Continuous sliding‐mode control for singular systems

Singular systems with matched Lipschitz perturbations and uncertainties are considered in this paper. Since continuous solutions of an impulse‐free singular system require continuous input signals, a two‐step continuous sliding‐mode control strategy to compensate matched Lipschitz perturbations and uncertainties in singular systems is proposed. Our suggested methodology is tested in a singular representation of a DC motor pendulum of relative degree two. The performance of the proposed strategy is assessed by comparing the accuracy, in both cases, with and without considering small noise in the output, obtained through other continuous sliding‐mode control, and reconstruction/compensation of perturbations and uncertainties techniques.     

On the sliding‐mode control of fractional‐order nonlinear uncertain dynamics

This paper deals with applications of sliding‐mode‐based fractional control techniques to address tracking and stabilization control tasks for some classes of nonlinear uncertain fractional‐order systems. Both single‐input and multi‐input systems are considered. A second‐order sliding‐mode approach is taken, in suitable combination with PI‐based design, in the single‐input case, while the unit‐vector approach is the main tool of reference in the multi‐input case. Sliding manifolds containing fractional derivatives of the state variables are used in the present work. Constructive tuning conditions for the control parameters are derived by Lyapunov analysis, and the convergence properties of the proposed schemes are supported by simulation results. Copyright © 2015 John Wiley & Sons, Ltd.     

High‐order sliding mode control design based on adaptive terminal sliding mode

High‐order sliding mode control techniques are proposed for uncertain nonlinear SISO systems with bounded uncertainties based on two different terminal sliding mode approaches. The tracking error of the output converges to zero in finite time by designing a terminal sliding mode controller. In addition, the adaptive control method is employed to identify bounded uncertainties for eliminating the requirement of boundaries needed in the conventional design. The controllers are derived using Lyapunov theory, so the stability of the closed‐loop system is guaranteed. In the first technique, the developed procedure removes the reaching phase of sliding mode and realizes global robustness. The proposed algorithms ensure establishment of high‐order sliding mode. An illustrative example of a car control demonstrates effectiveness of the presented designs. Copyright © 2011 John Wiley & Sons, Ltd.     

High‐order sliding‐mode observer–based input‐output linearization

The problem of output control in multiple‐input–multiple‐output nonlinear systems is addressed. A high‐order sliding‐mode observer is used to estimate the states of the system and identify the discrepancy between the nominal model and the real plant. The exact and finite‐time estimation may be tackled as long as the system presents the algebraic strong observability property. Thus, a continuous robust input‐output linearization strategy can be obtained with respect to a prescribed output. As a consequence, the closed‐loop dynamics performs robustly to uncertainties/perturbations. To illustrate the advantages of the proposed method, we introduce a study case that demands a robust linear system behavior: the self‐oscillations induced in an underactuated mechanical system through a two‐relay controller. Experiments with an inertial wheel pendulum illustrate the feasibility of the proposed approach.     

Reduced‐order design of high‐order sliding mode control system

To design an rth (r>2) order sliding mode control system, a sliding variable and its derivatives of up to (r ? 1) are in general required for the control implementation. This paper proposes a reduced‐order design algorithm using only the sliding variable and its derivatives of up to (r ? 2) as the extension of the second‐order asymptotic sliding mode control. For a linear time‐invariant continuous‐time system with disturbances, it is found that a high‐order sliding mode can be reached locally and asymptotically by a reduced‐order sliding mode control law if the sum of the system poles is less than the sum of the system zeros. The robust stability of the reduced‐order high‐order sliding mode control system, including the convergence to the high‐order sliding mode and the convergence to the origin is proved by two Lyapunov functions. Simulation results show the effectiveness of the proposed control algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Fault detection and isolation for nonlinear systems via high‐order‐sliding‐mode multiple‐observer

In this paper, fault detection and isolation problems are studied for a certain class of nonlinear systems. Under some structural conditions, multiple high‐order sliding‐mode observers are proposed. The value of the equivalent output injection is used for detecting faults and the multiple‐model approach for isolating particular faults in the system. The proposed method provides fast detection and isolation of actuator and plant faults. Simulation results support the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

An adaptive solution for robust control based on integral high‐order sliding mode concept

A new high‐order sliding mode controller is proposed. The main features are gain adaptivity and the use of integral sliding mode concept. The gain adaptation allows a reduction of the chattering and gives a solution to control uncertain nonlinear systems whose the uncertainties/perturbations have unknown bounds. The concept of real high‐order sliding mode detector is introduced given that it plays a key role in the adaptation law of the gain. This new control approach is applied by simulation to an academic example to evaluate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd.     

