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14
Tracking control of nonlinear systems using sliding surfaces with application to robot manipulators
 International Journal of Control
, 1983
"... We develop a methodology of feedback control to achieve accurate tracking in a class of nonlinear, timevarying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control, resulting in the state trajectory &apos ..."
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Cited by 157 (1 self)
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We develop a methodology of feedback control to achieve accurate tracking in a class of nonlinear, timevarying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control, resulting in the state trajectory 'sliding ' along a timevarying sliding surface in the state space. This idealized control law achieves perfect tracking; however, nonidealities in its implementation result in the generation of an undesirable high frequency component in the state trajectory. To rectify this, we show how continuous control laws may be used to approximate the discontinuous control law to obtain robust tracking to within a prescribed accuracy and decrease the extent of high frequency signal. The method is applied to the control of a twolink manipulator handling variable loads in a flexible manufacturing system environment.
Oneparameter Bifurcations in Planar Filippov Systems
 Int. J. Bifurcation and Chaos
, 2002
"... We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classif ..."
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Cited by 49 (0 self)
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We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classifying sliding bifurcations, i.e. bifurcations in which some sliding on the discontinuity boundary is critically involved. The full catalog of local and global bifurcations is given, together with explicit topological normal forms for the local ones.
Selfoscillations and sliding in relay feedback systems: Symmetry and bifurcations
 INT. J. BIFURCATION & CHAOS
, 2001
"... This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedba ..."
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Cited by 25 (9 self)
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This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedback system can exhibit asymmetric periodic solutions. Moreover, the occurrence of periodic solutions characterized by one or more sections lying within the system discontinuity set is outlined. The mechanisms underlying their formation are carefully studied and shown to be due to an interesting, novel class of local bifurcations.
Limit cycles with chattering in relay feedback systems
 In: Proc. 36th IEEE Conference on Decision and Control
, 1997
"... Abstract—Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In this paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay ..."
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Cited by 22 (8 self)
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Abstract—Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In this paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived. A result on existence of limit cycles with chattering is given, and it is shown that the limit cycles can have arbitrarily many relay switchings each period. Limit cycles with regular sliding modes are also discussed. Examples illustrate the results. Index Terms—Discontinuous control, hybrid systems, nonlinear dynamics, oscillations, relay control, sliding modes. I.
The DragFree Satellite
 Department of Aeronautics and Astronautics, Stanford University
, 1964
"... A scientific earth satellite that is guided in a dragfree orbit by a shielded, freefalling proof mass has been proposed by a number of investigators. This paper examines the feasibility and some of the applications of this scheme. The control and guidance system is analyzed with respect to system ..."
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Cited by 5 (0 self)
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A scientific earth satellite that is guided in a dragfree orbit by a shielded, freefalling proof mass has been proposed by a number of investigators. This paper examines the feasibility and some of the applications of this scheme. The control and guidance system is analyzed with respect to system performance and gas usage requirements. The principal trajectory errors that are due to vehicle gravity, stray electric and magnetic fields, and sensor forces are investigated. I t is found that drag and solar radiation pressure forces may be effectively reduced by three to five orders of magnitude for 100 to 500mile orbits and that the deviation from a purelygravitational orbit may be made as small as 1 m/yr. Such a satellite could be used to make precise measurements in geodesy and aeronomy; and, if a spherical proof mass is spun as a gyroscope, its random drift rate would probably be less than 0.1 secarc/yr. Such a gyroscope could be used to measure the effects that would ultimately limit the performance of the best terrestrial or satelliteborne gyros, and it might also be good enough to perform the experiment proposed by G. E. Pugh and L. I. Schiff to test general relativity. Nomenclature = direction cosine matrix
ON THE ROBUSTNESS OF PERIODIC SOLUTIONS IN RELAY FEEDBACK SYSTEMS
 15TH TRIENNIAL WORLD CONGRESS, BARCELONA, SPAIN
"... Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It i ..."
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Cited by 5 (1 self)
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Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It is shown analytically that certain stable periodic solutions in relay feedback systems are robust to relay perturbations.
