Boris Andrievsky

• ScD
• Fellow at Institute of the Problems of Mechanical Engineering

In brief the synchronization problem for nonlinear systems under communication constraints and bounded exogenous disturbances is analyzed. The main contribution is in the evaluation of the synchronization error as a function of transmission rate and the upper bounds of the disturbances. Relevance of passifiability condition for controlled synchroni...

This paper investigates the formation of vibration fields in a mechatronic setup driven by dual induction motors, relying on the controlled synchronization of unbalanced rotors. The proposed algorithm enables precise control over rotor speeds and phase shifts. Experimental results from a multi-resonance vibration laboratory setup demonstrate this a...

This paper delves into the challenge of controlling the multiple synchronizations in mechatronic vibration machines featuring a duo of unbalanced rotors. Its primary aim is to not only attain specific rotation speeds but also to ensure the desired phase shift between these rotors. To tackle this issue, the paper employs a control law integrating cr...

This study explores the effect of incorporating steel fibres and fly ash into self‐compacting concrete (SCC) in various combinations on its mechanical properties. The study begins with thoroughly investigating the fresh properties to ensure compliance with SCC standards when adding steel fibres. Subsequently, mixes that meet SCC standards are evalu...

This study explores the effect of incorporating steel fibres and fly ash into self-compacting concrete (SCC) in various combinations on its mechanical properties. The study begins with thoroughly investigating the fresh properties to ensure compliance with SCC standards when adding steel fibres. Subsequently, mixes that meet SCC standards are evalu...

The demand for the development of cyber-physical systems remains high across various production sectors. While some industries have made significant strides, others still require ongoing research and development efforts. This article delves into the application of feedback control for equipment in the processing industry, using a two-rotor vibratio...

This paper successfully developed and studied a phase shift control system for a two-rotor vibration mechatronic setup, aiming to maintain the desired revolving speed of the rotors. The sliding mode motion was achieved by utilizing a relay controller in the phase loop, while PI controllers were employed in the velocity control loops. Through numeri...

The paper is devoted to the adaptive control of pneumatic drives for the Stewart platform with six degrees of freedom. Based on the approach known as the method of the implicit reference model, the synthesis of parametric and signal-parametric adaptive controllers is carried out. The use of both a group of pneumatic valves and a spool valve in the...

With the digitalization of mechatronic systems in the conditions of a shortage of available bandwidth of digital communication channels, the problem of ensuring the transfer of information between various components of the system can arise. This problem can be especially challenging in the observation and control of spatially distributed objects du...

In this paper, the solution to the problem of robust control of the phase shift during rotation at a given speed of the unbalanced rotors for a two-rotor vibratory machine is presented. The solution to this problem is relevant for the development of vibration technologies (for example, a vibro-transportation of bulk materials). The proposed control...

The nonlinear correction method is widely used in automatic control systems to increase stability margins and quality rating. This method has also found application in piloted aircraft control tasks, where the loss of stability and the occurrence of oscillations are unacceptable. This paper discusses new nonlinear correcting devices. Their structur...

The paper is devoted to the problem of the decentralized control of unmanned aerial vehicle (UAV) formation in the case of parametric uncertainty. A new version of the feedback linearization approach is proposed and used for a point mass UAV model transformation. As result, a linear model is obtained containing an unknown value of the UAV mass. Emp...

The paper is devoted to the problem of spacecraft attitude control using reaction wheels. The control system should ensure switching between less accurate to more accurate flight modes, resistance to external environmental influences, and, in some cases, the survival of the spacecraft. In these modes, the reaction wheel drives can reach their maxim...

The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, mixing of bulk materials, is...

The paper is devoted to a human operator control for an electromechanical remote manipulator. It is assumed that a human operator in a closed-loop achieves the goal of control by deflecting the joystick. A saturation nonlinearity is taken into account in the paper. To compensate for the negative phase delay in the system performance, a corrective f...

This paper deals with computer-controlled pneumatic actuators for the Gough-Stewart platform with 6 degrees of freedom. An important feature considered in the paper pneumatic actuator is the use of a group of valves rather than a spool valve to control the pressure in the chambers, which leads to a significant quantization in terms of the level of...

