Showing papers on "Variable structure control published in 1993"
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: It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay and a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced.
Abstract: The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.
2,714 citations
TL;DR: A new approach based on a new method called the reaching law method, and complemented by a sliding-mode equivalence technique, facilitate the design of the system dynamics in all three modes of a VSC system including the sliding, reaching, and steady-state modes.
Abstract: A new approach for the design of variable structure control (VSC) of nonlinear systems is presented. It is based on a new method called the reaching law method, and is complemented by a sliding-mode equivalence technique. They facilitate the design of the system dynamics in all three modes of a VSC system including the sliding, reaching, and steady-state modes. Invariance and robustness properties are discussed. The approach is applied to a robot manipulator to demonstrate its effectiveness. >
1,165 citations
TL;DR: In this paper, a variable-structure control for the deterministic discrete-time system based on the minimum variance and generalized minimum variance control is proposed, which is then extended so that self-tuning control is realized for the plants with uncertain parameters by identifying the control law online.
Abstract: Discrete variable-structure control and its application to self-tuning control are considered. The proposed variable structure control does not use state variables but uses present and past output or input-output signals. Variable-structure control for the deterministic discrete-time system based on the minimum variance and generalized minimum variance control is proposed. The method is then extended so that self-tuning control is realized for the plants with uncertain parameters by identifying the control law online. A simulation study shows the effectiveness of the proposed algorithm. >
183 citations
TL;DR: In this article, two main results for uncertain time-delay systems are derived, namely, the robustness and stability degree of perturbed systems in the sliding mode, and the successful application of variable structure control to the stabilization problem of uncertain time delay systems.
Abstract: In this paper, two main results for uncertain time-delay systems are derived. The first result is the presentation of a new robust stability criterion for uncertain time-delay systems. The second result is the successful application of the concept of variable structure control to the stabilization problem of uncertain time-delay systems. The robustness and stability degree of perturbed systems in the sliding mode are also discussed. Last, some examples are included to illustrate our results.
181 citations
15 Dec 1993
TL;DR: This paper deals with the generalization of the concept of "sliding mode control" for arbitrary dynamic systems governed by a shift operator, and the design procedures are presented for different classes of dynamic systems.
Abstract: This paper deals with the generalization of the concept of "sliding mode control" for arbitrary dynamic systems governed by a shift operator This class embraces continuous- and discrete-time, finite- and infinite-dimensional systems, and systems described by difference-differential equations The new concept rests upon the singularity property of a shift operator in systems with sliding modes The design procedures are presented for different classes of dynamic systems >
129 citations
TL;DR: The results show that the VSS control is effective in reducing the torque ripple of the motor, compensating for the nonlinear torque characteristics, and making the drive insensitive to parameter variations and disturbances.
Abstract: The applications of a variable-structure system (VSS) to the control of a switched reluctance motor (SRM) drive is presented. After reviewing the operation of an SRM drive, a VSS-based scheme is formulated to control the drive speed. The scheme is then designed and tested by simulation. The results show that the VSS control is effective in reducing the torque ripple of the motor, compensating for the nonlinear torque characteristics, and making the drive insensitive to parameter variations and disturbances. >
125 citations
TL;DR: In this paper, the authors proposed a new switching surface which is initially designed to pass arbitrary initial conditions, and subsequently move towards a predetermined switching surface by rotating or/and shifting.
Abstract: Most of the switching surfaces proposed so far for a variable structure control system (VSCS) have been determined independently of initial conditions. The VSCS with these typical switching surfaces may be sensitive to parameter variations and extraneous disturbances during the reaching phase. To overcome this drawback, we propose a new switching surface which is initially designed to pass arbitrary initial conditions, and subsequently move towards a predetermined switching surface by rotating or/and shifting. We call it a moving switching surface (MSS). Using the MSS a low sensitivity system is obtained through shortening the reaching phase. Furthermore, the system robustness is guaranteed during whole intervals of control action by eliminating the reaching phase. To illustrate the advantages of the proposed method, a simple second-order linear system subjected to external disturbance is considered as a preliminary example followed by a two-link manipulator.
113 citations
TL;DR: In this paper, a discrete-time sliding-mode controller based on the theory of variable structure systems is presented, where a predictive corrective scheme is utilized in the calculation of the control inputs and no a priori knowledge of the uncertainty bounds is required.
Abstract: A discrete-time sliding-mode controller is presented in this paper, based on the theory of variable structure systems. It is assumed that the parameters of the system are uncertain and external disturbances are present. A measure of these effects is obtained through the deviations from the desired sliding surface, and this information is incorporated in the control law. A predictive corrective scheme is utilized in the calculation of the control inputs and, as a result, no a priori knowledge of the uncertainty bounds is required. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. The convergence and disturbance rejection properties of the approach are verified, and its performance is tested for the tracking control of an industrial robot.