Global Analysis Of ThirdOrder Relay Feedback Systems
, 1996
"... Relays are common in automatic control systems. It is wellknown that a linear dynamical system under relay feedback can give complex oscillations. In this paper it is proved that several of these phenomena can actually be captured by thirdorder systems. It is shown that there exist systems giving ..."
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Cited by 3 (1 self)
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Relays are common in automatic control systems. It is wellknown that a linear dynamical system under relay feedback can give complex oscillations. In this paper it is proved that several of these phenomena can actually be captured by thirdorder systems. It is shown that there exist systems giving arbitrarily fast relay switches similar to sliding modes. A novel method for analyzing linear dynamical systems under relay feedback is also introduced. Trajectories for a class of third order systems are shown to converge in a certain sense.
Optimal Slidingmode Control Scheme for the Position Tracking Servo System
 WSEAS TRANSACTIONS on SYSTEMS YuCheng Chen, YinTien Wang ISSN: 11092777 1040 Issue 8
, 2008
"... Abstract: Systems having structural uncertainties or a known complicated structure are difficult to control. Modeling of the uncertainties or handling the deterministic complexity are typical problems frequently encountered in the field of systems and control engineering. The dynamic characteristic ..."
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Abstract: Systems having structural uncertainties or a known complicated structure are difficult to control. Modeling of the uncertainties or handling the deterministic complexity are typical problems frequently encountered in the field of systems and control engineering. The dynamic characteristics of such systems are usually very complex and highly nonlinear. A new design approach of an optimal slidingmode variable structure controller with integral compensation is presented for the position tracking servo control system in this paper. The method for obtaining switching function, integral gain and control function is also given. It can achieve accurate servo tracking in the presence of the disturbance and the plant parameter variation. Simulation results show that the new control algorithm exhibits the better control performance than the classical control method, and the rapidness and robustness of the system are improved. Moreover, its realization is simple and convenient. KeyWords: Nonlinear system, variable structure control, sliding mode, switching function, control function,
Hidden dynamics in models of discontinuity and switching
, 2014
"... Sharp switches in behaviour, like impacts, stickslip motion, or electrical relays, can be modelled by differential equations with discontinuities. A discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model. The theory of piecewisesmooth dynamics descri ..."
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Cited by 1 (1 self)
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Sharp switches in behaviour, like impacts, stickslip motion, or electrical relays, can be modelled by differential equations with discontinuities. A discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model. The theory of piecewisesmooth dynamics describes what happens assuming we can solve the system of equations across its discontinuity. What this typically neglects is that effects which are vanishingly small outside the discontinuity can have an arbitrarily large effect at the discontinuity itself. Here we show that such behaviour can be incorporated within the standard theory through nonlinear terms, and these introduce multiple sliding modes. We show that the nonlinear terms persist in more precise models, for example when the discontinuity is smoothed out. The nonlinear sliding can be eliminated, however, if the model contains an irremovable level of unknown error, which provides a criterion for systems to obey the standard Filippov laws for sliding dynamics at a discontinuity. 1 Dynamics at a jump It is common to assume that underlying any physical system are a set of welldetermined, and moreorless smoothly varying, physical laws. Nevertheless, smooth variations can give rise to discontinuities by means of, for example, bifurcations, shocks, or singular perturbations. Discontinuities are a common feature of empirical models in engineering and biology particularly, for example in rigid body impact, stickslip due to friction, and switches in electrical, biochemical, or social dynamics. The question arises: if an observer is able to reconstruct a set of physical laws only at the piecewisesmooth level, i.e. to the extent that they involve a discontinuity, to what extent can the system dynamics be uniquely determined? The key to handling switches in dynamical systems lies in recognising that a discontinuous vector field places certain restrictions on the flow it generates.
Author's Accepted Manuscript Stability notions and lyapunov functions for sliding mode control systems Stability Notions and Lyapunov Functions for Sliding Mode Control Systems
"... Abstract The paper surveys mathematical tools required for stability and convergence ..."
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Abstract The paper surveys mathematical tools required for stability and convergence