Tracking control of non-linear systems using sliding surfaces with application to robot manipulators
22 Jun 1983-Vol. 38, Iss: 2, pp 132-135
TL;DR: In this paper, the authors present a methodology of feedback control to achieve accurate tracking for a class of nonlinear time-varying systems in the presence of disturbances and parameter variations.
Abstract: A methodology is presented of feedback control to achieve accurate tracking for a class of nonlinear time-varying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control laws, resulting in the state trajectory `sliding' along a discontinuity surface in the state space. The idealized form of the methodology results in perfect tracking of the required signals; however certain non-idealities associated with its implementation cause the trajectory to 'chatter' along the sliding surface resulting in the generation of an undesirable high-frequency component which may excite high-frequency unmodelled dynamics of the control systems. To rectify this situation, it is shown how continuous control laws which approximate the discontinuous control law may be used to obtain disturbance and parameter variation insensitive tracking. At the same time, the continuous control laws decrease the extent of unwanted high-frequency signals.
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TL;DR: A tutorial account of variable structure control with sliding mode is presented, introducing in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach.
Abstract: A tutorial account of variable structure control with sliding mode is presented. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. >
2,884 citations
TL;DR: In this paper, an adaptive robot control algorithm is derived, which consists of a PD feedback part and a full dynamics feed for the compensation part, with the unknown manipulator and payload parameters being estimated online.
Abstract: A new adaptive robot control algorithm is derived, which consists of a PD feedback part and a full dynamics feedfor ward compensation part, with the unknown manipulator and payload parameters being estimated online. The algorithm is computationally simple, because of an effective exploitation of the structure of manipulator dynamics. In particular, it requires neither feedback of joint accelerations nor inversion of the estimated inertia matrix. The algorithm can also be applied directly in Cartesian space.
2,117 citations
TL;DR: An accurate assessment of the so-called chattering phenomenon is offered, which catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding Mode control research.
Abstract: Presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the so-called chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research.
2,082 citations
TL;DR: The main arguments in favor of sliding-mode control are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converters.
Abstract: The basic concepts, mathematics, and design aspects of variable-structure systems as well as those with sliding modes as a principle operation mode are treated. The main arguments in favor of sliding-mode control are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converters. The control algorithms and data processing used in variable structure systems are analyzed. The potential of sliding mode control methodology is demonstrated for versatility of electric drives and functional goals of control. >
1,890 citations
01 Mar 1988
TL;DR: In this paper, the design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented.
Abstract: The design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented. Using the Utkin-Drazenovic method of equivalent control and generalized Lyapunov stability concepts, the VSC design is described in a unified manner. Complications that arise due to multiple inputs are examined, and several approaches useful in overcoming them are developed. Recent developments are investigated, as is the kinship of VSC and the deterministic approach to the control of uncertain systems. All points are illustrated by numerical examples. The recent literature on VSC applications is surveyed. >
1,860 citations
References
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Book•
30 Sep 1988
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Abstract: Approach your problems from the right end It isn't that they can't see the solution It is and begin with the answers Then one day, that they can't see the problem perhaps you will find the final question G K Chesterton The Scandal of Father 'The Hermit Clad in Crane Feathers' in R Brown 'The point of a Pin' van Gulik's The Chinese Maze Murders Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes They draw upon widely different sections of mathematics
6,398 citations
TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
Abstract: Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.
5,076 citations
1,589 citations
01 Feb 1978
TL;DR: It is verified through hybrid simulation that trajectories which are close to ideal sliding modes exist when the controller is designed according to theory.
Abstract: A new control algorithm is developed for manipulators using the theory of variable structure systems. The control is designed so that a new type of state space trajectories called sliding mode exists. Due to delays, neglected small time constants, and other idealizations, ideal sliding modes as predicted by the theory do not exist. We have verified through hybrid simulation that trajectories which are close to ideal sliding modes exist when the controller is designed according to theory. To illustrate the design procedures, a two-joint manipulator is considered.
595 citations
TL;DR: In this paper, three nonlinear methods are presented, two of which are direct design procedures for industrial robots, based on a suitable partition of the dynamic equation of the industrial robot and provide directly applicable, explicit control laws for each drive.
Abstract: Models of industrial robots are characterized by highly nonlinear equations with nonlinear couplings between the variables of motion. In this paper, three nonlinear methods are presented, two of which are direct design procedures for industrial robots. These direct nonlinear methods are based on a suitable partition of the dynamic equation of the industrial robot and provide directly applicable, explicit control laws for each drive. The design procedures presented greatly simplify the derivation of the algorithm for computer-controlled industrial robots. The methods are applied to two different types of industrial robots.
470 citations