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.     

Discrete second‐order sliding mode control based on optimal sliding function vector for multivariable systems with input–output representation

The technique of linear matrix inequalities is a powerful method for solving optimization problems. In this paper, a sliding function vector was calculated using linear matrix inequalities approach. This technique provided optimal values of the coefficients of the sliding function vector, which led to the reduction of the reachability phase. Then, a discrete second‐order sliding mode control for multivariable systems was developed using this optimal sliding function vector. Two examples were used in order to illustrate the effectiveness of the proposed strategy. Simulation results prove good performances in terms of reduction of the reachability phase. Copyright © 2016 John Wiley & Sons, Ltd.     

SLIDING MODE PREDICTION TRACKING CONTROL DESIGN FOR UNCERTAIN SYSTEMS

In this paper, a tracking control algorithm based on sliding mode prediction for a class of discrete‐time uncertain systems is presented. By creating a special model to predict the future sliding mode function value and by combining feedback correction and receding horizon optimization approaches, which are extensively applied in predictive control strategy, a discrete‐time sliding mode control law for tracking problem is constructed. With the designed control law, closed‐loop systems have strong robustness to matched or unmatched uncertainties as they eliminate chattering. Besides, in the robustness analysis, the boundary condition for uncertainties, which is a universal presupposition in sliding mode control method, is not required. Numerical simulation and cart‐pendulum experiment results illustrate the validity of the proposed algorithm.     

Robust ℋ︁∞ sliding mode control for nonlinear stochastic systems with multiple data packet losses

In this paper, an ??_∞ sliding mode control (SMC) problem is studied for a class of discrete‐time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state‐feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete‐time system considered is also subject to norm‐bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete‐time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ??_∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete‐time SMC controller is designed capable of guaranteeing the discrete‐time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete output feedback sliding‐mode control with integral action

This paper presents a novel approach to the problem of discrete time output feedback sliding‐mode control design. The method described applies to uncertain systems (with matched uncertainties) which are not necessarily minimum phase or relative degree one. A new sliding surface is proposed, which is associated with the equivalent control of the output feedback sliding‐mode controller. Design freedom is available to select the sliding surface parameters to produce an appropriate reduced‐order sliding motion. In order for this to be achieved, a static output feedback condition associated with a certain reduced‐order system obtained from the original plant must be solvable. The practicality of the results are demonstrated through the implementation of the controller on a small DC motor test rig. Copyright © 2005 John Wiley & Sons, Ltd.     

On the multi‐input second‐order sliding mode control of nonlinear uncertain systems

This note addresses the multi‐input second‐order sliding mode control design for a class of nonlinear multivariable uncertain dynamics. Among the most important peculiarities of the considered control problem, the considered sliding vector variable has a uniform vector relative degree [2,2, … ,2] with respect to the vector control variable, and only the sign of the sliding vector and of its derivative are available for feedback. Additionally, the symmetric part of the state‐dependent control matrix is supposed to be positive definite. Under some further mild restrictions on the uncertain system's dynamics, a control algorithm that realizes a multi‐input version of the ‘twisting’ second‐order sliding mode control algorithm is suggested. Simple controller tuning conditions are derived by means of a constructive Lyapunov analysis, which demonstrates that the suggested control algorithm guarantees the semiglobal asymptotic convergence to the sliding manifold. Simulation results, which confirm the good performance of the proposed scheme and investigate the actual accuracy obtained under the discrete‐time implementation effects, are given. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Dynamic output feedback sliding mode control for nonminimum phase linear systems with disturbance attenuation

A sliding mode control algorithm using output information only is developed in this paper for a linear system with mismatched disturbance. The nominal system is allowed to be nonminimum phase. A scheme designed to combine the output‐dependent integral sliding surface with a reduced‐order observer is proposed. Utilizing an H_∞ control analytical technique, once the system is in the sliding mode, the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solution to one algebraic Riccati inequality can be found. A controller is designed to satisfy the reaching and sliding condition in line with the reduced‐order observer. Finally, a numerical example is explained to show the applicability of the proposed scheme. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

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.     

Analysis and design of chattering‐free discrete‐time sliding mode control

In this paper, the disturbance observer–based chattering‐free discrete‐time sliding mode control (DSMC) approach is proposed for systems with external disturbances. The proposed disturbance observer, which makes full use of the state and input information at the current and last steps, improves the estimation accuracy and achieves accurate compensation for disturbances. Then, with the help of disturbance observer, a new reaching law, which contains not only a nonsmooth term with a dynamically adjusted gain parameter but also a second order difference of the disturbance, is proposed to reduce the range of the quasi‐sliding mode band and eliminate chattering. The proposed DSMC approach realizes the active disturbance rejection and strong robustness. Finally, a simulation example is presented to verify the effectiveness of the proposed method.     

