Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140505
A. Antipov, S. Krasnova
The tracking problem for the twin rotor MIMO electromechanical system is considered in the conditions of parametric uncertainties and under action of uncontrolled external disturbances. According to the block approach, the two procedures with the different types of local feedbacks are developed for the solution of the problem: with the nonlinear and with the piecewise-linear functions in feedbacks. These functions provide invariance to disturbances and satisfaction of the restrictions on the state variables and control actions.
{"title":"Block Approach to Controlling a Twin Rotor Electromechanical System","authors":"A. Antipov, S. Krasnova","doi":"10.1109/STAB49150.2020.9140505","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140505","url":null,"abstract":"The tracking problem for the twin rotor MIMO electromechanical system is considered in the conditions of parametric uncertainties and under action of uncontrolled external disturbances. According to the block approach, the two procedures with the different types of local feedbacks are developed for the solution of the problem: with the nonlinear and with the piecewise-linear functions in feedbacks. These functions provide invariance to disturbances and satisfaction of the restrictions on the state variables and control actions.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128993880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140491
V. Saurin, V. Poliakov
The paper studies the modeling and optimization of the dynamic behavior of heterogeneous beam structures. Usually, a boundary-value problem is formulated as a general differential equation with variable coefficients. One of the common characteristic features inherent in boundary-value problems of mathematical physics is a certain ambiguity in their formulation. By introducing new variables that characterize the behavior of the system, the boundary-value problem reduces to three ordinary differential equations with variable coefficients. New variables have a clear physical meaning. One function is the linear momentum density, and the other a bending moment in the beam cross section. Such a formulation of the problem of free vibrations of a beam of variable cross section allows us to reduce the system of differential equations to one fourth-order equation, but written in terms of the momentum or moments functions. This equations are equivalent to the original one formulated in displacements, but have different forms. The state equations are taken into account integrally in accordance with the ideas of the method of integrodifferential relations. A numerical algorithm is developed for solving direct and inverse problems of the beam dynamics with variable cross section based on the Ritz method and the technique of semidiscrete polynomial approximations of the desired functions. The effectiveness of the approach is demonstrated by the example of controlled movements of a thin rectilinear elastic inhomogeneous rod. The control problem is to optimally transfer the rod from the initial to the given final state. The results of numerical analysis are presented.
{"title":"A variational approach to modeling and optimization of the dynamics for an elastic beam with variable cross section","authors":"V. Saurin, V. Poliakov","doi":"10.1109/STAB49150.2020.9140491","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140491","url":null,"abstract":"The paper studies the modeling and optimization of the dynamic behavior of heterogeneous beam structures. Usually, a boundary-value problem is formulated as a general differential equation with variable coefficients. One of the common characteristic features inherent in boundary-value problems of mathematical physics is a certain ambiguity in their formulation. By introducing new variables that characterize the behavior of the system, the boundary-value problem reduces to three ordinary differential equations with variable coefficients. New variables have a clear physical meaning. One function is the linear momentum density, and the other a bending moment in the beam cross section. Such a formulation of the problem of free vibrations of a beam of variable cross section allows us to reduce the system of differential equations to one fourth-order equation, but written in terms of the momentum or moments functions. This equations are equivalent to the original one formulated in displacements, but have different forms. The state equations are taken into account integrally in accordance with the ideas of the method of integrodifferential relations. A numerical algorithm is developed for solving direct and inverse problems of the beam dynamics with variable cross section based on the Ritz method and the technique of semidiscrete polynomial approximations of the desired functions. The effectiveness of the approach is demonstrated by the example of controlled movements of a thin rectilinear elastic inhomogeneous rod. The control problem is to optimally transfer the rod from the initial to the given final state. The results of numerical analysis are presented.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130039024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140515
M. Dosaev, L. Klimina, B. Lokshin, E. Shalimova, Ching-Huei Lin
Mathematical model of a double-rotor vertical axis wind turbine is studied. Aerodynamic and electromechanical load is taken into account. The model is represented in the form of a fourth-order dynamical system. Under some assumptions about initial conditions and parameters, an averaging of the system over two angles is performed. Fixed points of the averaged system are studied as an initial approximation for operation modes of the wind turbine.