102 citations
TL;DR: A dynamical discontinuous feedback strategy of the sliding mode type is presented for asymptotic output tracking problems in nonlinear dynamical systems, especially suitable for the control of some mechanical and electromechanical systems.
Abstract: A dynamical discontinuous feedback strategy of the sliding mode type is presented for asymptotic output tracking problems in nonlinear dynamical systems. N. Fliess' (1989, 1990) generalized observability canonical form (GOCF) is used in the derivation of the dynamical variable structure feedback controller. For a large class of nonlinear systems, a truly effective smoothing of the sliding mode controlled responses is possible, while substantially reducing the chattering for the control output. For this reason, the technique is especially suitable for the control of some mechanical and electromechanical systems. An example, including simulations, is provided. >
100 citations
Book•
01 Feb 1993
TL;DR: The state-of-the-art K-K.D. Young variable structure systems and sliding mode are described in this article, where the authors present a robust control of a robot arm with sliding mode.
Abstract: Introduction, K-K.D. Young variable structure systems and sliding mode - state-of-the-art assessment, V.I. Utkin nonlinear pulse width modulation controller design, H. Sira-Ramirez variable structure control and observation of nonlinear/uncertain systems, S.H. Zak et al decentralized systems, U. Oezguener and H. Chan variable structure control of AC electric drives, H.G. Kwatny adaptive sliding mode control of a magnetic suspension system, J.K. Hedrick and W.H. Yao sliding mode for constrained robot motion control, K-K.D. Young variable structure control of redundant mechanisms, K-K.D. Young et al robust control of robot arm with sliding mode - engineering design considerations, H. Hashimoto variable structure control and learning controls for robotic manipulators, R. Shoureshi variable structure control of flexible manipulators, K-K.D. Young et al bandwidth-limited robust sliding control of multi axial spacecraft pointing and tracking manoeuvres, T.A.W. Dsyers III and J. Kim.
01 Jan 1993
TL;DR: In this article, an integral compensated variable structure control (IVSC) has been proposed to improve the dynamic response of brushless DC position control systems with unknown external load disturbance and plant parameter variations.
Abstract: This paper considers brushless DC position control systems with unknown external load disturbance and plant parameter variations Since the dynamic characteristics of such systems are very complex and highly nonlinear, a conven- tional linear controller design may not assure satisfactory requirements To improve the dynamic response of such systems, an integral- compensated variable structure control (IVSC) has been proposed The approach comprises an integral controller for achieving a zero steady- state error response under step input, and a vari- able structure controller for enhancing the robustness Simulation results show that the pro- posed approach gives a rather accurate servo- tracking result and is fairly robust to plant parameter variations and external load dis- turbance
01 Jan 1993
TL;DR: In this paper, a new class of output feedback variable structure controllers and state estimators for uncertain/nonlinear dynamic systems with bounded uncertainties and/or nonlinearities are proposed.
Abstract: In the paper a new class of output feedback variable structure controllers and state estimators (observers) for uncertain/nonlinear dynamic systems with bounded uncertainties and/or nonlinearities are proposed. No statistical information about the uncertain elements is assumed. A variable structure systems (VSS) approach together with the geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed output feedback controllers and state estimators. The role of system zeros in the output feedback stabilisation and state estimation, using the VSS approach, is discussed. Numerical examples included illustrate the feasibility of the proposed stabilisation and state estimation schemes.
15 Dec 1993
TL;DR: In this paper, a control law for stabilizing multiple input chained-form control systems is given. But the authors do not consider the problem of stabilizing the origin of a three-input control system that models the kinematics of a fire truck.
Abstract: This paper gives a control law for stabilizing multiple input chained form control systems. This extends an earlier result of Teel, Murray, and Walsh (1992) on stabilizing the above class of systems which have two inputs. In addition, the authors generalize this law to control dynamical control systems and construct a transformation from general chained form systems with multiple generators to a power form. A control law which stabilizes the origin of a three-input control system that models the kinematics of a fire truck is simulated, confirming the theoretical results. >
TL;DR: In this paper, a variable structure control law based on the Lyapunov's second method was developed for trajectory planning problems of robotic systems, and a modified approach to the formulation of the sliding domain equations in terms of tracking errors was presented.
Abstract: A new variable structure control law based on the Lyapunov's second method that can be used in trajectory planning problems of robotic systems is developed. A modified approach to the formulation of the sliding domain equations in terms of tracking errors has been presented. This approach possesses three distinct advantages: (i) it eliminates the reaching phase, (ii) it provides means to predict the entire motion and directly control the evolution of tracking errors, (iii) it facilitates the trajectory planning process in the joint and/or cartesian spaces. A planar, five-link bipedal locomotion model has been developed
TL;DR: A method of nonlinear feedback control that introduces fuzzy interference into sliding-mode control, to treat nonlinearities and reduce chattering is proposed.