The purpose of this work is to demonstrate the application of the nonlinear correction method to prevent attitude oscillations of flying vehicles. This paper investigates the complications of manual control tasks in aeronautics caused by employing the integral component in the control loop. If the actuators of aircraft controlling surfaces reach th...

This survey deals with the problem of the group motion of spacecraft, which is rapidly developing and relevant for many applications, in terms of developing the onboard control algorithms to ensure the fulfillment of a given mission. The paper provides a comprehensive overview of spacecraft formation flight control. The bibliography is divided into...

The development of automation technologies in various fields of human life poses the problem of studying human-machine systems interaction and the influence of human on machine actions. The varied human behavior and the complexity of his central nervous system organization are a disability to his mathematical description. However, despite this, the...

The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine-Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are...

Artificial intelligence is becoming an increasingly popular tool in more and more areas of technology. New challenges in control systems design and application are related to increased productivity, control flexibility, and processing of big data. Some kinds of systems require autonomy in real-time decision-making, while the other ones may serve as...

The paper is devoted to development of the speed-gradient method in the IPME RAS in 1986–2021 and its applications to the problems of mechanical engineering.KeywordsSpeed gradientMechanical engineeringNonlinear dynamicsControlAdaptationIdentificationEnergyOscillations

In the paper, a new adaptive model of a neuron based on the Hindmarsh–Rose third-order model of a single neuron is proposed. The learning algorithm for adaptive identification of the neuron parameters is proposed and analyzed both theoretically and by computer simulation. The proposed algorithm is based on the Lyapunov functions approach and reduce...

The talk is devoted to research and suppression of hidden oscillations in manned aircraft flight altitude control. Active action from the pilot during landing can lead to saturation in the speed of the steering surface drive, and due to the erroneous reaction of the pilot, cause the appearance of hidden oscillations of the aircraft (the so-called p...

This work is devoted to the study of the possibility of the appearance and localization of hidden vibrations in the system of adaptive suppression of the flexural-torsional flutter of the wing. The control algorithm, built in the form of a modified adaptive controller with an implicit reference model, uses measurements of the wing torsion angle and...

The paper is devoted to the problem of controlling the rotation speed of unbalanced rotors of a vibration machine. The solution to this problem is important for vibration technologies, such as transportation and mixing of bulk media. Since the characteristics of the rotor drives can vary in the wide range depending on the mode (operating rotation s...

The present paper focuses on the robustness issues of the speed-gradient energy control design for the one-dimensional sine-Gordon system. The energy stabilization of a non-zero level is addressed as the energy reference tracking problem. In the paper, the “relay” speed gradient algorithm, using state feedback with in-domain actuators, is designed...

In the paper, the adaptive synchronization problem is studied for a class of time-varying nonlinear systems. The only assumption imposed is the boundedness of the rate of change of the controlled system parameters, while the initial uncertainty can be quite large. The adaptation algorithms in the discrete-time form are derived based on adaptive con...

In the paper, a digital control law for adaptive suppression of the flexural-torsional wing flutter has been developed and analyzed. The control law uses measurements of the wing twist angle (“angle of attack”) and its time derivative. The implicit reference model (IRM) method was used for the synthesis of the so-called “simple adaptive controller”...

In this paper, the closed-loop human-machine system is studied under the framework of the control systems theory. The human operator model is considered concerning the human's ability for adaptation to the current operational conditions. For flying vehicles this property corresponds the crossover model by McRuer. In the paper, the actuator is model...

In the paper the adaptive synchronization problem is studied for a class of time-varying non-linear systems. A number of approaches to the control of such systems are based on the construction of an internal model of parameter variations. In this paper, the only assumption imposed is the boundedness of the rate of change of the controlled system pa...

In the paper, the problem of forming and maintaining the small satellites formation in the near-earth projected circular orbits is considered. The satellite formation reconfiguration and formation-keeping control laws are proposed by employing the passivity-based output feedback control. For the complete nonlinear and time-dependent dynamics of the...

