Pub Date : 2020-06-01DOI: 10.1109/STAB49150.2020.9140475
A. Ilyina, A. Krasinskiy
We consider mechatronic systems with nonlinear geometric constraints, cyclic coordinates and one or more electric drives with DC motors. It is assumed that control is carried out by changing the voltage on the anchor windings of the motors. The solvability condition for the nonlinear stabilization problem of possible stationary motions and a method for determining control actions are investigated. A mathematical model of the system dynamics is constructed using the Lagrange variables. The nonlinearity of the constraints was taking into account by means of the vector-matrix equations in the form of Shulgin with redundant coordinates. The equations of actuators dynamics were explicitly included into the constructed mathematical model. It is shown that the stability of stationary motions of such systems is possible only in critical cases. The number of zero roots of the characteristic equation is not less than the number of constraints. We analyze the structure of the obtained vector-matrix equations using the results of the theory of critical cases and then formulate a theorem on a sufficient condition for the stabilization of stationary motions. Coefficients of stabilizing effects can be found by the method of N. N. Krasovsky by solving the linear-quadratic stabilization problem for a controlled subsystem of lower dimension.
我们考虑具有非线性几何约束、循环坐标和一个或多个直流电动机的机电系统。假设控制是通过改变电机锚绕组上的电压来实现的。研究了可能静止运动的非线性镇定问题的可解性条件和确定控制动作的方法。利用拉格朗日变量建立了系统动力学的数学模型。利用带冗余坐标的舒尔金向量矩阵方程考虑了约束的非线性。将作动器动力学方程明确地包含在所构建的数学模型中。证明了这类系统的稳定运动只有在临界情况下才有可能。特征方程的零根个数不小于约束的个数。利用临界情况理论的结果，对得到的向量矩阵方程的结构进行了分析，并给出了静止运动稳定的充分条件定理。通过求解低维被控子系统的线性二次镇定问题，利用N. N. Krasovsky的方法可以求出镇定效应系数。
{"title":"Stabilization of steady motions of systems with geometric constraints and cyclic coordinates","authors":"A. Ilyina, A. Krasinskiy","doi":"10.1109/STAB49150.2020.9140475","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140475","url":null,"abstract":"We consider mechatronic systems with nonlinear geometric constraints, cyclic coordinates and one or more electric drives with DC motors. It is assumed that control is carried out by changing the voltage on the anchor windings of the motors. The solvability condition for the nonlinear stabilization problem of possible stationary motions and a method for determining control actions are investigated. A mathematical model of the system dynamics is constructed using the Lagrange variables. The nonlinearity of the constraints was taking into account by means of the vector-matrix equations in the form of Shulgin with redundant coordinates. The equations of actuators dynamics were explicitly included into the constructed mathematical model. It is shown that the stability of stationary motions of such systems is possible only in critical cases. The number of zero roots of the characteristic equation is not less than the number of constraints. We analyze the structure of the obtained vector-matrix equations using the results of the theory of critical cases and then formulate a theorem on a sufficient condition for the stabilization of stationary motions. Coefficients of stabilizing effects can be found by the method of N. N. Krasovsky by solving the linear-quadratic stabilization problem for a controlled subsystem of lower dimension.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"32 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":"125153110","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/STAB49150.2020.9140471
E. K. Kostousova
A conflict control problem for a linear discrete time system with two controls / disturbances is considered, where the aim of the first one is to steer the trajectory of the system into a given terminal set, whereas the aim of the second one is opposite. Two subproblems arise here, namely the approach problem and the evasion one. In the paper, a quick method for construction of feed-back controls for solving the evasion problem is proposed based on the calculation of parallelotope-valued tubes. An illustrative example is presented.
{"title":"On a Polyhedral Method for Solving an Evasion Problem for Linear Discrete-Time Systems","authors":"E. K. Kostousova","doi":"10.1109/STAB49150.2020.9140471","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140471","url":null,"abstract":"A conflict control problem for a linear discrete time system with two controls / disturbances is considered, where the aim of the first one is to steer the trajectory of the system into a given terminal set, whereas the aim of the second one is opposite. Two subproblems arise here, namely the approach problem and the evasion one. In the paper, a quick method for construction of feed-back controls for solving the evasion problem is proposed based on the calculation of parallelotope-valued tubes. An illustrative example is presented.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"2 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":"130546893","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/STAB49150.2020.9140489
I. Matrosov, Yury V. Morozov, A. Pesterev
A robot-wheel with a pendulum, which is described by a system of differential and algebraic equations, is considered. The problem of synthesizing control law is set that brings the system from an arbitrary initial position on a straight line to a given one, with the velocity of motion being limited. To solve this problem, a simpler, "reference," system of differential-algebraic equations is introduced the solutions of which satisfy the given phase and control constraints. Solutions of the reference system are taken to be the set of target trajectories for the original system. The feedback is found by numerical integration with projections of the original system together with the reference one. Results of numerical experiments demonstrate the effectiveness of the proposed approach.