Sliding Mode ∑‐Δ Modulation Control of the Boost Converter

A switched implementation of average dynamic output feedback laws trough a ∑‐Δ‐modulator, widely known in the classic communications and analog signal encoding literature, not only frees the sliding mode control approach from state measurements and the corresponding synthesis of sliding surfaces in the plant's state space, but it also allows to effectively transfer all desired closed loop features of an uniformly bounded, continuous, average output feedback controller design into the more restrictive discrete‐valued (ON‐OFF) control framework of a switched system. The proposed approach is here used for the input‐output sliding mode stabilization of the “boost” DC‐to‐DC converter. This is achieved by means of a well known passivity based controller but any other output feedback design would have served our purposes. This emphasizes the flexibility of the proposed sliding mode control design implementation through ∑‐Δ‐modulators.     

Discrete time output feedback sliding mode tracking control for systems with uncertainties

This paper describes a method for designing discrete time static output feedback sliding mode tracking controllers for uncertain systems that are not necessarily minimum phase or of relative degree one. In this work, a procedure for realizing discrete time controllers via a particular set of extended outputs is presented for systems with uncertainties. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to synthesize a control law that minimizes the effect of the disturbance on the sliding mode dynamics and the augmented outputs is given. The proposed control law is then applied to a benchmark aircraft problem taken from the literature that represents the lateral dynamics of a F‐14 aircraft under powered approach. Copyright © 2013 John Wiley & Sons, Ltd.     

An improved continuous sliding mode controller for flexible air‐breathing hypersonic vehicle

An improved continuous sliding mode control algorithm is proposed for a flexible air‐breathing hypersonic vehicle (FAHV), including nonsingular fast fixed‐time sliding surface (NFFS) and dual‐layer adaptive continuous twisting reaching law (DACTL). Firstly, the nonlinear control‐oriented model of FAHV is processed using input/output feedback linearization method with the significant flexible effects modeling as unknown matched disturbances. Secondly, a novel NFFS is improved from conventional fixed‐time sliding surface by adjusting power exponent to accelerate convergence rate. In the meanwhile, in order to avoid singularity aroused by fractional power term, an exponential convergent sliding surface is switched when tracking error approaches zero. Thirdly, a DACTL is proposed to realize finite‐time convergence of sliding mode variable with higher convergence precision and less chattering. Dual‐layer adaptive law is utilized to adjust the gain in DACTL based on equivalent control concept so as to enhance robustness automatically and avoid overestimation of control gain. Meanwhile, disturbances can be compensated without knowledge of Lipschitz constants. Ultimately, simulations on longitudinal control of FAHV demonstrate the control algorithm proposed is superior to conventional quasi‐continuous sliding mode controller in the aspect of convergence accuracy and chattering suppression.     

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

A robust consensus controller is proposed for heterogeneous higher‐order nonlinear multi‐agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time‐varying nonhomogeneous finite‐time disturbance observer and sliding mode control is designed to realize the network consensus of higher‐order multi‐agent systems. The time‐varying finite‐time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite‐time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Sliding mode output‐feedback causal output tracking for a class of discrete‐time nonlinear systems

The output tracking (OT) of arbitrary references in discrete‐time (DT) nonlinear systems is addressed by designing an output‐feedback control. A set of difference‐algebraic equations is proposed as an exact solution of the problem. Using a novel technique of approximating DT functions, the system disturbance and steady states, characterized by tracking error identically zero, for both the system state and the control input, are represented as signals generated by a disturbed dynamic system. Using the mentioned dynamics, the control system is extended. Then, a state observer is proposed to estimate the resulting extended system state. Finally, a DT sliding mode controller is designed to achieve the approximate OT. Simulations show the effectiveness of the proposed control scheme.     

不确定离散时间系统的复合非线性反馈积分滑模控制

针对不确定离散时间系统,提出一种基于离散复合非线性反馈的积分滑模(DCNF-ISM)控制策略,并将该算法应用于扰动下的磁盘跟踪问题.该算法由离散复合非线性反馈(DCNF)控制律与积分滑模(ISM)控制律两部分组成,其中DCNF控制律用于保证系统具有较好瞬态性能,基于改进的离散趋近律设计的ISM控制律用于保证系统鲁棒性.基于Lyapunov稳定性理论对本文提出的控制策略的稳定性进行了推导证明,证明了离散时间系统的一致最终有界性.仿真结果表明,本文提出的控制策略能保证系统在扰动下仍然能够精确跟踪给定的参考信号,与传统的DCNF控制相比,该算法能够保证系统具有响应速度快超调量小、鲁棒性强等优点.     

Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete‐time nonlinear sliding mode observer for state and unknown input estimations of a class of single‐input/single‐output nonlinear uncertain systems. The uncertainties are characterized by a state‐dependent vector and a scalar disturbance/unknown input. The discrete‐time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete‐time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

A robust optimal sliding‐mode control approach for magnetic levitation systems

This paper presents a robust optimal sliding‐mode control approach for position tracking of a magnetic levitation system. First, a linear model that represents the nonlinear dynamics of the magnetic levitation system is derived by the feedback linearization technique. Then, the robust optimal sliding‐mode control developed from the linear model is proposed. In the proposed control scheme, the integral sliding‐mode control with robust optimal approach is developed to achieve the features of high performance in position tracking response and robustness to the matched and unmatched uncertainties. Simulation and experimental results from the computer‐controlled magnetic levitation system are illustrated to show the validity of the proposed control approach for practical applications. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society