Authors: None

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00001

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: c1-c1

Authors: None

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00050

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: c4-c4

Authors: Brian D. O. Anderson; Arvin Dehghani

Abstract: This paper reviews three different types of challenges to adaptive control. The first group comprises challenges met in the subject's development. They include difficulties associated with the MIT rule, bursting, the Rohr's counterexample and unplanned instability in iterative identification and control. An understanding of these phenomena and mitigating strategies are now available. The second group comprises difficulties that are intrinsic to virtually any adaptive control algorithm, and that have frequently been overlooked. For example, if a plant is unknown, and a control objective is set, the objective may in practical terms be unachievable, and any adaptive control algorithm needs to deal with that possibility. The third group comprises some issues to which researchers are currently devoting significant attention, including multiple model adaptive control and model free design.

Keywords: adaptive control,adaptive systems,multiple model adaptive control,model free design

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00002

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 1-12

Authors: Felix L. Chernousko

Abstract: Progressive motions of two-mass systems in resistive media are analyzed. The motion control is implemented by means of periodic relative displacements of the masses. Different kinds of resistance forces acting upon the system are considered, including linear and nonlinear resistance depending on the velocity, as well as Coulomb's dry friction forces. Constraints are imposed on the relative displacements and velocities of the masses. Optimal periodic motions are determined that correspond to the maximal average speed of the system as a whole. Experimental data confirm the theoretical results obtained. Models of mobile minirobots are described which are based on the principle presented in the paper.

Keywords: multibody system,periodic motions,periodic control,optimal control,mobile robots

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00003

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 13-19

Authors: Miroslav Krstic; Andrey Smyshlyaev

Abstract: This paper presents several recently developed techniques for adaptive control of PDE systems. Three different design methods are employed--the Lyapunov design, the passivity-based design, and the swapping design. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. It is then shown how to extend the designs to reactionadvection-diffusion PDEs in 2D. Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.

Keywords: backstepping,distributed parameter systems,adaptive control

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00004

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 20-31

Authors: Anton S. Shiriaev; Leonid B. Freidovich; Ian R. Manchester

Abstract: This paper provides an introduction to several problems and techniques related to controlling periodic motions of dynamical systems. In particular, we define and discuss problems of motion planning and orbit planning, analysis methods such as the classical Poincaré first-return map and the transverse linearization, and exponentially orbitally stabilizing control designs. We begin with general nonlinear systems, and then specialize to a class of underactuated mechanical systems for which a particularly rich structure allows many of the problems to be solved analytically. The paper concludes with a discussion of numerical issues related to control design via periodic Riccati equations.

Keywords: transverse linearization,orbital stabilization,periodic motions,underactuated mechanical systems,virtual holonomic constraints

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00005

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 32-43

Authors: J. C. A. de Bruin; A. Doris; N. van de Wouw; H. Nijmeijer

Abstract: An experimental implementation of an output-feedback controller on a rotor dynamic system with set-valued friction is presented. The system exhibits coexisting stable/unstable equilibria and undesired friction-induced limit cycles. In the system, the friction and actuation are non-collocated, which prevents the application of standard friction compensation techniques. Therefore, an output-feedback control strategy is proposed that eliminates the friction-induced limit cycling, stabilizes the desired equilibrium and is robust for uncertainties in the friction model. The effectiveness of the proposed control strategy is shown both in simulations and experiments.

Keywords: setpoint control,discontinuous systems,set-valued friction,limit cycles

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00006

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 44-48

Authors: N. V. Kuznetsov; G. A. Leonov; H. Nijmeijer; A. Pogromsky

Abstract: The synchronization of two metronomes placed on a freely moving base is examined. The existence of an inphase regime is proved under special conditions.

Keywords: synchronization of metronomes,inphase regime

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00007

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 49-52

Authors: Igor Belykh; Vladimir Belykh; Martin Hasler

Abstract: We extend the connection graph stability method, originally developed for symmetrically coupled networks, to the general asymmetrical case. The principal new component of the method is the transformation of the directed connection graph into an undirected graph. The extension of the method to asymmetrical coupling consists in symmetrizing the graph and associating a weight to each path. This weight involves the node unbalance of the two nodes. The synchronization condition for this symmetrized-and-weighted network then also guarantees synchronization in the original non-symmetrical network.

Keywords:

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00008

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 53-58

Authors: A. Yu. Pogromsky; R. A. van den Berg; J. E. Rooda

Abstract: The paper deals with the performance analysis of harmonically forced nonlinear systems of Lur'e type.

Keywords: harmonic linearization,describing functions,periodic solutions,direct Lyapunov method

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00009

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 59-64

Authors: A. Pogromsky; H. Nijmeijer; J. E. Rooda

Abstract: A condition which ensures the absence of periodic orbits for nonsmooth dynamical systems is presented. A connection to methods for estimating the Hausdorff dimension is emphasized. For a class of hybrid systems described by a linear system with relay feedback the conditions are presented in the form of linear matrix inequalities.