{"title":"Control of the robot-wheel with a pendulum","authors":"I. Matrosov, Yury V. Morozov, A. Pesterev","doi":"10.1109/STAB49150.2020.9140489","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140489","url":null,"abstract":"A robot-wheel with a pendulum, which is described by a system of differential and algebraic equations, is considered. The problem of synthesizing control law is set that brings the system from an arbitrary initial position on a straight line to a given one, with the velocity of motion being limited. To solve this problem, a simpler, \"reference,\" system of differential-algebraic equations is introduced the solutions of which satisfy the given phase and control constraints. Solutions of the reference system are taken to be the set of target trajectories for the original system. The feedback is found by numerical integration with projections of the original system together with the reference one. Results of numerical experiments demonstrate the effectiveness of the proposed approach.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"498 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":"116326972","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/STAB49150.2020.9140463
Petr Makhmudov, V. Samsonov, M. Dosaev, L. Klimina, Y. Vershinin
The flat motion of a trolley rolling along a horizontal absolutely rough plane is considered. A guide is mounted on the trolley parallel to the line connecting the centers of mass of wheels. A slider moves along this guide. Slider motion control is carried out by setting its relative acceleration. An algorithm is proposed for the cyclic relative slider motion, leading to nonzero displacement of the trolley.
{"title":"Planning a motion of a wheeled robot controlled by a motion of internal mass","authors":"Petr Makhmudov, V. Samsonov, M. Dosaev, L. Klimina, Y. Vershinin","doi":"10.1109/STAB49150.2020.9140463","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140463","url":null,"abstract":"The flat motion of a trolley rolling along a horizontal absolutely rough plane is considered. A guide is mounted on the trolley parallel to the line connecting the centers of mass of wheels. A slider moves along this guide. Slider motion control is carried out by setting its relative acceleration. An algorithm is proposed for the cyclic relative slider motion, leading to nonzero displacement of the trolley.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"21 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":"126229159","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/STAB49150.2020.9140664
V. Boichenko, A. Belov
In this paper the spectral method of the analysis of continuous linear time-invariant systems is considered. Within the framework of this approach a novel result on σ-entropy norm computation in the state space is established.
{"title":"On Calculation of σ-entropy Norm of Continuous Linear Time-Invariant Systems","authors":"V. Boichenko, A. Belov","doi":"10.1109/STAB49150.2020.9140664","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140664","url":null,"abstract":"In this paper the spectral method of the analysis of continuous linear time-invariant systems is considered. Within the framework of this approach a novel result on σ-entropy norm computation in the state space is established.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"76 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":"133617468","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/STAB49150.2020.9140629
V. Smirnova, A. Proskurnikov, N. V. Utina
In this paper we go on with the analysis of the asymptotic behavior of Lur’e–type systems with periodic nonlinearities and infinite sets of equilibria. It is well known by now that this class of systems can not be efficiently investigated by the second Lyapunov method with the standard Lur’e–Postnikov function ("a quadratic form plus an integral of the nonlinearity"). So several new methods have been elaborated within the framework of Lyapunov direct method. The nonlocal reduction technique proposed by G.A. Leonov in the 1980s is based on the comparison principle. The feedback system is reduced to a low-order system with the same nonlinearity and known asymptotic behavior. Its trajectories are injected into Lyapunov function of the original system. In this paper we develop the method of nonlocal reduction. We propose a new Lyapunov–type function which involves both the trajectories of the comparison system and a modified Lur’e–Postnikov function. As a result a new frequency–algebraic criterion ensuring the convergence of every solution to some equilibrium point is obtained.
{"title":"Leonov’s method of nonlocal reduction for pointwise stability of phase systems","authors":"V. Smirnova, A. Proskurnikov, N. V. Utina","doi":"10.1109/STAB49150.2020.9140629","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140629","url":null,"abstract":"In this paper we go on with the analysis of the asymptotic behavior of Lur’e–type systems with periodic nonlinearities and infinite sets of equilibria. It is well known by now that this class of systems can not be efficiently investigated by the second Lyapunov method with the standard Lur’e–Postnikov function (\"a quadratic form plus an integral of the nonlinearity\"). So several new methods have been elaborated within the framework of Lyapunov direct method. The nonlocal reduction technique proposed by G.A. Leonov in the 1980s is based on the comparison principle. The feedback system is reduced to a low-order system with the same nonlinearity and known asymptotic behavior. Its trajectories are injected into Lyapunov function of the original system. In this paper we develop the method of nonlocal reduction. We propose a new Lyapunov–type function which involves both the trajectories of the comparison system and a modified Lur’e–Postnikov function. As a result a new frequency–algebraic criterion ensuring the convergence of every solution to some equilibrium point is obtained.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"45 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133782962","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/STAB49150.2020.9140662
S. Solodusha
An approach based on Volterra polynomials with vector input signals has been developed for numerical modeling of the process of controlling the dynamics of an "input-output" type object. The nonparametric identification problem is considered as a conjugate one with respect to the deconvolution problem. The paper focuses on a new algorithm of identifying Volterra polynomials of the second degree that is based on the active experiment by the test sets of inputs. New classes of Volterra integral equations of the first kind are defined. They appear when the duration of the rise front is taken into account in test signals. The test signals are chosen considering specific features of the inputs arising in practice as applied to dynamics of wind turbines with horizontal rotation axis. The inversion formulas for indicated classes of one-and two-dimensional Volterra integral equations of the first kind are obtained.
