Dynamic output feedback integral sliding mode control design for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. Once the system is in the sliding mode, the proposed output‐dependent integral sliding surface can robustly stabilize the closed‐loop system and obtain the desired system performance. Two types of mismatched disturbances are considered and their effects on the sliding mode are explored. By introducing an additional dynamics into the controller design, the developed control law can guarantee that the system globally reaches and is maintained on the sliding surface in finite time. Finally, the feasibility of the proposed method is illustrated by numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Second‐order sliding mode controller design subject to mismatched unbounded perturbations

The dynamics of the second‐order sliding mode (SOSM) can be obtained by directly taking the second derivative on the sliding variable when it has a relative degree of 2 with respect to the control input. However, there will always appear some state‐dependent certain or uncertain terms in the first derivative of the sliding variable, and the derivative directly imposed on these terms could enlarge the uncertainties in the control channel. One method to reduce the uncertainties in the control channel is to hold this information in the dynamics of the first derivative of the sliding variable, while the original SOSM dynamics could be transformed to be a SOSM system with a mismatched unbounded perturbation. This paper focuses on the controller design problem for SOSM dynamics subject to mismatched unbounded perturbation. By using Lyapunov analysis, a novel backstepping‐like design methodology will be proposed. The rigorous mathematical proof will show that under the derived SOSM controller, the closed‐loop sliding mode dynamics is globally finite‐time stable. Meanwhile, the frequently used constant upper bound assumptions for the standard SOSM system can also be extended to the state‐dependent hypotheses in this paper. An academic example is illustrated to verify the effectiveness of the proposed method. Copyright © 2017 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.     

Robust Adaptive Fractional‐Order Terminal Sliding Mode Control for Lower‐Limb Exoskeleton

This paper introduces a robust adaptive fractional‐order non‐singular fast terminal sliding mode control (RFO‐TSM) for a lower‐limb exoskeleton system subject to unknown external disturbances and uncertainties. The referred RFO‐TSM is developed in consideration of the advantages of fractional‐order and non‐singular fast terminal sliding mode control (FONTSM): fractional‐order is used to obtain good tracking performance, while the non‐singular fast TSM is employed to achieve fast finite‐time convergence, non‐singularity and reducing chattering phenomenon in control input. In particular, an adaptive scheme is formulated with FONTSM to deal with uncertain dynamics of exoskeleton under unknown external disturbances, which makes the system robust. Moreover, an asymptotical stability analysis of the closed‐loop system is validated by Lyapunov proposition, which guarantees the sliding condition. Lastly, the efficacy of the proposed method is verified through numerical simulations in comparison with advanced and classical methods.     

Sliding mode learning control for T-S fuzzy system and an application to hypersonic flight vehicle

Sliding mode-based learning control is presented for T-S fuzzy system. A T-S fuzzy model with both uncertainties and unmodeled dynamics is proposed firstly, in which the information of uncertainties and unmodeled dynamics are assumed to be unknown. Then, according to a given reference model, state-tracking error system is built. Respecting facts, the input matrices of the built T-S fuzzy model are different from each other. An extended state observer is built for estimating the unknown uncertainties and unmodeled dynamics, and a corresponding sliding surface is proposed. A learning controller is then presented for the closed loop system. Moreover, a numerical simulation result on hypersonic flight vehicles is considered to testify the controller's availability.     

Closed‐loop input shaping control of vibration in flexible structures using discrete‐time sliding mode

Input shaping technique is widely used in reducing or eliminating residual vibration of flexible structures. It is easy to implement and achieve the exact elimination of the residual vibration if the dynamics of the system are known accurately. However, it is not very robust to parameter uncertainties and external disturbances. In this paper, a closed‐loop input shaping method is developed for reducing or eliminating residual vibration of flexible structure systems with parameter uncertainties and external disturbances. The algorithm is based on input shaping control and discrete‐time sliding mode control. It is shown that the proposed scheme guarantees closed‐loop system stability, and yields good performance and robustness in the presence of parameter uncertainties and external disturbances as well. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. The knowledge of upper bound of uncertainties is not required. Furthermore, it is shown that increasing the robustness to parameter uncertainties does not lengthen the duration of the impulse sequence. Simulation results demonstrate the efficacy of the proposed closed‐loop input shaping control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

A Robust Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators

In this paper, a robust adaptive terminal sliding mode controller is developed for n-link rigid robotic manipulators with uncertain dynamics. An MIMO terminal sliding mode is defined for the error dynamics of a closed loop robot control system, and an adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties in the Lyapunov sense. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated and a finite time error convergence in the terminal sliding mode can be guaranteed. Also, a useful bounded property of the derivative of the inertial matrix is explored, the convergence rate of the terminal sliding variable vector is investigated, and an experiment using a five bar robotic manipulator is carried out in support of the proposed control scheme.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

Switched Second‐Order Sliding Mode Control with Partial Information: Theory and Application

This paper proposes a novel switched second order sliding mode (S‐SOSM) control strategy in a partial information setting, i.e., when only the sliding variable is accessible for measurements. Such a control approach allows one to deal with systems characterised by different levels of uncertainties associated with different regions of the state space and to accommodate different control objectives in the different regions by switching among appropriate SOSM controllers. The proposed approach is shown to ensure global finite‐time convergence to the origin of the closed‐loop system trajectory. The braking control of two‐wheeled vehicles is considered as a case‐study to test the controller performance.     