The paper focuses on a manned aircraft landing control system. It is known that actuator level and rate limitations can cause pilot-induced oscillations. This phenomenon occurs during intensive pilot control in a closed-loop system under certain initiating conditions associated with both the influence of the external environment and changes in the...

In the paper the problem of multiple controlled synchronization of a pair of unbalanced rotors is considered. A new bidirectional control law is proposed for multiple synchronization of rotors. A linear analysis of the dynamics of a simplified system model is presented, demonstrating the control system robustness with respect to the parameters of t...

The paper is devoted to preventing oscillations in the angular motion of piloted aircraft by the pseudo-linear correcting device. The prime cause of this event is the unfavorable interaction between the pilot and the vehicle or the so-called pilot-induced oscillations. In this connection, it becomes necessary to consider the human influence on the...

The survey examines the current state of the speed gradient method, developed in the1970–80s for synthesizing control and adaptation algorithms in nonlinear systems, as well asnumerous applications of the method to solving scientific and engineering problems. Briefinformation about speed gradient algorithms and conditions of their applicability, op...

In the paper a flight control system for a piloted aircraft on the pitch angle is considered, taking into account the rate saturation of the aircraft controlling surface. To prevent occurrence of the non-linear pilot-involved oscillations (PIO), a nonlinear correcting device is introduced into the control loop. On the basis of the pilot’s adaptatio...

Depending on the flight mode, the airflow can either damp aircraft oscillations, or, conversely, the oscillating structure takes energy from the incoming flow, as a result of which a rapid increase in amplitude of oscillations may occur. This dangerous phenomenon has become a significant obstacle to the development of high-speed aviation. Since the...

The paper deals with the navigation data exchange between two satellites moving in a swarm. It is focused on the reduction of the inter-satellite demanded communication channel capacity taking into account the dynamics of the satellites relative motion and possible erasures in the channel navigation data. The feedback control law is designed ensuri...

The paper is focused on the navigation data exchange between two satellites moved in a swarm. The feedback control law is designed ensuring regulation of the relative satellites motion. The adaptive binary coding/decoding procedure for data transmission over the limited capacity communication channel is proposed and studied for the cases of ideal a...

This work is the second part of a survey devoted to disturbance observers that appeared in the theory and practice of automatic control back in the mid-1960s. The first part of the survey was devoted to theoretical results. This part of the survey is devoted to practical application of disturbance observers. We consider such applications as control...

The survey is devoted to an exposition of the history of development and the current state of theoretical methods for constructing disturbance observers, whose appearance in control theory and practice dates back to the middle of the 1960s and is associated with the expansion of algebraic methods in controller synthesis, the emergence of computer-b...

Roll angular motion of the modern aircraft operating in non-linear flight modes with a high angle of attack often demonstrates the limit cycle oscillations, which is commonly known as the wing rock phenomenon. Wing rock dynamics are represented by a substantially non-linear model, with parameters varying over a wide range, depending on the flight c...

The present survey paper provides a historical overview of the method of passification and its applications to nonlinear and adaptive control problems from 1980 to present days.

This brief is devoted to the experimental study of possibilities for control of the phase shift between two vibration actuators. The control laws for frequency stabilization simultaneously with the prescribed phase shift between the rotors angular positions are proposed and experimentally studied by means of the mechatronic vibration test bed. It i...

The present investigation focuses on the output energy control of the nonlinear sine-Gordon model in a practical situation where only spatially sampled sensing and actuation are available. The speed-gradient method that has corroborated its utility for the sine-Gordon model, controlled through the manipulable parameters of the external field and bo...

The paper is devoted to such an important problem of piloted aircraft control as an unfavorable aircraft-pilot coupling. Mainly, the so-called Pilot-Induced Oscillations, i.e., long uncontrolled irregular oscillations which may happen due to the controlling surface magnitude and rate limitations when pilot attempts to control the aircraft with the...

The paper provides a historical overview of the Speed-gradient method and its applications to adaptive control and identification problems since mid-1970-th, when the method was originated, till the present days. It is demonstrated that it is an efficient and an useful tool for solving a wide range of engineering problems.

