The main purpose of the research is the extending of the concept of qualitative exponential stability and instability for a wider class of dynamical systems and plants with estimating of regions of exponential stability as well as developing of analytic and calculating technologies for analyzing the quality of processes and projecting of control devices for control systems. And if the property of asymptotic stability indicates the convergence or divergence of the processes in time, the exponential stability provides information about the speed of convergence or divergence processes, thereby characterizing the rapidness of the system. Meeting the conditions of quality exponential stability evaluates the average rate of convergence or divergence of processes, as well as ongoing processes of deviations of the time-average behavior, the last gives information about the behavior of transients (oscillation, overshoot). Development of analytical and computational techniques for the analysis of stability and instability of comparison systems and, as a result of mul tiply-connected systems, as well as the processes quality is almost an essential task for the study multi-agent control algorithms and biologically inspired control algorithms in nonlinear systems, because the same systems should be related to each other and has a predetermined degree of exponential stability for the required control. Proposed results can be using in the developing flying and terrestrial robots based on biological control algorithm of living organism such as insects or bees.

Discrete (finite-difference) systems are widely used in modern nonlinear control theory. One of the main problems of a qualitative study of such systems is the problem of stability of the zero equilibrium position, which has great generality. In most works, such a stability problem is analyzed with respect to all variables that determine the state of the system. However, for many cases important in applications, it becomes necessary to analyze a more general problem of partial stability: the stability of the zero equilibrium position not for all, but only with respect to some given part of the variables. Such a problem is often also considered as auxiliary problem in the study of stability with respect to all variables. In this way, the corresponding concepts and problems of detectability of the studied system arise, which play an important role in the process of analysis of nonlinear controlled systems. Then, more general problems of partial detectability were posed, within the framework of which the situation was studied when stability from a part of variables implies stability not with respect to all, but with respect to more part of the variables. This article studies a nonlinear discrete (finite-difference) system of a general form that admits a zero equilibrium position. Easily interpreted conditions are found on the structural form of the system under consideration that determine its partial detectability, for which stability over a given part of the variables of the zero equilibrium position means its stability with respect to the other, more part of the variables. In this case, the stability with respect to the remaining part of the variables is uncertain and can be investigated additionally. In the process of analyzing this problem of partial detectability, the concept of partial null-dynamics of the system under study is introduced. An application of the obtained results to the stabilization problem with respect to part of the variables of nonlinear discrete controlled systems is given.

The paper addresses issues of temperature control in heating furnaces using the example of a strand-type furnace for steel strip annealing of a continuous hot-dip galvanizing unit. The authors demonstrate that one of the main problems is variability of dynamic properties in the controlled object upon flexible production management with changes in the furnace capacity. Using a model of thermal state of the furnace cavity and metal, considering the impact of furnace temperature conditions on heat losses, variation limits of the parameters in a simplified model of object dynamics are determined. Issues of controlling a temperature object with variable dynamic parameters are reviewed. Advantages and disadvantages of systems used to control such objects, based on fuzzy logic and sliding mode control, are studied. It is shown that, in controlling a temperature object, a sliding mode control system can lead to fluctuating transient responses due to the absence of amplitude modulation in the control action when approaching the set-point. The authors suggest a system for automatic stabilization of the controlled parameter of a temperature object where sliding mode control and fuzzy logic are combined. In the stabilization system suggested, the direction of changes in the control action is determined using sliding mode control, while the control action level is determined using fuzzy logic. The paper provides results of simulation experiments comparing the efficiency of control using the system suggested and efficiency of control using the system based only on fuzzy logic. During those experiments, optimal system setting parameters were determined using complete enumeration and computer simulation of control for an object with the set variation of dynamic properties. Computer simulation was performed in the VisSim environment. The paper also shows that, with constant values of signal scaling parameters used in fuzzy logic, the requirement for qualitative transient responses with various set-point change levels results in the significantly reduced response speed in comparison with the system that combines fuzzy logic and sliding mode control. The authors demonstrate that it is possible to adjust quality of transient responses in the system that combines fuzzy logic and sliding mode control, changing dynamic properties of the object.

In the present study, a new hybrid passive adhesion method for a mobile wall-climbing robot (WCR) is proposed. This method is based on a combination of magnetic and glue adhesion. For its implementation, a flexible magnetic tape with glue on one side is used to fasten the tape to the working surface. Holding and climbing of the WCR on the magnetic tape, fixed by the robot in the process of movement, occurs with the help of the tracked locomotion mechanism. Permanent magnets are placed in the tracks of the WCR interacting with the tape as the robot climbs along a vertical surface. The concept of the adhesion and locomotion mechanisms, as well as the design of the WCR prototype is developed. Experimental studies of the magnetic properties of the proposed locomotion mechanism have been carried out. They showed its feasibility and efficiency. Also from experimental studies were obtained quantitative characteristics of the interaction of the WCR with tape, used in the construction of its mathematical model. A feature of this WCR concept, working on the magnetic-tape adhesion, is the possibility of moving it without using magnetic tape on ho rizontal surfaces, as well as on vertical ferromagnetic surfaces — only with tracks with permanent magnets. The WCR with a hybrid magnetic-tape adhesion mechanism is designed to move on various surfaces indoor spaces.