Keywords: linearization,periodic solutions,direct Lyapunov method

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00010

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 65-70

Authors: D. V. Efimov; A. L. Fradkov

Abstract: The problem of resonance regime stabilization is considered for the case of unknown natural frequency of vibration machine. A solution for fourth order linear model of the machine with uncertain parameters, external disturbances and partial noisy measurements is proposed.

Keywords: resonance control,adaptive control,oscillations

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00011

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 71-76

Authors: Ilya V. Burkov

Abstract: In some cases the desired uniform motion may be described by a pair of first integrals of the system with zero control input. These two integrals and the integration of nonlinear function of saturation are used to construct Lyapunov function The control is designed from the condition of decreasing Lyapunov function on the trajectories of the closed loop system. This control may be chosen a priori bounded and linear in a small viciniti of the desired motion. This method is applied to stabilize rotating body beam, for damping the oscillations of blades of an elastic propeller and for stabilization of the uniform transition of the pendulum on a cart.

Keywords: Lyapunov methods,nonlinear systems,saturation,cranes,robots,damping

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00012

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 77-82

Authors: Yurii Dusavitskii

Abstract: It is accepted for the systems: autonomy, quick and slow motions, the feedback switchings with hysteresis, the variable structure on the intervals. The mathematical description is m differential equations of the nth order, which change one to another periodically. Some values of the intervals during (tk) are put under the cycles equations, which are changed into algebraic instead of transcendental. Then the surfaces for cycles (SC) are calculated and constructed. The switching conditions are put under SC. The intersections of the curves make the parameters of oscillations. It is proved the existence and the unique of SC. They have special points and lines and may by Multisheeted. It is possible to find the required switching conditions. There are two numerical examples.

Keywords: self-excited oscillations,cycles,switching

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00013

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 83-86

Authors: G. A. Leonov; N. V. Kuznetsov

Abstract: The new method for the computation of Lyapunov quantities for the second-order dynamical system, permitting us to narrow the requirements on a smoothness of system, is obtained.

Keywords: Lyapunov quantities,polynomial system,small amplitude limit cycle

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00014

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 87-89

Authors: Y. Orlov; L. T. Aguilar; L. Acho; A. Ortiz

Abstract: A well-known Van der Pol oscillator is modified to be introduced into the synthesis as an asymptotic harmonic generator of the periodic motion. The proposed modification possesses a limit cycle, producing a single harmonic as opposed to multi-harmonics of a standard harmonic oscillator. The parameters of the asymptotic harmonic generator are shown to specify damping, amplitude, and frequency of the limit cycle production. A model orbit stabilization approach to swing up control of a two-link pendulum robot (Pendubot) is used as a case of study. The quasihomogeneous control synthesis is utilized to design a variable structure controller that drives the actuated link of the Pendubot to a periodic reference orbit in finite time. Performance issues of the controller constructed are illustrated in an experimental study.

Keywords: variable structure control,orbital stabilization,Van der Pol equation

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00015

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 90-94

Authors: Olga Tomchina; Irina Kudryavtseva

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00016

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 95-102

Authors: Dmitry Tomchin

Abstract: The switching control algorithm for passing through resonance zone for the two-rotor vibration unit is proposed. The algorithm is based on speed-gradient method and leads to the significant reduction of the required level of the controlling torque. The dynamics of the overall hybrid system and its robustness against changes of spring stiffness, excentricity of rotors and damping is analyzed by computer simulation.

Keywords: mechatronic systems,design methodologies,identification and control methods,control of oscillations

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00017

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 103-108

Authors: Nikolai N. Bolotnik; Mikhail Pivovarov; Igor Zeidis; Klaus Zimmermann

Abstract: A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The coefficient of friction between the bodies and the plane is assumed to be small. The motion of the system is excited by two identical unbalance rotors based on the respective bodies. Major attention is given to the steady-state velocity-periodic motion. A nearly-resonant excitation mode, for which the angular velocities of the rotor are close to the natural frequency of the system, is considered. It is shown that control of the steady-state motion can be provided by changing the phase shift between the rotations of the rotors and the sign of the resonant detuning measured by the difference between the angular velocity of the rotors and the natural frequency of the system. By varying the phase shift one can control the magnitude of the average velocity and varying the detuning enables one to change the direction of the motion.

Keywords: vibration-driven systems,dry friction,dynamics,control

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00018

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 109-114

Authors: V. V. Saurin; G. V. Kostin

Abstract: Equations describing small free oscillations of a rectilinear elastic beam with a rectangular cross section have been obtained within the framework of the linear theory of elasticity and solved using the method of integrodifferential relations (IDR). The influence of geometry and elastic characteristics on the frequencies and shapes of free beam oscillations is studied. It is shown that the longitudinal motions admit two types of displacement and internal stress fields. The lateral oscillations obtained are specified by two frequency bands, which correspond to different types of the characteristic equation roots. Numerical examples of free beam oscillations are presented and discussed.