Passivity‐based sliding mode controller/observer for second‐order nonlinear systems

A passivity‐based sliding mode control for a class of second‐order nonlinear systems with matched disturbances is proposed in this paper. Firstly, a nonlinear sliding surface is designed using feedback passification, in which the passivity is employed to guarantee the closed‐loop system's stability. The passivity‐based controller comprising a discontinuous term guarantees globally asymptotical convergence to the sliding surface. A sliding mode‐based control law that satisfies the reaching and sliding condition is also developed. Moreover, the passivity‐based sliding mode observer is also developed to effectively estimate the system states. Compared with conventional sliding mode control, the proposed control scheme has a shorter reaching time; and hence, the system performance is less affected by disturbances, thus eliminating the need to increase the control input gain. Finally, simulation results demonstrate the validity of the proposed method.     

Unmatched uncertainties compensation based on high‐order sliding mode observation

The problem of compensation of the effects of unmatched uncertainties ∕ perturbations is considered. High‐order sliding mode observers are employed for exact state and uncertainties ∕ perturbations reconstruction. A sliding mode control design is proposed ensuring theoretically exact compensation of the uncertainties ∕ perturbations for the corresponding unmatched states based on the identified perturbation values. An inverted pendulum simulation example is considered illustrating the feasibility of the proposed approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty

The research on discrete‐time higher‐order sliding mode has received a considerable attention recently. Systems with unmatched uncertainties are common in practice; however, the existing discrete‐time higher‐order sliding mode control algorithms are designed considering only matched uncertainty. This paper proposes a technique to design discrete‐time higher‐order sliding mode control for an uncertain LTI system in the presence of unmatched uncertainty. The proposed technique is numerically simulated and experimentally validated on an electromechanical rectilinear plant. Various experiments are conducted considering the several operational conditions of electromechanical systems in industries to verify the performance of the proposed controller.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.     

A new non‐linear sliding‐mode torque and flux control method for an induction machine incorporating a sliding‐mode flux observer

In this paper a novel sliding‐mode control algorithm, based on the differential geometry state‐co‐ordinates transformation method, is proposed to control motor torque directly. Non‐linear feedback linearization theory is employed to decouple the control of rotor flux magnitude and motor torque. The advantages of this method are: (1) The rotor flux and the generated torque can be accurately controlled. (2) Robustness with respect to matched and mismatched uncertainties is obtained. Additionally, a varying continuous control term is proposed. As a result, chattering is eliminated without sacrificing robustness and precision. The control strategy is based on all motor states being available. In practice the rotor fluxes are not usually measurable, and a sliding‐mode observer is derived to estimate the rotor flux. The observer is designed to possess invariant dynamic modes which can be assigned independently to achieve the desired performance. Furthermore, it can be shown that the observer is robust against model uncertainties and measurement noise. Simulation and practical results are presented to confirm the characteristics of the proposed control law and rotor flux observer. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order sliding‐mode observer for linear time‐varying systems with unknown inputs

In this article, an observer for linear time variant systems affected by unknown inputs is suggested. The proposed observer combines the deterministic least squares filter and the high‐order sliding‐mode differentiator to provide exact state reconstruction in spite of bounded unknown inputs and system instability. The cascade structure of the algorithm provides a correct state reconstruction for the class of linear time variant systems that satisfy the structural property of strong observability. Simulations illustrate the performance of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics

Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional‐order dynamics. After making a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The first one is based on the conventional discontinuous first‐order sliding mode control technique. The second scheme is based on the chattering‐free second‐order sliding mode approach that leads to the same robust performance but using a continuous control action. Simple controller tuning formulas are constructively developed along the paper by Lyapunov analysis. The simulation results confirm the expected performance. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonsingular fast terminal sliding‐mode control for nonlinear dynamical systems

