The problem of feedback linearization (FL) of continuous and discrete nonlinear MIMO systems is considered. The idea of FL method consists in converting the original nonlinear system into a linear one by means of feedback. Then, the methods of control theory for linear systems are used for system design. A widespread approach to FL design is based on the method of normal form, that uses a nonsingular transformation of system state variables z = T(x). In order to obtain a normal form of the nonlinear system in the neighbor of a some point, it is necessary to determine a special function - the system virtual output, for which a relative degree (in the case of single input) or a vector relative degree (in the case of multiple input) is determined. Applicability of the normal form method for FL is provided by the conditions of controllability and involutivity for the considered nonlinear system, which are not always true. Moreover, when developing a linearizing control law, the main difficulty lies in the transition from transformed variables z to state variables x of the original system. In this paper, we propose another approach, based on representing the original nonlinear system into a state-dependent coefficient form and applying the canonical similarity transformation z = T(x)x, that allow getting the system to canonical form, that considerably simplifies the FL problem. Such similarity transformation allow accomplishing linearization of system without determining of the virtual system output. Another advantage of the proposed method is that the technique of the transition from the transformed variables z to the state variables x of the original system is simpler. The results are illustrated by examples for continuous and discrete nonlinear systems.

It is can identify three main classes of problems broadly characterizing partial stability of a dynamical systems, viz., (1) stability with respect to a part of the variables of the zero equilibrium position (Lyapunov-Rumyantsev partial stability problem), (2) stability of the "partial"zero equilibrium position, and (3) stability with respect to a part of the variables of the "partial"zero equilibrium position. In the problem of stability with respect to a part of the variables of the zero equilibrium position of systems of ordinary differential equations with continuous right-side assumes the domain of initial perturbations to be a sufficiently small neighborhood of the zero equilibrium position. Along with this statement, the case then initial perturbations can be large with respect to one part of non-controlled variables and arbitrary with respect to their other part is also considered. On the other hand, for stability problem of "partial" zero equilibrium positions of systems of ordinary differential equations also naturally assume that initial perturbations of variables that do not define the given equilibrium position can be large with respect to one part of the variables and arbitrary with respect to their other part. Contrary the assumptions that initial perturbations of this variables are either only arbitrary or only large the combined assumption made it possible an admissible trade-off between the meaning sense for notion of stability and the respective requirements on the Lyapunov functions. The article studies the problem of partial stability for nonlinear discrete-time systems: stability with respect to a part of the variables of "partial" equilibrium position. Initial perturbations of variables that do not define the given equilibrium position can be large (belonging to an arbitrary compact set) with respect to one part of the variables and arbitrary with respect to their other part. A conditions of stability of this type are obtained in the context of a discrete analog of the Lyapunov functions method, which generalize a number of existing results. Example is given. The problem of unification of process of studying partial stability problems of stationary and non-stationary nonlinear discrete-time systems is also discussed

We formulate and solve the problem of regulator design with minimal transient time (in terms of classical control theory) under specified constraints on control and overregulation. The problem is solved in a class of linear high-order control systems described by a transfer function having a constant in the numerator.The main stage of the proposed design approach consists in the determination of optimal transfer function of closed-loop control system with the structure composed by the sequential connection of specific number of aperiodic and oscillatory links. We prove the theorem establishing that for even order control systems these links must have the same values of time constants to provide the minimum transient time, and time constants must be selected from the condition of satisfying the control constraints. Correspondingly, damping coefficients of oscillatory links must be determined from the condition of providing the specified overregulation value of designed system. The theorem is proved for the special, but important for control practice case of specifying the permissible system overregulation value being equal to the value of the zone, using which the transient time of this control system is determined. This predetermine the possibility of theorem application to the solution (in the linear approximation) of so-called problem of time-optimality for one phase coordinate of an object, which is actual for engineering practice. Conditions of theorem are not only necessary, but also sufficient conditions of time-optimality for several subclasses of control systems. Systems with monotonic transient processes with prohibited overregulation having, correspondingly, only negative real poles are an example of such subclass. After determination of optimal transfer function of closed-loop control system subject to theorem conditions, it is recommended to perform regulator design providing the time-optimality by the synthesis method according to the desired transfer function or by the method of modal control depending on the technical conditions of regulator realization.

