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.     

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

A new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.     

AN ASYMPTOTIC SECOND‐ORDER SMOOTH SLIDING MODE CONTROL

Presented is a method of smooth sliding mode control design to provide for an asymptotic second‐order sliding mode on the selected sliding surface. The control law is a nonlinear dynamic feedback that in absence of unknown disturbances provides for an asymptotic second‐order sliding mode. Application of the second‐order disturbance observer in a combination with the proposed continuous control law practically gives the second‐order sliding accuracy in presence of unknown disturbances and discrete‐time control update. The piecewise constant control feedback is “smooth” in the sense that its derivative numerically taken at sampling rate does not contain high frequency components. A numerical example is presented.     

Practical stability analysis of sliding‐mode control with explicit computation of sampling time

Sliding‐mode control is a wide‐spread approach to a number of practical problems. The classical stability analyses of sliding‐mode control had to face the difficulty of defining a trajectory of a system whose dynamics are discontinuous in the state variable. Different generalizations of the system trajectory were suggested, such as Filippov solutions. Another generalization is based on the sample‐and‐hold framework, where the system dynamics are in continuous time and the control is changed only at certain discrete times. The current work addresses the sample‐and‐hold stability analysis of sliding‐mode control with special attention to an explicit computation of the required controller sampling time. A computational example is provided.     

Optimal discrete higher‐order sliding mode control of uncertain LTI systems with partial state information

The concept of discrete higher‐order sliding mode has received increased attention in the recent literature. This paper presents an optimal discrete higher‐order sliding mode control for an uncertain discrete LTI system using partial state information, which has been missing in literature. A new technique is proposed to design an optimal time‐varying higher‐order sliding surface and control input through the minimization of a quadratic performance index. Moreover, disturbance estimation technique is utilized to modify the control algorithm to reduce the width of the discrete higher‐order sliding mode band. The proposed algorithm is experimentally validated on a rectilinear plant. Copyright © 2017 John Wiley & Sons, Ltd.     

Discrete Sliding‐Mode Control of Mimo Linear Systems

This paper introduces a discrete sliding‐mode control for linear time‐invariant systems in the presence of matched uncertainties. The switching surface is constructed by applying the pole‐assignment method applying to the overall system, not the system in the sliding mode. Importantly, the control algorithm is derived to handle the rate of convergence to the sliding mode and to prevent the control law from encountering any unreasonably large variations. As for the system stability, it can be found that the system is stabilized and finally restricted to a known region. A numerical example is also included to demonstrate all the features of the developed discrete sliding‐mode control.     

Novel sliding mode control for multi‐input–multi‐output discrete‐time system with disturbance

This paper investigates sliding mode control for multi‐input–multi‐output discrete‐time system with disturbances. First of all, a novel nonlinear sliding surface, named as hyperbolic hybrid switching sliding surface, is proposed. Two different types of hyperbolic functions are introduced into the proposed sliding surface. Due to the changing of values of the hyperbolic functions, sliding surface switching occurs during the control process, which ensures that both settling time and overshoot can be decreased. The sliding mode controller is obtained based on a novel nonlinear reaching law. The nonlinear reaching law contains several parameters, and by properly designing these parameters, we can decrease the bounds of the sliding variables to small values. The stability analysis of the sliding motion is carried out from singular system viewpoint. Finally, simulation examples and comparison examples are presented to illustrate that the system performance is improved obviously by proposed novel sliding mode control, and the system is robust to the disturbances.     

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.     

Composite stratified anti‐disturbance control for a class of MIMO discrete‐time systems with nonlinearity

Anti‐disturbance control and estimation problem are investigated for nonlinear system subject to multi‐source disturbances. The disturbances classified model is proposed based on the error and noise analysis of priori knowledge. The disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with discrete‐time sliding‐mode control (DSMC), a novel type of composite stratified anti‐disturbance control scheme is presented for a class of multiple‐input–multiple‐output discrete‐time systems with known and unknown nonlinear dynamics, respectively. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

A Discrete‐Time Global Quasi‐Sliding Mode Control Scheme with Bounded External Disturbance Rejection

A global quasi‐sliding mode control (GQSMC) scheme is introduced to ensure zigzag motion with a smaller bound than that offered by Gao's method and to provide disturbance rejection throughout the entire response in discrete time. The design of an augmented forcing function is followed by three conditions in discrete time extended from global sliding mode control (GSMC) in continuous time. Furthermore, we adopt a switching gain, which is auto‐tuned as a function of sliding surface s(k), such that chattering phenomena can be considerably alleviated during the steady‐state, significantly reducing switching control applied to the plant. The proposed GQSMC scheme can provide more advantages such as an even distribution of the control input throughout the entire response and an improvement in the accuracy and speed of the desired performance, guaranteeing a quasi‐sliding mode throughout the entire response. In addition, we also consider the input disturbance rejection according to the norm‐bounded exogenous signal. Results from both the simulation and the experiments are reported. The results further verify that we can use the global sliding surface to curtail reaching the phase stage.     

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.     

A new practical robust control of cable‐driven manipulators using time‐delay estimation

In this paper, a new practical robust control scheme is proposed and investigated for the cable‐driven manipulators under lumped uncertainties. There are three parts in the proposed method, ie, a time‐delay estimation (TDE) part, a modified super‐twisting algorithm (STA) part, and a fractional‐order nonsingular terminal sliding mode (FONTSM) error dynamics part. The TDE uses intentionally time‐delayed system signals to estimate the lumped dynamics of the system and ensures an attractive model‐free control structure. The STA is applied to guarantee high performance and chattering suppression simultaneously in the reaching phase. The FONTSM error dynamics is utilized to obtain fast convergence and strong robustness in the sliding mode phase. Thanks to the above three parts, the proposed control scheme is model free and can ensure high control performance under lumped uncertainties. The stability considering the FONTSM error dynamics and modified STA scheme is analyzed. Comparative simulation and experiments were conducted to demonstrate the effectiveness and superiorities of the newly proposed control scheme. Corresponding experimental results show that our newly proposed control scheme can provide more than 20% improvement of the steady control accuracy under three different reference trajectories.     

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.     

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.     

Adaptive terminal angle constraint interception against maneuvering targets with fast fixed‐time convergence

In this paper, a modified adaptive fast nonsingular terminal sliding mode guidance law is proposed based on the theory of fixed‐time convergence, which is applied for intercepting maneuvering targets considering terminal angle constraint. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and provides no singularity and globally rapid convergence property by accelerating the convergence rate when the system is close to the origin. The upper bound of settling time can be obtained in advance by the controller's parameters. Besides, in order to achieve chattering‐free property, a continuous adaptive switching control is introduced and the achieved acceleration‐magnitude constraints are rigorously enforced. Finally, the fixed‐time convergence of the sliding mode manifold and the system states is demonstrated by Lyapunov stability theory. Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law.     

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.     

A Novel Sliding Mode Control for a Class of Second‐order Mechanical Systems

This paper considers the tracking control problem of a class of second‐order mechanical systems involving parametric uncertainty and external disturbance by a sliding mode control (SMC) without reaching phase. Specifically, an SMC strategy with modified variable‐gain proportional–integral–derivative (PID)‐type sliding function is proposed, by which the existence of a sliding mode throughout an entire response of the system starting from the initial time instance is ensured. Meanwhile, the introduction of a variable gain in the sliding function design effectively solves the dilemma between quicker response and smaller overshoot. The effectiveness of the proposed strategy is verified by both theoretical analysis and simulation results.