{"title":"Double-Frequency Averaging in the Dynamical Model of a Double-Rotor Wind Turbine","authors":"M. Dosaev, L. Klimina, B. Lokshin, E. Shalimova, Ching-Huei Lin","doi":"10.1109/STAB49150.2020.9140515","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140515","url":null,"abstract":"Mathematical model of a double-rotor vertical axis wind turbine is studied. Aerodynamic and electromechanical load is taken into account. The model is represented in the form of a fourth-order dynamical system. Under some assumptions about initial conditions and parameters, an averaging of the system over two angles is performed. Fixed points of the averaged system are studied as an initial approximation for operation modes of the wind turbine.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"392 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124594720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140553
M. Gusev
The reachable sets of nonlinear systems are usually quite complicated. They, as a rule, are non-convex and arranged to have rather complex behavior. In this paper, the asymptotic behavior of reachable sets of nonlinear systems affine in control variables at small time intervals is studied. We assume that the initial state of the system is fixed, and the control is bounded in the L2 norm. The subject of the study is the applicability of the linearization method for a sufficiently small length of a time interval. We provide sufficient conditions under which the reachable set of a nonlinear system is convex and asymptotically equal to the reachable set of a linearized system. The concept of asymptotic equality is determined using the Banach-Mazur metric in the space of sets.
{"title":"On Applicability of Linearization Approach in Calculating Small-Time Reachable Sets of Nonlinear Control Systems","authors":"M. Gusev","doi":"10.1109/STAB49150.2020.9140553","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140553","url":null,"abstract":"The reachable sets of nonlinear systems are usually quite complicated. They, as a rule, are non-convex and arranged to have rather complex behavior. In this paper, the asymptotic behavior of reachable sets of nonlinear systems affine in control variables at small time intervals is studied. We assume that the initial state of the system is fixed, and the control is bounded in the L2 norm. The subject of the study is the applicability of the linearization method for a sufficiently small length of a time interval. We provide sufficient conditions under which the reachable set of a nonlinear system is convex and asymptotically equal to the reachable set of a linearized system. The concept of asymptotic equality is determined using the Banach-Mazur metric in the space of sets.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130663737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140551
V. Tkhai
We study a mechanical system subject to the action of positional forces. It is assumed that, on a fixed set of the system, the acting force is nonzero everywhere except for the equilibrium points. We study symmetric periodic motions (SPMs). The general theorem on the global bilateral extension of the SPM to the boundary of the region of existence of the SPMs is proved. The global continuation of the Lyapunov family with the inheritance of a monotonic change in the period is given. It is shown that when the period decreases, the family goes to infinity, accompanied by a period tending to zero. An increase in the period on the family occurs unlimitedly. In this case, the family either goes to infinity, or adjoins a saddle-type equilibrium. In this way the center and the saddle are connected by a family of symmetric oscillations. Poincare law on the change in the nature of equilibria extends to a system with n > 1 degrees of freedom. All families of DNA base pair oscillations that bind equilibria are found.
{"title":"A Family of Oscillations That Connects Equilibria","authors":"V. Tkhai","doi":"10.1109/STAB49150.2020.9140551","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140551","url":null,"abstract":"We study a mechanical system subject to the action of positional forces. It is assumed that, on a fixed set of the system, the acting force is nonzero everywhere except for the equilibrium points. We study symmetric periodic motions (SPMs). The general theorem on the global bilateral extension of the SPM to the boundary of the region of existence of the SPMs is proved. The global continuation of the Lyapunov family with the inheritance of a monotonic change in the period is given. It is shown that when the period decreases, the family goes to infinity, accompanied by a period tending to zero. An increase in the period on the family occurs unlimitedly. In this case, the family either goes to infinity, or adjoins a saddle-type equilibrium. In this way the center and the saddle are connected by a family of symmetric oscillations. Poincare law on the change in the nature of equilibria extends to a system with n > 1 degrees of freedom. All families of DNA base pair oscillations that bind equilibria are found.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"764 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132936243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140548
A. Andreev, O. Peregudova
In this paper, an overview of the direct Lyapunov method development in the motion stabilization problem of multi-link robot manipulators is presented. Various robot models are considered such as ones with prismatic and cylindrical joints taking into account the elasticity properties of the connecting elements of the links.