The links, presently used in most of the industrial robots-manipulators, are rigid and heavy, which allows us to neglect deformations during the working operations. Such kind of a robot has certain drawbacks: low speed; high energy consumption; low payload-to-weight ratio, etc. Application of the robots with lightweight links gives a number of advantages. Namely: better payload-to-weight ratio; higher speed of movement; increased safety; lower energy consumption; bigger working space with the use of lengthened links; and lower cost. However, such type of a manipulator has an essential drawback - flexibility of a link, which complicates its mathematical model. The flexible single-link manipulator considered in the article as a control object has been attractive for the control specialists for a long time. A regular approach to the design control systems begins with development of a mathematical model of a plant, which describes its dynamic properties in the best way. However, an analysis of the numerous articles and monographs on the problem revealed noticeable distinctions in the used mathematical models, while the initial data concerning the design and operation of the manipulator were the same. Especially this concerns the boundary conditions, the orthogonality conditions and expressions for the flexible mode shapes. In this paper all the formulas for the free and forced motions of the flexible manipulator were received only on the basis of the Hamilton's principle and assumed mode method, namely: the governing equation of motion - Euler-Bernoulli equations, boundary conditions, orthogonality conditions, expressions for the mode shapes and also finite dimensional approximation of the model in the state space. The development of the appropriate formulas is described in every detail.

Briefly considers the current state of the problem of precision measurement of parameters of capacitive sensors and measuring converters for their definition. It is established that at present, a proliferation of methods for the determination of parameters of capacitive sensors on individual instant values of the transition process in the measuring circuit when connected it to a DC voltage. In these methods the time measurement does not depend on the time constant of the measuring circuit, and is determined mainly by the measurement time of the instantaneous values of the signals and the implementation of the algorithm processing the measured values and the duration of the exemplary time interval. One of the problems arising in the implementation of measuring means fhaf use such methods, is fhe effect o/ unin/ormafive parameters o/ fhe measuring circuit and fheir instability on fhe result off fhe determination off in/ormafive parameters. Using fhe unin/ormafive elements off fhe equivalent circuit off fhe sensor allows fo determine fheir in/uence on in/ormafive parameters. A disadvantage off fhe known methods separate measurement sensors paramefers is fhaf fhey do nof allow fo de/ine along wifh fhe capacify fhe mulfiple unin/ormafive paramefers. The aim o/ fhis work is fo study a new method off measurement off parameters off capacitor sensors, which allows fo determine fhe resistance o/ fhe connecfing conducfors fhaf connecf fhe sensor fo fhe measuring circuif, and equivalenf resisfance due fo losses in fhe in-sulafing dielecfric and leakage currenfs, which allows fo increase fhe accuracy o/ measuremenf o/ capacifance.

Relay control systems are widely used in engineering. Simple construction, reliability and low cost are the main advantages of such systems. Relay control systems are used in industrial control systems and also in moving objects control systems. Real values of control system plant parameters almost always differ from design (nominal) values. /t also applies to relay self-oscillating control systems. Deviations of relay self-oscillating control system plant parameters may lead to perceptible reduction of input signals tracking accuracy, and in special case - to instability of periodic motions in the system. /t makes the system unusable. So it's very important to control parametrical sensitivity of system characteristics at the stage of relay self-oscillating system synthesis. With the participation of the authors of this article effective methods of research of nonlinear tracking relay self-oscillating systems parametrical sensitivity were developed. These methods allow to research parametrical sensitivity of the system periodic motions and the system tracking mode. /n this article the synthesis of the relay self-oscillating power volume hydraulic drive by setting limits on the sensitivity of its characteristics to changes of the pump drive motor rotation speed is considered using designed methods. Such hydraulic drives are often used in control systems of moving technical objects. The main drawbacks of volume hydraulic drives, which limits their application in tracking control systems, are difficulty of variable pump controlling and also significant dependence of drive characteristics on the rotation speed of the drive motor of the hydraulic pump. /ts instability adversely affects on accuracy characteristics and efficiency of the drive. As a result, the synthesis could provide high accuracy and efficiency of hydraulic drive.