Tracking control of uncertain Euler–Lagrange systems with finite‐time convergence

A unified solution is presented to the tracking control problem of Euler–Lagrange systems with finite‐time convergence. A reconstruction module is designed to estimate the overall of unmodeled dynamics, disturbance, actuator misalignment, and multiple actuator faults. That reconstruction is accomplished in finite time with zero error. A nonsingular terminal sliding mode controller is then synthesized, and the resultant closed‐loop system is also shown to be finite‐time stable with the reference trajectory followed in finite time. Unlike most sliding mode control methods to handle system uncertainties, the designed control has less conservativeness and stronger fault tolerant capability. A rigid spacecraft system is used to demonstrate the effectiveness and potential of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Force tracking neural block control for an electro‐hydraulic actuator via second‐order sliding mode

This paper presents a novel scheme for identification and control of an electro‐hydraulic system using recurrent neural networks. The proposed neural network has the nonlinear block control form structure. A sliding‐mode control technique is applied then to design a discontinuous controller, which is able to track a force reference trajectory. Due to the presence of an unmodelled dynamics, the standard sliding‐mode controller produces oscillations (or ‘chattering’) in the closed‐loop system. The second‐order sliding mode is used to eliminate the undesired chattering effect. Simulations are presented to illustrate the results. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

This paper deals with the design of a robust sliding mode‐based extremum‐seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input–output linearizing method with variable‐structure feedback, such that the closed‐loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum‐seeking control algorithms, the control scheme includes a dynamic modelling‐error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient‐based optimization algorithm. Practical stabilizability for the closed‐loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive sliding mode control of interleaved parallel boost converter for fuel cell energy generation system

This paper deals with the problem of controlling energy generation systems including fuel cells (FCs) and interleaved boost power converters. The proposed nonlinear adaptive controller is designed using sliding mode control (SMC) technique based on the system nonlinear model. The latter accounts for the boost converter large-signal dynamics as well as for the fuel-cell nonlinear characteristics. The adaptive nonlinear controller involves online estimation of the DC bus impedance ‘seen’ by the converter. The control objective is threefold: (i) asymptotic stability of the closed loop system, (ii) output voltage regulation under bus impedance uncertainties and (iii) equal current sharing between modules. It is formally shown, using theoretical analysis and simulations, that the developed adaptive controller actually meets its control objectives.     

Sliding mode control of singularly perturbed systems and its application in quad-rotors

This paper presents a sliding mode control scheme for tracking control of nonlinear singularly perturbed systems in the presence of model errors and external disturbances. A dual-loop feedback control is developed to provide accurate tracking capability and sufficient robustness to system uncertainties. A sliding mode controller is proposed in the outer-loop feedback design such that the plant states are stabilised for given reference trajectories, while an additional robust controller is designed in the inner loop to increase the adaptability to uncertainties, and reduce the effect of unmodelled high-frequency dynamics on plant dynamics. An appealing feature of the control scheme is the attenuation of chattering. The effectiveness and merits of the new control scheme developed are shown via a verification example of velocity control of a quad-rotor.     

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.     

Adaptive Chattering Free Neural Network Based Sliding Mode Control for Trajectory Tracking of Redundant Parallel Manipulators

In this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.     

Robust Integral Sliding Mode Control of Uncertain Networked Control Systems with Multiple Data Packet Losses

In this paper, a robust integral sliding mode control problem for networked control systems with multiple data packet losses is investigated. The data packet losses occur in both sensor-to-controller and controller-to-actuator channels in a random way and they are modelled by independent Bernoulli binary distributed white sequences. The considered class of system is also subject to matched uncertainties and external disturbances presence. A specific sliding mode surface which take into consideration the stochastic nature of the system is proposed to generate a stable sliding mode dynamics for closed loop system. An integral sliding mode controller is designed to ensure the reachability of the specified sliding mode domain. Finally, simulation results, carried out on a linearized model of cart pendulum system, illustrate the effectiveness of the proposed approach.     

非匹配不确定非线性系统的自适应反演滑模控制

针对一类具有非匹配不确定性的最小相位仿射非线性系统,研究其在未知扰动作用下的调节问题。基于自适应反演设计方法和变结构控制设计了控制方案,实现不确定系统的鲁棒调节。与经典反演设计相比,本方案允许非参数化不确定性,增强了控制系统的鲁棒性。     

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

In this study, the problem of finite‐time practical control of a class of nonlinear switched systems in the presence of input nonlinearities is investigated. The subsystems of the switched system are considered as complex nonlinear systems with a cascade structure. Each subsystem is fluctuated by lumped uncertainties. Moreover, some parts of the system's dynamics are considered to be unknown in advance. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the aim is to propose a controller to work under any arbitrary switching signals. After providing a smooth sliding manifold, a simple adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite‐time sense. The adopted control signal does not use the upper bounds of the lumped uncertainties, and it is robust against unknown nonlinear parts of the subsystems. It is proved that the origin is the (practical) finite‐time stable equilibrium point of the overall closed‐loop system. Subsequently, the proposed control rule is modified to handle the same switched system with no input nonlinearities. Computer simulations via 2 chaotic electric direct current machines demonstrate the robust performance of the derived variable structure control algorithm against system fluctuations and nonlinear inputs.