Elio Usai

A survey of applications of second-order sliding mode control to mechanical systems

The effective application of sliding mode control to mechanical systems is not straightforward because of the sensitivity of these systems to chattering. Higher-order sliding modes can counteract this phenomenon by confining the switching control to the higher derivatives of the mechanical control variable, so that the latter results are continuous. Generally, this approach requires the availability of a number of time derivatives of the sliding variable, and, in the presence of noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, could be helpful both in reducing the number of differentiator stages in the controller and in dealing with unmodelled actuator dynamics. In this paper different second-order sliding mode controllers, previously presented in the literature, are shown to belong to the above cited class, and some challenging control problems involving mechanical systems are addressed and solved. Simulations and experimental results are provided throughout the paper.

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.

Analysis of Chattering in Systems With Second-Order Sliding Modes

A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized suboptimal (2-SMC G-SO) algorithms is evaluated. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincare maps. For linear systems driven by 2-SMC G-SO algorithms, analysis tools based on the frequency-domain methods are developed. The first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions. The second technique represents a modified Tsypkins method and provides for a relatively simple, theoretically exact, approach to evaluate the periodic motion parameters. Examples of analysis and simulation results are given throughout this paper.

Output tracking control of uncertain nonlinear second-order systems

Abstract The solution of a tracking problem for a secondorder nonlinear system with uncertain dynamics and incomplete state measurement is obtained by means of a procedure directly inspired by the solution of the classical minimum-time optimal control problem. Two different types of uncertainty are considered in the paper: in the first case a constant bound on the uncertain dynamics is assumed to be known; in the second case, the bound is a function of both the measurable and the unmeasurable state variable of the system. In both cases, the possibility of applying the proposed control algorithms is proved to be determined by a proper choice of the control signal features. The resulting system is characterized by a suitable feedback switching logic and the convergence of the system trajectory to the desired one (or to a δ-vicinity of this latter) is proved also in the uncertain case.

Second-order sliding-mode control of container cranes

Moving a suspended load along a pre-speci0ed path is not an easy task when strict speci0cations on the swing angle and on the transfer time need to be satis0ed. Intuitively, minimizing the cycle time and the load swing are con5icting requirements, and their satisfaction requires proper control actions, especially if some uncertainties in the system dynamics are present. In this paper we propose a simple control scheme, based on second-order sliding modes, which guarantees a fast and precise load transfer and the swing suppression during the load movement, despite of model uncertainties and unmodeled dynamic actuators. Such controller has been tested on a laboratory-size model of the crane, and some experimental results are reported. ? 2002 Elsevier Science Ltd. All rights reserved.

Sliding mode control: A survey with applications in math

Abstract: The paper presents a brief survey on Variable Structure Control Systems with Sliding Modes. Starting from a general case of sliding modes in dynamical systems with discontinuous right-hand side, classic approaches to sliding mode control systems are considered and some basic results about the control of uncertain systems are given. Then, Higher-Order Sliding Modes are presented as a tool to remove discontinuity from the control action, to deal with higher relative degree systems and to improve the accuracy of the real sliding mode behavior when the discrete time implementation is considered. Finally, three applications of the sliding mode control theory to applied math problems are presented: the numerical solution of constrained ODEs, the real-time differentiation, and the problem of finding the zeroes of nonlinear algebraic systems. The first is an almost straightforward application of the sliding mode control theory, while the last two are accomplished by computing the solution of properly defined dynamical systems. Some simulations are reported to clarify the approach.

Cascade Control of PM DC Drives Via Second-Order Sliding-Mode Technique

This paper presents a novel scheme for the speed/position control of permanent-magnet (PM) DC motor drives. A cascade control scheme, based on multiple instances of a second-order sliding-mode control (2-SMC) algorithm, is suggested, which provides accurate tracking performance under large uncertainty about the motor and load parameters. The proposed scheme has been implemented and tested experimentally on a commercial PM DC motor drive. The experimental results confirm the precise and robust performance, and the ease of tuning and implementation, featured by the proposed scheme.