{"title":"The Direct Lyapunov Method in the Motion Stabilization Problems of Robot Manipulators","authors":"A. Andreev, O. Peregudova","doi":"10.1109/STAB49150.2020.9140548","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140548","url":null,"abstract":"In this paper, an overview of the direct Lyapunov method development in the motion stabilization problem of multi-link robot manipulators is presented. Various robot models are considered such as ones with prismatic and cylindrical joints taking into account the elasticity properties of the connecting elements of the links.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129738662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140467
A. Kanatnikov, O. Tkacheva
The work is devoted to the construction of an asymptotic observer for a pacemaker model based on the Van der Pol equation. The cardiac system can be represented as a combination of three oscillatory circuits: the sino-atrial node (pacemaker), the atrio-ventricular node, and the ventricular conducting system, models of which can be constructed using the Van der Pol equation. In practice, only the values of the potentials of the nodes are measurable, while the rates of their changes are not directly measured. The work of the asymptotic observer with linear dynamics of error constructed in the work is illustrated by the mathematical modeling.
本文研究了基于Van der Pol方程的起搏器模型的渐近观测器的构造。心脏系统可以表示为三个振荡回路的组合:窦房结(起搏器)、房室结和心室传导系统，其模型可以使用Van der Pol方程构建。在实践中，只有节点的电位值是可测量的，而它们的变化率是不能直接测量的。用数学模型说明了文中构造的具有线性误差动力学的渐近观测器的工作。
{"title":"Observer for a pacemaker model based on the van der Pol equation","authors":"A. Kanatnikov, O. Tkacheva","doi":"10.1109/STAB49150.2020.9140467","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140467","url":null,"abstract":"The work is devoted to the construction of an asymptotic observer for a pacemaker model based on the Van der Pol equation. The cardiac system can be represented as a combination of three oscillatory circuits: the sino-atrial node (pacemaker), the atrio-ventricular node, and the ventricular conducting system, models of which can be constructed using the Van der Pol equation. In practice, only the values of the potentials of the nodes are measurable, while the rates of their changes are not directly measured. The work of the asymptotic observer with linear dynamics of error constructed in the work is illustrated by the mathematical modeling.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124229765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140701
A. Masterova, Y. Selyutskiy, A. Zubkov, R. Garziera
An empirical model intended for describing the aerodynamic torque acting upon Savonius rotor is proposed. This model allows for parametric analysis of complex mechanical and electromechanical systems containing Savonius rotor using methods of the general mechanics and the theory of dynamical systems. The model is verified using wind tunnel experiments. As an example, a wheeled cart driven by Savonius rotor is considered. Numerical simulation of dynamics of such cart is performed.
{"title":"On Empirical Model of Aerodynamic Torque Acting on Savonius Rotor","authors":"A. Masterova, Y. Selyutskiy, A. Zubkov, R. Garziera","doi":"10.1109/STAB49150.2020.9140701","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140701","url":null,"abstract":"An empirical model intended for describing the aerodynamic torque acting upon Savonius rotor is proposed. This model allows for parametric analysis of complex mechanical and electromechanical systems containing Savonius rotor using methods of the general mechanics and the theory of dynamical systems. The model is verified using wind tunnel experiments. As an example, a wheeled cart driven by Savonius rotor is considered. Numerical simulation of dynamics of such cart is performed.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128757454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140645
M. Morozov
This paper considers periodic selector-linear differential inclusions with asymptotically stable sets. The criterium of asymptotic stability is obtained by means of the variational technique and the equivalence of the properties of uniform asymptotic stability and uniform exponential stability for the considered class of inclusions is proved.
{"title":"On Stability of Periodic Selector-Linear Differential Inclusions with Asymptotically Stable Sets","authors":"M. Morozov","doi":"10.1109/STAB49150.2020.9140645","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140645","url":null,"abstract":"This paper considers periodic selector-linear differential inclusions with asymptotically stable sets. The criterium of asymptotic stability is obtained by means of the variational technique and the equivalence of the properties of uniform asymptotic stability and uniform exponential stability for the considered class of inclusions is proved.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117029206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140479
Y. Dolgii, A. Sesekin
The problem of optimal impulse stabilization for a linear autonomous system with aftereffect and quadratic quality criterion is considered. The optimal stabilization problem is formalized as an extreme problem in the functional spaces of states and control. A system of governing equations is obtained for the coefficients of the quadratic Bellman functional. The optimal stabilizing control is found.
{"title":"Optimal pulse stabilization of autonomous linear systems of differential equations with aftereffect","authors":"Y. Dolgii, A. Sesekin","doi":"10.1109/STAB49150.2020.9140479","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140479","url":null,"abstract":"The problem of optimal impulse stabilization for a linear autonomous system with aftereffect and quadratic quality criterion is considered. The optimal stabilization problem is formalized as an extreme problem in the functional spaces of states and control. A system of governing equations is obtained for the coefficients of the quadratic Bellman functional. The optimal stabilizing control is found.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131034424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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