In this article, the authors consider the problem of coordinate transformation in computer vision systems (CVS) of robotic system (RS) for laser welding. Laser welding is a highly efficient technological operation in many respects superior to common types of welding due to the high concentration of energy at the welding point. However, laser welding has a number of requirements, including a high requirement for the accuracy of positioning the laser head relative to the welding joint. Adaptive control systems based on CVS allow to provide the required accuracy. The main task of CVS is to determine the three-dimensional coordinates of the welding joint using a video sensor, convert the received coordinates into a coordinate system in which the RS is controlled, and the converted coordinates are transferred to the control system. Note, the accuracy and determination of coordinates are important factors. To accomplish this task, it is necessary to consider the coordinate transformation as a set of actions performed taking into account the specifics of using CVS as part of an RS for laser welding. For this purpose, the article analyzes typical schemes for placing CVS on industrial robots and proposes the most suitable configuration for laser welding. A methodology was also developed for measuring the three-dimensional coordinates of the welding joint using the triangulation method. The authors carried out a comparative analysis of the main existing methods for calibrating CVS video sensors and proposed an original method for calibrating videosensors taking into account the specifics of the functioning of the RS for laser welding. As a result, the article presents the rationale for the need to consider coordinate conversion to CVS as part of an RS for laser welding, as well as a set of methods that allows to perform conversions from a virtual coordinate system of a video sensor to a coordinate system of a robot, which allows direct control based on CVS data. In conclusion, the authors give a method for calibrating a video sensor, which allows achieving the requirements specified in the article for the accuracy of determining the coordinates of the welding joint.

Dynamic problem of optimal reorientation from an arbitrary initial attitude into the given final angular position with restricted control which minimizes kinetic energy of spacecraft rotation was solved. Termination time of maneuver is known. Quadratic criterion of quality is applied for finding the optimal control program. Use of integral index in special form concerning angular velocity has helped solve the formulated problem by analytical way. Control law was written down in explicit form. Designing the optimal control is based on quaternion variables and models. It is shown that during optimal turn, the controlling moment is parallel to the straight line which is immobile in the inertial space, and direction of spacecraft’s angular momentum in the process of rotation is constant relative to the inertial coordinate system. Special control regime was studied in detail, and conditions of the impossibility of occurrence of this regime are formulated. It is proven that spacecraft rotates by inertia in special control regime if it exists. The formalized equations and computational expressions for determining the optimal rotation program and duration of acceleration and braking were written. A dependence of control variables on phase coordinates is presented also. The proposed control algorithm allows the spacecraft’s reorientation to be carried out within the fixed time period with minimal angular kinetic energy. Analytical expressions for computing the time characteristics of reorientation maneuver are given, and condition for determination of the moment of the beginning of the braking, based on factual kinematic parameters of motion judging by principles of terminal control is formulated, that provides high accuracy of orientation. A comprehensive solution to the control problem is presented for a dynamically symmetric spacecraft: the dependences as explicit functions of time for the control variables are obtained, and relations for calculating the key parameters of the turn maneuver’s control law are given also. A numerical example and the results of mathematical simulation of spacecraft’s motion with optimal control are presented, which demonstrate the practical feasibility of the designed method for controlling the spacecraft attitude. Presence of ready formulas for synthesis of optimal motion program during reorientation maneuver does the executed research as practically significant and suitable for direct use in practice of space flights.

Development of an aircraft active sidestick control is an actual direction in modern flight control systems which allows to increase safety, to improve cabin ergonomics and to reduce the mass and weight of control levers. The article devoted to simulation modeling of a pair active sidesticks based on electromechanical actuators coupled by a frameless kinematic scheme, providing identical dynamic characteristics for the pitch and roll channels. MATLAB, Simulink, Simscape, with SimMechanics and SimPowerSystems libraries was used to create the mathematical model. Parameters such as moments of inertia was count based on the 3D model of the active sidestick. The complex model includes two active sidesticks units, three blocks as the input source ("Autopilot", blocks of the 1st and 2nd pilots), a block that compute a loading characteristic for the manual control mode and a block with logic for switching from automatic to manual mode. The model of each active sidestick unit consists of three main blocks: a regulator, an electric motor with a control system, and a block of mechanics. The regulator block includes a PID regulator and a PWM modulator. The electric motor unit includes a power source, a three-phase bridge inverter, a model of a brushless three-phase electric motor from the SimPowerSystems library and a power switch control unit. The mechanics block includes a planetary gearbox, hinge mechanism, handle, moments of inertia, a position sensor, a torsion rod equal to tension springs which are used in device, a nonlinear speed damper and a torque source unit, depending on the force applied by the pilot. Developed model makes it possible to get static and dynamic characteristics of the actuators, to check control algorithms to simulate operating modes in automatic and manual control, including piloting by both pilots at the same time and the interruption in automatic control mode. Including in model a " hold position block" allowed to simulate situation when in manual control mode the 1st pilot tries to hold the handle in a position that he considers correct, despite the intervention of the 2nd pilot.
The simulation results showed that developed device meets specified requirements for the aircraft active sidesticks.