Keywords: distributed-parameter systems,eigenvalue problems,frequency characteristics,verification

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00019

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 115-119

Authors: Vladimir N. Belykh; Evgeniya V. Pankratova

Abstract: The study of complete synchronization in networks of periodic and chaotic neurodynamical elements with different coupling configurations is performed. Using the connection graph stability method we obtain the sufficient conditions for achievement of synchronous behavior of all elements involved in these ensembles. The theoretical predictions we compare with the numerical results obtained for the networks composed of the classical Hodgkin-Huxley neuronal elements. The problem how to control the synchronization of networks growing in time is discussed.

Keywords: neural networks,synchronization,stability criteria,chaotic behavior

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00020

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 120-125

Authors: I. I. Blekhman; D. A. Indeitsev; A. L. Fradkov

Abstract: A nonlinear system with two degrees of freedom consisting of a rigid platform and mechanical vibroactuator is analyzed. The platform, connected to an immovable base by means of elastic and damping elements can move along a fixed direction. The mechanical vibroactuator is an unbalanced rotor, mounted on the platform and driven with an electric drive. Such a system is a model of many vibrational machines and technological units. During the speed up of the actuator to the working frequency ω* exceeding the free oscillation frequency p of the platform, a remarkable phenomenon can be observed: capture of the current frequency ω near resonance frequentcy p. Further increase of the supply power of the drive leads to a jump transition from ω≈p to an above resonance frequency ω1>p. Such a phenomenon was first described by an eminent German physicist A. Sommerfeld. In 1953 one of the authors of this paper gave physical explanation and mathematical description of this phenomenon and coined the term "Sommerfeld effect". Later a comprehensive study of Sommerfeld effect was provided by numerous researchers. Particularly, it was discovered that "semi-slow" oscillations of rotor frequency may appear during start-up mode. Such an effect can be interpreted as appearance of "internal pendulum" in the system. Using internal pendulum and semislow oscillations of the rotor is important for a number of methods for control of vibrational units with inertia excitation of vibrations allowing to significantly reduce the motor power required for passage through resonance zone. In the talk a brief survey of such control methods is given. The main contribution of the talk is analysis of existence and dynamics of an internal pendulum. The problem of passage through resonance zone is solved by iteration method combined with direct method of separation of motions. Though such an approach looks more primitive than the previous ones, it allows to obtain two autonomous second order equations for slow and semi-slow oscillations parameters which can be solved sequentially.

Keywords: mechatronic systems,design methodologies,identification and control methods,control of oscillations

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00021

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 126-131

Authors: A. Kruszewski; T. M. Guerra

Abstract: This paper deals with the stabilization of a class of discrete nonlinear models. The considered models are taken in the Takagi-Sugeno's form with periodic parameters. The main goal of this paper is to reduce the conservatism of the stabilization conditions using a special class of candidate Lyapunov functions.

Keywords:

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00022

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 132-137

Authors: Daniil V. Iourtchenko

Abstract: The paper discusses a problem of stochastic optimal control of a linear single-degree-of-freedom system subjected to external sinusoidal and white noise excitations. An external, bounded in magnitude control force is introduced into the system to reduce mean system response energy. The dynamic programming approach is used to derive the corresponding Hamilton-Jacobi-Bellman equation. Hybrid solution method is used to derive a solution to this equation, thereby found an optimal control policy.

Keywords: optimal control,stochastic control,dynamic programming

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00023

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 138-141

Authors: Nikolai N. Bolotnik; Tatiana Yu. Figurina

Abstract: An optimal control problem is solved for a rigid body that moves along a straight line on a rough horizontal plane due to the motion of two internal masses. One of the masses moves horizontally parallel to the line of motion of the system's main body and the other mass moves vertically. Such a mechanical system models a vibration-driven robot able to move in a resistive medium without special propelling devices (wheels, legs or caterpillars). A periodic motion of the internal masses is constructed to ensure a velocity-periodic motion of the main body with a maximum average velocity, provided that the period is fixed and the accelerations of the internal masses relative to the main body lie within prescribed limits. This statement does not constrain the amplitude of vibrations of the internal masses. Based on the solution of the problem, a suboptimal control that takes this constraint into account is constructed.

Keywords: vibration-driven systems,optimal control,robotics

Digital Object Identifier (DOI): 10.3182/20070829-3-RU-4912.00024

Conference: 3rd IFAC Workshop on Periodic Control Systems, 2007

Location: Anichkov Palace, Russia

Start Date: Wed Aug 29 2007 - End Date: Fri Aug 31 2007

Page Numbers: 142-147