This paper investigates fast finite‐time control of nonlinear dynamics using terminal sliding‐mode (TSM) scheme. Some new norms of fast TSM strategies are proposed, and a faster convergence rate is established in comparison with the conventional fast TSM. A novel concept of nonsingular fast TSM, which is able to avoid the possible singularity during the control phase, is adopted in the robust high‐precision control of uncertain nonlinear systems. Numerical simulation on a two‐link rigid robot manipulator demonstrates the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust nonovershooting tracking control for fractional‐order systems

A robust tracking control is proposed for the fractional‐order systems (FOSs) to achieve a tracking response with no overshoot, even in the presence of a class of disturbances. The control proposed makes use of a newly designed integral sliding mode technique for FOSs, which is capable of rejecting the bounded disturbances acting through the input channel. The proposed integral sliding mode control design has two components: a nominal control component and a discontinuous control component. The overshoot in the system response is avoided by the nominal control designed with the use of Moore's eigenstructure assignment algorithm. The sliding mode technique is used for the design of discontinuous part of the control that imparts the desired robustness properties.     

Black‐box position and attitude tracking for underwater vehicles by second‐order sliding‐mode technique

In this work we address the tracking control problems for autonomous underwater vehicles (AUVs). The proposed solution is based on the variable structure systems (VSS) theory and, in particular, on the second‐order sliding‐mode (2‐SM) methodology. The tuning of the controller is carried out via black‐box approach, dispensing with the knowledge of the actual AUV parameters, by simply progressively increasing a single gain parameter. The presented stability analysis includes explicitly the unmodelled actuator dynamics and the presence of external uncertain disturbances. The good performance of the proposed scheme is verified by means of simulations on a 6‐DOF AUV. Copyright © 2009 John Wiley & Sons, Ltd.     

High‐order mismatched disturbance rejection control for small‐scale unmanned helicopter via continuous nonsingular terminal sliding‐mode approach

In this paper, the problem of finite‐time control for small‐scale unmanned helicopter system with high‐order mismatched disturbance is investigated via continuous nonsingular terminal sliding‐mode control approach. The key idea is to design a novel nonlinear dynamic sliding‐mode surface based on finite‐time disturbance observer. Then, the finite‐time convergence and chattering attenuation capability is guaranteed by the continuous nonsingular terminal sliding‐mode control law. Additionally, rigorous finite‐time stability analysis for the closed‐loop helicopter system is given by means of the Lyapunov theory. Finally, some simulation results demonstrate the effectiveness and predominant properties of the proposed control method for the small‐scale unmanned helicopter even in the presence of high‐order mismatched disturbance.     

Decentralized sliding‐mode control for attitude synchronization in spacecraft formation

This paper addresses attitude synchronization and tracking problems in spacecraft formation in the presence of model uncertainties and external disturbances. A decentralized adaptive sliding mode control law is proposed using undirected interspacecraft communication topology and analyzed based on algebraic graph theory. A multispacecraft sliding manifold is derived, on which each spacecraft approaches desired time‐varying attitude and angular velocity while maintaining attitude synchronization with the other spacecraft in the formation. A control law is then developed to ensure convergence to the sliding manifold. The stability of the resulting closed‐loop system is proved by application of Barbalat's Lemma. Simulation results demonstrate the effectiveness of the proposed attitude synchronization and tracking methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

UNIVERSAL OUTPUT‐FEEDBACK SISO CONTROLLERS

It is proved in the paper that practically all known higher‐order sliding controllers can be combined with recently developed 2‐sliding‐mode‐based differentiators yielding universal output‐feedback Single‐Input‐Single‐Output (SISO) controllers. These controllers can be applied at least locally, whenever the system relative degree is known. The convergence is global, provided the system relative degree is permanent and few boundedness restrictions hold. No detailed mathematical model of the system is needed. The proposed output‐feedback controller provides for the exact finite‐time‐convergent output tracking of real‐time‐given smooth signals if the output measurements are exact. Otherwise the tracking accuracy is proportional to the magnitude of the sampling noise. The control may be made arbitrarily smooth, thereby removing the chattering effect. The theoretical results are illustrated by computer simulation.