{"title":"New Classes of Volterra Integral Equations of the First Kind Related to the Modeling of the Wind Turbine Dynamics","authors":"S. Solodusha","doi":"10.1109/STAB49150.2020.9140662","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140662","url":null,"abstract":"An approach based on Volterra polynomials with vector input signals has been developed for numerical modeling of the process of controlling the dynamics of an \"input-output\" type object. The nonparametric identification problem is considered as a conjugate one with respect to the deconvolution problem. The paper focuses on a new algorithm of identifying Volterra polynomials of the second degree that is based on the active experiment by the test sets of inputs. New classes of Volterra integral equations of the first kind are defined. They appear when the duration of the rise front is taken into account in test signals. The test signals are chosen considering specific features of the inputs arising in practice as applied to dynamics of wind turbines with horizontal rotation axis. The inversion formulas for indicated classes of one-and two-dimensional Volterra integral equations of the first kind are obtained.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"5 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":"133848176","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/STAB49150.2020.9140714
A. Andreev, O. Peregudova
In this paper, the trajectory tracking control problem of a mobile robot with four omni wheels is considered. The robot moves on a horizontal surface when the wheels slip. A dynamic model of the robot is constructed taking into account wheel slippage during braking. The movement of the wheeled robot is controlled by four independent direct current (DC) motors. Moreover, the torques developed by the engines are linear with respect to the voltage supplied to the engine and the angular velocity of the rotor. Based on the Lyapunov function method, a nonlinear control law is constructed that solves the trajectory tracking problem. Theorem on the asymptotic stability of the set of the closed-loop system equilibrium positions is proved.
{"title":"On the Trajectory Tracking Control of a Wheeled Mobile Robot Based on a Dynamic Model with Slip","authors":"A. Andreev, O. Peregudova","doi":"10.1109/STAB49150.2020.9140714","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140714","url":null,"abstract":"In this paper, the trajectory tracking control problem of a mobile robot with four omni wheels is considered. The robot moves on a horizontal surface when the wheels slip. A dynamic model of the robot is constructed taking into account wheel slippage during braking. The movement of the wheeled robot is controlled by four independent direct current (DC) motors. Moreover, the torques developed by the engines are linear with respect to the voltage supplied to the engine and the angular velocity of the rotor. Based on the Lyapunov function method, a nonlinear control law is constructed that solves the trajectory tracking problem. Theorem on the asymptotic stability of the set of the closed-loop system equilibrium positions is proved.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"341 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":"115450785","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/STAB49150.2020.9140560
M. Khrustalev
Necessary and, at the same time, sufficient conditions are obtained in the optimal control problem for systems described by ordinary differential equations with discontinuous right-hand sides.
对于右手边不连续的常微分方程所描述的系统，得到了最优控制问题的充分必要条件。
{"title":"Both Necessary and Sufficient Global Optimality Conditions for Discontinuous Dynamical Systems","authors":"M. Khrustalev","doi":"10.1109/STAB49150.2020.9140560","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140560","url":null,"abstract":"Necessary and, at the same time, sufficient conditions are obtained in the optimal control problem for systems described by ordinary differential equations with discontinuous right-hand sides.","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":"125850389","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/STAB49150.2020.9140488
V. N. Chestnov, D. V. Shatov
Robust stabilization problem for a linear multivariable system with parametric uncertainty is considered. In addition it is required to provide stability margins at the physical input/output of a control plant. Solution of the problem is based on a H∞ optimization formulated in the special way. Numerical solution of such a problem uses linear matrix inequalities (LMI) technique developed in the well-known MATLAB-package Robust Control Toolbox. Illustrative example of the considered problem solution is presented.
{"title":"Simultaneous Providing of Stability Margins Under Parametric Uncertainty and at a Plant Input/Output","authors":"V. N. Chestnov, D. V. Shatov","doi":"10.1109/STAB49150.2020.9140488","DOIUrl":"https://doi.org/10.1109/STAB49150.2020.9140488","url":null,"abstract":"Robust stabilization problem for a linear multivariable system with parametric uncertainty is considered. In addition it is required to provide stability margins at the physical input/output of a control plant. Solution of the problem is based on a H∞ optimization formulated in the special way. Numerical solution of such a problem uses linear matrix inequalities (LMI) technique developed in the well-known MATLAB-package Robust Control Toolbox. Illustrative example of the considered problem solution is presented.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"33 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":"129419905","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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