The paper is devoted to the numerical performance evaluation of the speed-gradient algorithms, recently developed in (Orlov et al., 2018; Orlov et al., 2019) for controlling the energy of the sine-Gordon spatially distributed systems with several in-domain actuators. The influence of the level quantization of the state feedback control signal (poss...

In the paper the energy control problems for Frenkel–Kontorova Model are posed and their connection to the pendula chains control is discussed. Speed-gradient based energy control algorithm is proposed and analyzed. Simulation results illustrating the convergence of the proposed algorithm are presented.

In this paper, we present and numerically study an adaptive coding procedure for data transfer among quadrotors moving in a formation. The quadrotor’s parameters are identified using experimental data from a digital communication channel with limited bandwidth. We compare the obtained results with theoretical expectations and illustrate the efficie...

The output energy control is developed for 1-D string model with fixed endpoints. It is considered a practical situation where a finite number of spatially-sampled sensing and actuation are available. First, the speed-gradient method is generalized in the present framework to pump/dissipate the energy of underlying model to a desired level provided...

A new control problem is posed and solved: regulation problem for the one-dimensional Klein-Gordon and semilinear wave equations with Neumann boundary conditions in the case when the control acts at both ends of the space interval (“two-point control”). A control algorithm based on the speed-gradient method is proposed. The global exponential stabi...

The paper is devoted to experimental study of possibilities for consensus control of the unbalanced rotors for the machine used in the vibration technology. This problem is treated as an ensuring the prescribed phase shift between the vibrating rotor actuators and has a significant value for the various kinds of the vibration technology, such as vi...

In the paper, the control problem with limitations on the magnitude and rate of the control action in aircraft control systems, is studied. Existence of hidden limit cycle oscillations in the case of actuator position and rate limitations is demonstrated by the examples of piloted aircraft PIO phenomenon and the airfoil flutter suppression system.

In the paper the quadrotor spatial motion adaptive control based on the passification method is considered. It is assumed that adaptive controller for quadrotor attitude is already designed and the attention is focused on the quadrotor spatial motion control. Problem of quadrotor group motion in the formation with adaptive positioning controller is...

Modern aircraft, operating in nonlinear flight regimes at high angle of attack often exhibit a limit cycle oscillation in the roll angle known as the ”wing rock phenomenon.” When the wing rock appears, the roll angle trajectory undergoes oscillations of growing amplitude and asymptotically converges to the stable limit cycle. The wing rock dynamics...

In the paper the coordinated flight of an autonomously controlled group of UAVs is considered. In the system, the position information exchange between the separate group agents for keeping the formation shape and fulfillment the prescribed flight mission is organized. Data transferring quality, as one of the most important navigation problems, is...

Foundations for the passification method were laid out by A.L. Fradkov in 1974 in the context of the adaptive stabilization problem for the output of a linear dynamic plant. Over the past decade, the passification method has been further developed, and new applications have appeared both in the field of systems theory and in practical control probl...

The boundary energy control problem for the sine-Gordon and the nonlinear Klein–Gordon equations is posed. Two control laws solving this problem based on the speed-gradient method with smooth and nonsmooth goal functions are proposed. The control law obtained via a nonsmooth goal function is proved to steer the system to any required nonzero energy...

In this paper the output feedback energy control problem for the sine-Gordon model is studied. An observer for the sine-Gordon equation and a speed-gradient boundary control law for solving this problem are analysed. Explicit inequalities on system's parameters ensuring the exponential decay of the estimation error are obtained. Under an additional...

We study synchronization of nonlinear systems with robustness to disturbances that arise when measurements sent from the master system to the slave system are affected by quantization and time sampling. Viewing the synchronization problem as an observer design problem, we invoke a recently developed theory of nonlinear observers robust to output me...

In the paper, the Simple Adaptive Control scheme based on the implicit reference model and the passification theorem is designed for active suppressing the airfoil flutter. This approach leads to low-order adaptation algorithms despite that the plant model order may be high. Another merit of such a kind of adaptive controllers is a possibility of u...

In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman's conjecture (as well as Aizerman's) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of ab...

