Vadim I. Utkin

Variable structure systems with sliding modes

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.

A control engineer's guide to sliding mode control

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.

Sliding mode control design principles and applications to electric drives

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. >

Integral sliding mode in systems operating under uncertainty conditions

The paper generalized a new sliding mode design concept, namely integral sliding mode (ISM). The order of the motion equation in ISM is equal to the order of the original system, rather than reduced by the number of dimension of the control input. As the result, robustness of the system can be guaranteed throughout an entire response of the system starting from the initial time instance. Uniform formulations of the ISM design principle are developed in the paper. It is shown through examples that our generalized ISM scheme enables a wide scope of application areas. In the case that the given control matrix can not be used directly for generating the sliding mode, the associated decoupling problem was also discussed based on the concept of sliding mode transformation. To alleviate chattering, we remove the discontinuous control action from the real control path and insert it to an internal dynamic process for generating the sliding mode.

Chattering suppression methods in sliding mode control systems

Abstract The implementation of sliding mode control is often irritated by high frequency oscillations known as “chattering” in system outputs issued by dynamics from actuators and sensors ignored in system modeling. This paper provides analysis of chattering in such systems with unmodeled based on the Lyapunov theory and the describing function method. It also describes various approaches to reduce chattering including methods based on relay control gain adaptation. And for those systems to which the methods are not applicable, chattering frequency control using hysteresis loop will be provided.

On multi-input chattering-free second-order sliding mode control

A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)]=0 in the system state space, with s/spl dot/[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s/spl uml/[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.

Sensorless sliding-mode control of induction motors

This paper develops the ideas of speed- and flux-sensorless sliding-mode control for an induction motor illustrated in previous work by one of the authors. A sliding-mode observer/controller is proposed in this paper. The convergence of the nonlinear time-varying observer along with the asymptotic stability of the controller is analyzed. Pulsewidth modulation implementation using sliding-mode concepts is also discussed. Major attention is paid to torque control, and then the developed approach is utilized for speed control. Computer simulations and experiments have been carried out to test the proposed estimation and control algorithm. The experimental results demonstrated high efficiency of the proposed estimation and control method.

Linear and nonlinear controller design for robust automatic steering

For an automatic steering problem of a city bus the reference maneuvers and specifications are introduced. The robustness problem arises from large variations in velocity, mass, and road-tire contact. Two controller structures, both with feedback of the lateral displacement and the yaw rate, are introduced: a linear controller and a nonlinear controller. The controller parameters are first hand-tuned and then refined by performance vector optimization. Both controllers meet all specifications. Their relative merits are analyzed in simulations for four typical driving maneuvers. >

Sliding mode observers. Tutorial

Discusses the problem of designing observers for state estimation using sliding modes. The theory and design principles are presented for linear and nonlinear systems. For linear systems the observers are developed using a block-observable form which is similar to a lower triangular matrix form. Compared with known approaches such observers have better robustness properties. In the case of nonlinear systems an equivalent control concept makes it possible to develop finite-time observers for a wide class of systems.

Adaptive sliding mode control in discrete-time systems

Abstract Discrete-time sliding mode control is considered. The case of known parameters is first analyzed, leading to a new definition of the so-called ‘equivalent control’ as the piecewise-constant control that reduces to zero, in finite time, the distance of the system state from the sliding manifold. In the presence of bounded parametric uncertainties, an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented. The main feature of this approach is the reduction of the order of the relevant error equation, and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process.