Currently relevance of modeling problems of analysis and synthesis of mathematical models of discrete logic control and computing devices persists. Particularly important is fhe task of estimating fhe oufpuf of difficulty in presenting a Boolean function (BF) in fhe classes of formulas and schemes of functional elements (FE). This problem is sfill relevant today. Because of ongoing research in fhe field of mathematical cybernetics and discrete mathematics should be fhaf obtaining fhe required minimum solutions using dimensions of complexify inevitably involves fhe use of nature exhaustive search algorithms. The re-sulf is a greafer complexify (including compufafional complexify and labor inpuf) obfaining such a decision has fhe funcfions of small dimension. This required fhe development of new approaches formulation of fhe problem and ifs solutions, significantly differ in fhe complexify of exhaustive search [1-3]. So, fhe problem of fhe realization of Boolean functions in fhe class of formulas and - circuits made of functional elements in different bases. Obtained in this scheme are applied in discrete logic devices, and managemenf informafion processing, fhe complexify (qualify) of fhe main characferisfics of which depend on com-pufing and confrol engineering. And if nofed fhaf fhe symmefric Boolean funcfions are increasingly being used in fhe design of computing devices due fo fheir specific properties [7-8].The purpose of this paper is fo clarify fhe upper bounds for fhe complexify of symmetric BF in sfandarf and Zhegalkin bases, as well as fhe development of algorithms fo automate fhe synthesis of discrefe informafion processing devices. An efficienf consfrucfive mefhod synfesis of digifal circuifs and formulas is offered. This mefhod is based on recurrence relafions (funcfional equafions - FE [9]) and is accompanied by a receipf in advance analyfically upper esfimafes of various indicafors of complexify (fhe number of leffers, number of subformulas; according fo fhe number of functional elements), including schemes for minimum complexify. In this paper we consider some classes of func-fions, which are accurafe upper bounds for fhe complexify mefrics. To aufomafe fhe process and expanding fhe sfudy of individual cases fhe algorithm implemented structural and functional decomposition [2] is used. A convenient model for fhe rep-resenfafion of a Zhegalkin polynomial form fhaf used in fhe algorifhm fhe mafrix represenfafion has been designed. The resulfs are applicable as in fhe synthesis device (af fhe logical design) in multiprocessor computing and control systems, and fhe de-velopmenf of algorifhms for fhe effecfive operafion of fhese sysfems.

Thermal mode strip casting control is challenging at the present because twin-roll strip casting is characterized by the large time delay and high dynamics with low inertances. Nonlinearity and complexity of the thermal mode mathematical model, distribution and hard limitation of technological parameters are also the technology specific features and all it has a negative impact on fhe control and stability of fhe casting process. Famous control systems don'f fully allow ensure fhe implementation of given problems and need fo be revised. Thermal mode control system development is fhe complex problem fo date. Solution of this problem requires fo use special systems based on fhe new control principles. Structural synthesis of model-based predictive control sys-fems is creafed in fhis work. Disfincfive feafures of fhe proposed sfrucfure confrol scheme are fhe command module applicafion and ifs inferacfion wifh fhe moniforing and model seffing modules, providing real-fime opfimizafion performance and checking used models conformity with fhe real casting conditions. The proposed control system allows fo coordinate fhe casting and rolling processes temperature and speed modes. This system provides for fhe implementation of controlled rolling technology af fwin-roll strip casting unit by obtaining fhe required mass-average temperature of fhe strip before rolling in dynamic modes of operation. On fhe basis of simulafion resulfs if was concluded fhaf fhe proposed model-based predicfive confrol sysfem provides fransienf process sfabilify and safisfacfory femperafure confrol accuracy wifh confrollable and unconfrollable exfernal influences and sig-nificanf time delay caused by fhe strip movement from fhe casting mold fo fhe hof-rolling stand.

This article presents three-dimensional (3D) terminal guidance scheme for a spacecraft lunar landing maneuver. An analytical solution to a spacecraft terminal guidance problem for achieving the desired spot in the circumlunar space is proposed. The solution is obtained for constant acceleration trajectory when thrust throttling is used to maintain uniform braking deceleration. The pitch program and the yaw program are essentially linear with time. П achieve 6 terminal conditions (position and velocity terminal vectors components) 6 guidance law parameters are used: pitch angle and pitch rate, yaw angle and yaw rate, braking deceleration and time-to-go. The solution is executed in the coordinate frame associated with the desired terminal spot. Current spacecraft position and velocity relative to this frame is supposed to be known at any time during the guidance. The simulation results of spacecraft guidance and control using proposed solution are presented. Analysis of the simulation results validates the basic performance of the proposed terminal guidance scheme. It should be noted that as the proposed scheme presuppose thrust variation on an undisturbed trajectory it makes sense to look for ways of reducing of required throttling range. The next phase of this research will be intended to carrying out terminal errors analysis and comparison of the accuracy of the proposed scheme and some other schemes.