Abstract: Sliding-mode control can deal with nonlinearities of control systems and is robust. However, it has drawbacks, such as high control gain effect and control chattering. A method of nonlinear feedback control that introduces fuzzy interference into sliding-mode control, to treat nonlinearities and reduce chattering is proposed. The stability of the system is discussed using fuzzy stability theory based on Lyapunov's direct method. The method is applied numerically to the stabilizing control of an electric power system, and is shown to give good results. >
15 Dec 1993
TL;DR: The proposed method weakens some of the constraints due to the high frequency switching and full state accessibility requirements in continuous time variable structure control.
Abstract: This paper deals with discrete time sliding mode control with chattering reduction for sampled data systems. The pre-filtering and post-filtering settings are implemented to eliminate chattering with robustness. The proposed method weakens some of the constraints due to the high frequency switching and full state accessibility requirements in continuous time variable structure control. >
TL;DR: In this paper, two identification methodologies, the VSS-based direct and indirect identification methods, were proposed to deal with the parameter identification problems of both linear and nonlinear systems.
Abstract: This paper proposes two identification methodologies, the VSS-based direct and indirect identification methods, to deal with the parameter identification problems of both linear and nonlinear systems. Parameter identifiability and convergence are studied. The validity of proposed algorithms is confirmed through some numerical simulation examples.
15 Dec 1993
TL;DR: An advantageous combination of chattering-free dynamical sliding mode control and the adaptive backstepping technique is proposed for the regulation of exactly linearizable systems, placeable in parametric-pure feedback form and inparametric-strict feedback form.
Abstract: An advantageous combination of chattering-free dynamical sliding mode control and the adaptive backstepping technique is proposed for the regulation of exactly linearizable systems, placeable in parametric-pure feedback form and in parametric-strict feedback form. >
TL;DR: In this article, a control algorithm is presented which guarantees the occurrence of the sliding mode on nonlinear or time-varying manifolds, where the bounds needed for calculating the switching gains are determined in terms of parameter variations rather than bounds on the system matrices.
Abstract: Performance characteristics of a sliding mode controller depend essentially on a selected sliding manifold. Customarily, the variable-structure controllers operate with linear sliding surfaces. However, using nonlinear or time-varying manifolds may provide definite advantages; in particular, they may provide faster convergence. In this paper, a control algorithm is presented which guarantees the occurrence of the sliding mode on nonlinear or time-varying manifolds. The bounds needed for calculating the switching gains are determined in terms of parameter variations rather than bounds on the system matrices. The parameter bounds are usually evident and can be easily established or estimated, while matrix bounds can rarely be justified in practical problems. In this paper, we also present an adaptive version of the controller, which provides an automatic estimation of the parameter bounds. The robustness of the controller with respect to a class of state-dependent uncertainties is analysed by the Lyapunov m...
TL;DR: In this paper, a variable structure system approach is employed in the synthesis of the output feedback controllers, which guarantee the practical stability of the closed-loop system and give estimates of the regions of practical stability.
Abstract: We propose a new class of infinitely many bounded output feedback controllers for uncertain dynamic systems with bounded uncertainties. No statistical information about the uncertainties is assumed. A variable structure systems approach is employed in the synthesis of the proposed output feedback controllers. The role of the system zeros in the output feedback stabilization using the variable structure approach is discussed. We show that the proposed controllers guarantee the practical stability of the closed-loop system and give estimates of the regions of practical stability.
15 Nov 1993
TL;DR: The simulation of the pendulum control system shows that the VSS controller proposed in this paper is stable and robust to bounded parameter uncertainty.
Abstract: This paper presents an optimal and robust VSS controller for discrete-time systems. Firstly, a VSS control law is designed, which enables the system state to move into a sliding sector where the closed-loop system is stable. Then optimal control theory is used to design an optimal sliding sector. Finally, the bounded parameter uncertainty is taken into consideration, the robustness of the VSS control system is shown. The simulation of the pendulum control system shows that the VSS controller proposed in this paper is stable and robust to bounded parameter uncertainty. >
TL;DR: A theory is given to unify output sliding-mode control and classical control, leading to the development of a hybrid sliding-and-classical controller which retains the merits of both types of controllers but eliminates their respective limitations.
