a several valued representation of logical signals is used, as well as that recently, logical elements are being developed that implement four or more valued logic. Based on the analysis of the structure of the system of logical equations used in digital hardware simulation, using graph and logical models, an analysis is made of the existence of solutions and their number. Iterative methods of a simple and generalized iteration are analyzed, a relationship is shown between the number of solutions of the system of equations and its graph representation, which reflects a given circuit of connecting elements of the hardware of a digital control system. For the generalized iteration method, options with a different structure of the iteration trace are considered, in particular, it is shown that, with a certain structure of the iteration trace, the generalized iteration turns into a simple iteration or Seidel iteration. It is shown that the generalized iteration most adequately describes the process of simulating the switching of logical signals in a simulated circuit of digital control systems hardware. The correspondence between various options of functional-logical simulation of digital systems and the used methods of iterative solution of systems of logical equations is shown.

The paper deals with the development of algorithms for constructing the confidence interval for the mathematical expectation of the noise of a noisy signal. It is noted that the noise characteristics can be used as informative attributes of the beginning of the initiation of a defect in a technical object. It is also indicated that the problem of determining the dynamics of changes in the technical condition  of an  object is more important than the control of the onset of a malfunction. This is based on the fact that with a slight development of a malfunction or lack of development, there is no need to stop the object’s operation for repair. In contrast, strong dynamics of development of a defect requires urgent action. It is noted that a timely solution to this problem is especially relevant for oil and gas production facilities and other similar facilities. It is shown that confidence intervals for the noise characteristics of a noisy signal can be used as informative attributes of determining the dynamics of a malfunction. Algorithms for determining the confidence interval for the mathematical expectation of the noise are developed. Technologies are proposed for determining the latent period of the initiation of the malfunction of  technical  objects  and  the  dynamics  of  its  development  using  the  confidence  interval  for  the  mathematical  expectation of the noise. To this end, at the instant of time when the object is in a normal state, a confidence interval is constructed for the mathematical expectation of the noise, and a set of possible values that fall into this interval is compiled. After a certain period of time, this procedure is repeated. It is noted that when a malfunction occurs, the width of the confidence  interval increases. Therefore, the difference between the sets of possible values of the mathematical expectation of the noise at the previous and current instants is found. A correspondence is established between the value of this difference and the degree of damage development. By determining each time the differences of the sets of possible values of the mathematical expectation of the noise, the dynamics of the development of the malfunction in time is revealed. Then the corresponding conclusions are made, such as "the malfunction develops with uniform intensity", "the malfunction develops intensively", "the malfunction develops very intensively", etc. Depending on the degree of malfunction development, appropriate preventive or repair work is carried out with or without stopping the operation of the control object. To verify the reliability of the developed algorithm for constructing the confidence interval for the mathematical expectation of the noise of a noisy signal and the technology for determining the latent period of initiation of malfunction of technical objects and the dynamics of its development, computational experiments are carried out using the MATLAB computing environment.

In the automatic system, the presence of an object with a delay that exceeds the value of the maximum time parameter of the controlled object reduces the operating quality of generic controllers (integral, proportionally-integral, proportionally-integral-differential). The occurrence of this kind of delay in the system requires addressing a particular class of regulators that compensate for the negative effects of the delay. This paper examines the PI controller known for its advantages with variable or switchable parameters, which belongs to the class of controllers with variable structure (henceforward — VSC) that do not use sliding mode. Due to the fact that the controller used contains switchable parameters and the object with delay is considered, it is extremely difficult to use analytical approaches to parametric optimization of the system. This lays one under a necessity to use algorithmic methods. This work employs a gradient-based algorithm in which the components of the gradient are calculated using sensitivity functions with their known advantages. The generated Automatic Parametric Optimization (APO) Algorithm calculated the optimal VSC parameters for a given object, based on the minimum of the integrated quadratic criterion. The reliability of the found vector of the controller setting, formed by the APO algorithm, is confirmed by the computational methodology. With accuracy sufficient for practice, the APO algorithm solved the problem of parametric optimization. The positive experience of optimizing the PI controllers with variable parameters allows one to apply it to other VSC, which do not use a sliding mode, and thus further expand the practice of using a gradient-based algorithm based on sensitivity functions for such a class of VSC under various laws of switching structures of the controller.

The article views, that draw-backs of aircraft’s traditional air data systems (ADS), built based installed in incoming air flow and installed outside the fuselage the pitot tube booms, temperature braking receivers, vane sensors of incidence angle and gliding angle are eliminated in original ADS with motionless flush-mounted receiver of flow. The functional scheme of aircraft’s air data system with motionless flush-mounted receiver of flow, built based on the original ion-mark sensor of aerodynamic angle and true airspeed, on receiving board of which the hole-receiver is installed to perceive the static pressure of incoming air flow. Models of operator sensitivity and dynamic errors of instrumentation channels due to random stationary atmospheric turbulence and random flow pulsations at location of the ion-mark sensor on fuselage of the aircraft are presented. Recommended to use the optimal linear Wiener filter, the synthesis method of which is revealed on example of the true airspeed instrumentation channel to reduce the stationary dynamic errors of instrumentation channels of air data system with motionless flush-mounted receiver due to atmospheric turbulence. Recommended to use the principle of integration to reduce the stationary random dynamic errors of instrumentation channels of air data system with motionless flush-mounted receiver due to flow pulsations near fuselage at location of ion-mark sensor. Proposed to use aeromechanical measuring and computing system built based VIMI method with Luenberger observer as an additional component of integrated air data system. Integrated system simulates the movement of aircraft in this flight mode and by flight parameters measured with high accuracy using flush-mounted receivers "restores" air signals included in equations of movement of aircraft. The structure, method and algorithms for determining air signals in channels of aeromechanical measuring and computing system with a Luenberger observer are presented. Using the example of true airspeed measurement, the analysis and quantitative assessment of residual dynamic error of integrating channel of integrated aircraft’s air data system with motionless flush-mounted receiver of flow is carried out.

The use of low-orbit constellation of small or super-small satellites for solving problems of remote sensing of the Earth is a promising direction for the development of space activities. The implementation of this perspective requires the study of a wide range of fundamentally new tasks, one of which is the development of control systems for such constellations. A fundamentally new aspect in the content of this task is the possibility of using communication between satellites and the communication network of the space system as a whole. At the same time, the choice of approach to the development of the control system depends on the mode in which information exchange can take place, in real time or with time delays. The article discusses various options for the orbital construction of satellite groupings that determine the modes of information exchange. The object of research is a space system in which information exchange can occur with time delays. The aim of the research is to develop a methodology for assessing the impact of the communication network bandwidth on the efficiency of the space system. Efficiency indicators are the time of request execution and the performance of the space system — the data volumedelivered by a satellite constellation to the Earth over a certain period. The basis of the methodology is a simulation model that simulates the operation of satellites and ground infrastructure objects, the use of the developed prototype of the control system and the corresponding information exchange in the communication network.