The paper deals with development of algorithm for non-linear observers using the Pecora-Carroll scheme for information transmission by modulation chaotic signal and investigation of the accuracy of information coding based on robust synchronization with qDES observer, taking into account the possible distortion of data during transmission over the...

In the paper, the control problem with limitations on the magnitude and rate of the control action in aircraft control systems, is studied. Existence of hidden oscillations in the case of actuator position and rate limitations is demonstrated by the examples of piloted aircraft pilot involved oscillations (PIO) phenomenon and the airfoil flutter su...

The kinematics and dynamics of a Stewart platform supported by six pneumocylinders are considered. The differential equations of motion are written, and the forces providing the fulfillment of the formulated law of motion are calculated. The inertia and weight of pneumocylinders are introduced into consideration to refine the equations of motion. T...

An energy control problem is analyzed in the PDE (partial differential equation) setting. As opposed to the existing literature, the present control goal addresses not only decreasing the plant energy but also its increasing what is important, e.g., in vibrational technologies, in studying wave motion, etc. A benchmark linear wave equation, governi...

This review is devoted to the control problem with constraints on the magnitude and rate of change of the control action in aircraft control systems. In engineering practice, it is accepted to use actuators with a sufficiently large level of magnitude and energy supply. Theoretical investigations in the field of systems with saturation in the contr...

A general form of a distributed feedback control algorithm based on the speed–gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential e...

In the paper, the results of the Passification Method with the Implicit Reference Model (IRM) approach are applied for designing the simple adaptive controller for quadrotor attitude. The IRM design technique makes it possible to relax the matching condition, known for habitual MRAC systems, and leads to simple adaptive controllers, ensuring fast t...

For Lorenz-like systems with volume contractions, analytical criteria for the global stability and instability of stationary sets are obtained. Numerical experiments for the study of the qualitative behavior of trajectories of Lorenz-like systems are described and analyzed. It is shown that their interpretation can lead to incorrect conclusions unl...

In the paper, the properties of the novel mechatronic set-up – the Vibration Stand are studied. The set-up consists of a spring-suspended platform with electrically driven unbalanced rotors, a personal computer for control of the stand and processing the data of experiments, set of sensors, computer interface facilities and an amplification-transfo...

In the paper, the procedure of adaptive coding for data transmission between quadrotors, moving in formation, is presented and numerically studied. Quadrotor parameters identification is fulfilled based on processing the experimental data. The results are compared with the theoretical statements. Efficacy of the adaptive coding procedure is shown.

In this work the method of communication and maintenance of integrity of data in the decentralized network of autonomous mobile robots is suggested. The software and hardware feasibility of such method is proposed. For collective storage and maintain integrity of data in decentralized group of mobile robots the algorithm of checksum calculations is...

The paper is devoted to studying and prevention of a special kind of oscillations-the Pilot Involved Oscillations (PIOs) which may appear in man-machine closed-loop dynamical systems. The PIO of categories II and III are defined as essentially non-linear unintended steady fluctuations of the piloted aircraft, generated due to pilot efforts to contr...

The boundary energy control problem for the sine-Gordon equation is posed. Two control laws solving this problem based on Speed-Gradient method with smooth and nonsmooth goal functions are proposed. The control law obtained via a nonsmooth goal function is proved to steer the system to any required nonzero energy level in finite time. The results o...

In the paper the results of first experimental studies with the setup are described, including motor parameters identification, state estimation and control of rotation velocity. The presented results demonstrate that the setup is useful for study and for control of complex nonlinear oscillatory systems.

In the paper we study the problem of control under the magnitude and rate limitations imposed to the control input in application to flight control systems. In the case of the control surfaces magnitude and rate limitations, the self-oscillations of considerable amplitude may occur, which is often reffered to as “the loss of stability in large”. If...

Energy control problems are analyzed for infinite dimensional systems. Benchmark linear wave equation and nonlinear sine-Gordon equation are chosen for exposition. The relatively simple case of distributed yet uniform over the space control is considered. The speed-gradient method (Fradkov,1996) that has already successfully been applied to numerou...