Abstract: A theory is given to unify output sliding-mode control and classical control. The idea is based on defining the sliding variable in such a way that once the system begins to slide, the classical controller transfer function is realized. This idea leads to the development of a hybrid sliding-and-classical controller which retains the merits of both types of controllers but eliminates their respective limitations. The proposed method is robust and applies to non-minimum-phase single-input, single-output (SISO) systems. No state measurement is required. >
15 Nov 1993
TL;DR: Two approaches are proposed to handle different types of chattering in variable structure control systems, one makes use of plant augmentation and the other makesUse of a fuzzy technique.
Abstract: Variable structure control (VSC) has been known theoretically as a powerful control technique capable of providing very robust control, even invariant under certain conditions, with respect to system parameter variations and external disturbances. However, the technique has not had wide spread acceptance in the control engineering community, largely because of the worry of chattering which is ever-existing in any VSC system. In this paper, two approaches are proposed to handle different types of chattering. One makes use of plant augmentation and the other makes use of a fuzzy technique. Simulation results are given to illustrate the effectiveness of these methods. >
TL;DR: In this paper, the robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances has been studied and a comparison with a typical ‘static’ VS algorithm is made.
Abstract: This paper deals with the robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances. Modified Variable Structure control algorithms with additional integral terms are considered here and analysed. A comparison with a typical ‘static’ VS algorithm is made. Static VS algorithms can reject completely the disturbance only if the amplitude of the switching term, in the control input, is larger than the amplitude of the disturbance itself. This paper shows how it is possible, by adding an integral term in the VS control algorithm, to reach and remain in the sliding mode if the amplitude of the switching term is smaller than the amplitude of the disturbance. Some simulations supporting the theoretical results are reported and discussed.
15 Dec 1993
TL;DR: In this paper, a sliding mode control approach is used for a class of nonlinear systems with uncertain matrix B. The control design is based on the partition of the extended system state space onto the cells with fixed control vector inside each cell.
Abstract: The sliding mode control approach is used for a class of nonlinear systems x/spl dot/=f(t,x)+B(t,x)u with uncertain matrix B. The control design is based on the partition of the extended system state space onto the cells with fixed control vector inside each cell. That results in multiple stable equilibriums for the extended system. In general, these points are different for different values of B. Each equilibrium corresponds to the stability of the origin for the given system, If areas of attraction for the multiple stability points covers the entire state space the proposed control allows to stabilize the system even if the direction of the actuation is unknown. >
15 Dec 1993
TL;DR: The authors show that the controller can stabilize the closed-loop system and does not suffer from the peaking phenomenon which exists in previous designs.
Abstract: Considers the stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using variable structure output feedback control. In particular, the system can be transformed into a normal form with no zero dynamics. A robust high-gain observer is used to estimate the state variables while rejecting error disturbances. A globally bounded discontinuous variable structure controller is designed to compensate for modeling error. The authors show that the controller can stabilize the closed-loop system and does not suffer from the peaking phenomenon which exists in previous designs. >
TL;DR: In this article, a method for the solution of the asymptotic linearization of uncertain nonlinear systems by means of a continuous control law is presented, which is based on a continuous first-order estimator and control laws with piecewise continuous derivatives.
Abstract: In this paper a new method for the solution of the asymptotic linearization of uncertain nonlinear systems by means of a continuous control law is presented. The main feature of this approach consists of a continuous first-order estimator and control laws with piecewise continuous derivatives. As an important by-product of this theory we can deal easily with the case of some uncertain systems which do not satisfy the matching condition, and with systems presenting first order unmodelled dynamics.
TL;DR: It has been shown that, under the proposed learning control, the position, velocity, and acceleration tracking errors are asymptotically stable in the presence of highly nonlinear dynamics.
Abstract: For the trajectory following problem of a robot manipulator, a new linear learning control law, consisting of the conventional proportional-integral-differential (PID) control law, with respect to position tracking error, and an iterative learning term is provided. The learning part is a linear feedback control of position, velocity, and acceleration errors (PDD2). It has been shown that, under the proposed learning control, the position, velocity, and acceleration tracking errors are asymptotically stable in the presence of highly nonlinear dynamics. The proposed control is robust in the sense that exact knowledge about nonlinear dynamics is not required except for the bounding functions on their magnitudes. Further, neither is linear approximation of nonlinear dynamics nor repeatability of robot motion required.
TL;DR: In this article, the eigenvalues of the closed-loop system during sliding lying in a specified sector in the left-hand half-plane are investigated, and the effect of an arbitrary positive definite matrix in a complex Riccati equation on the positioning of the eigvalues within the sector is investigated.
Abstract: The design of the sliding hyperplanes of a variable structure control system is an important part of the controller design process, and will be considered in this paper. The method outlined here results in the eigenvalues of the closed-loop system during sliding lying in a specified sector in the left-hand half-plane. Numerical examples are given, and the effect of an arbitrary positive definite matrix in a complex Riccati equation on the positioning of the eigenvalues within the sector, is investigated.