Modern sliding mode control theory : new perspectives and applications

Part I Basic Theory.- Regularization of Second Order Sliding Mode Control Systems.- A comprehensive Analysis of Chattering in Second Order Sliding Mode Control Systems.- Analysis of Closed-Loop Performance and Frequency-Domain Design of Compensating Filters for Sliding Mode Control Systems.- Discontinuous Homogeneous Control.- Second-order Sliding Sector for Variable Structure Control.- On Eulers Discretization of Sliding Mode Control Systems with Relative Degree Restriction.- Part II Design Methods.- Circumventing the relative degree condition in sliding mode design.- HOSM driven output tracking in the nonminimum-phase causal nonlinear systems.- High Order Sliding Mode Neurocontrol for Uncertain Nonlinear SISO Systems: Theory and Applications.- A Generalized PI Sliding Mode and PWM Control of Switched Fractional Systems.- Stabilization of nonholonomic uncertain systems via adaptive second order sliding mode control.- Output Tracking with Discrete-Time Integral Sliding Mode Control.- Flatness, Backstepping and Sliding Mode Controllers for Nonlinear Systems.- Part III Observers and Fault Detection.- Observation and identification via high-order sliding modes.- High Order Sliding Mode Observers and Differentiators-Application to Fault Diagnosis Problem.- Vehicle Parameter and States Estimation via Sliding Mode Observers.- An alternative to the measurement of five-links biped robot absolute orientation: estimation based on high order sliding mode.- Part IV Applications.- Robust Orbital Stabilization of Pendubot: Algorithm Synthesis, Experimental Verification, and Application to Swing up and Balancing Control.- Higher Order SM Block-Control of Nonlinear Systems with Unmodeled Actuators. Application to electric power systems and electrohydraulic servo-drives.- Blood Glucose Regulation Via Double Loop Higher Order Sliding Mode Control and Multiple Sampling Rate.- Contact force regulation in wire-actuated pantographs.

Output-feedback control of an underwater vehicle prototype by higher-order sliding modes

This paper describes some experimental results concerning the practical implementation of a recently proposed nonlinear output-feedback control technique based on the higher-order sliding mode approach. The considered technique is applied to the motion control problem for an underwater vehicle prototype that is equipped with a special propulsion system based on hydro-jets with variable-section nozzles. To cope with the heavy uncertainties affecting the prototype dynamics the output-feedback control system has been developed by means of an observer-controller that combines a second-order sliding-mode controller and a second-order sliding-mode differentiator. The reported experiments show that the proposed approach is capable of guaranteeing fast and accurate response under several operating conditions. The control system design procedure, and the main implementation issues, are discussed in detail.

Tracking Control of the Uncertain Heat and Wave Equation via Power-Fractional and Sliding-Mode Techniques

In the present paper, preliminary results towards the generalization to the infinite-dimensional setting of some well-known robust finite-dimensional control algorithms are illustrated. More specifically, we deal with the tracking problem for some classes of linear uncertain infinite-dimensional systems evolving in Hilbert spaces. We design distributed variable-structure stabilizers that are shown to be effective in the presence of external disturbances. The main focus of the present paper is on the rejection of nonvanishing external disturbances. The generalization to the infinite-dimensional setting of the well-known finite-dimensional controllers, namely the “power-fractional” controller [S. P. Bhat and D. S. Bernstein, SIAM J. Control Optim., 38 (2000), pp. 751-766] and two “second-order sliding-mode” control algorithms (the “twisting” and “supertwisting” algorithms [L. Fridman and A. Levant, Higher order sliding modes as a natural phenomenon in control theory, in Robust Control via Variable Structure and Lyapunov Techniques, Springer-Verlag, Berlin, 1996, pp. 107-133; A. Levant, Internat. J. Control, 58 (1993), pp. 1247-1263]), is the main contribution of the present investigation. First, the “distributed twisting” control algorithm is developed to address the asymptotic state tracking of the perturbed wave equation. Next, the finite-time state tracking of the unperturbed heat equation is provided by means of a “distributed power-fractional” controller. Finally, the “distributed supertwisting” controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances. Constructive proofs of stability are developed via the Lyapunov functional technique, which leads to simple tuning rules for the controller parameters. Simulation results are discussed to verify the effectiveness of the proposed schemes.