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This article investigates the sliding-mode control design problem for uncertain time-varying delayed systems. A novel non-negative constraints approach is proposed, which can be used to determine the stability of the controlled systems during the sliding motion. A new stability condition is obtained, which is easy to satisfy and verify. The parameters of the sliding-mode surface can be calculated by solving the non-negative constraints-based optimization problem defined in this article. Simulation examples are presented to illustrate the effectiveness and advantages of the developed strategy. [ABSTRACT FROM AUTHOR]

In this article, a continuous terminal sliding mode control algorithm is proposed for servo motor systems. A novel full-order terminal sliding mode surface is proposed based on the bilimit homogeneous property, such that the sliding motion is finite-time stable independent of the system's initial condition. A new continuous terminal sliding mode control algorithm is proposed to guarantee that the system states reach the sliding surface in finite-time. Not only the robustness is guaranteed by the proposed controller but also the continuity makes the control algorithm more suitable for the servo mechanical systems. Finally, a numerical example is presented to depict the advantages of the proposed control algorithm. An application in the rotary servo system is done to validate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust stabilization of quantized feedback sliding-mode control (SMC) for a class of uncertain linear systems via an event-triggered approach. By introducing an event-triggered mechanism, the event-triggered state instead of the state itself is quantized. And the generated finite event-triggered quantized state signal is sent through a digital network to the decoder and used for constructing a sliding mode controller to stabilize the uncertain linear systems. The relation among the lower bound of the quantized measurement saturating parameter, the upper bound of the event-triggered threshold parameter and the robust stabilization condition of linear uncertain systems, is first presented. Then, under the relation and by the combination of the proposed event-triggered mechanism for the system state and the discrete on-line adjustment policy for the quantizer sensitivity, the established quantized and event-triggered SMC laws are shown to ensure the reachability of the desired switching surface and global robust stabilization of uncertain linear systems is achieved. The theoretical result is verified via simulation illustration finally. [ABSTRACT FROM AUTHOR]

This paper is concerned with quantized sliding mode control in the unified delta operator system framework. To solve the quantization measurement saturating problem, a dynamic quantization strategy including discrete on-line open-loop zooming-out and closed-loop zooming-in policies is presented. By analyzing the sign relation between the traditional linear switching function and the quantized linear switching function, a novel quantized sliding mode control method is proposed, and both the amplitude of the control gain and the value of the quantization measurement saturating parameter are reduced compared with previous results. Some simulation results are presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

To avoid the chattering problem in the reaching-law-based discrete-time sliding mode control (DSMC) and the generation of over-large control action in the equivalent-control-based DSMC, a new DSMC method based on non-smooth control is proposed in this paper. Since there is no use of any switching term in the proposed DSMC, it is a chattering-free SMC method. Meanwhile, it is shown that the newly proposed non-smooth control-based DSMC can guarantee the same level of accuracy for the sliding mode motion as that of an equivalent control-based DSMC. To demonstrate the effectiveness of the proposed approach, a simulation example is presented. [ABSTRACT FROM AUTHOR]

This paper addresses the sliding mode control problem for uncertain MIMO linear Markovian jump systems. Firstly, by using the linear matrix inequality approach, sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the system on the sliding surfaces. Secondly, an equivalent control based sliding mode control is proposed, such that the closed-loop system can be driven onto the desired sliding surfaces in a finite time. Finally, combining with multi-step state transition probability, the reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. Simulation results are presented to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, an equivalent control based sliding mode control is proposed for single input linear Markovian jump systems which guarantees the asymptotical stability. Furthermore, by using the stochastic system theory, a multi-step state transition conditional probability function is introduced for the continuous Markovian process, which is used to define the reaching and sliding probabilities. Furthermore, the formulas for calculating reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. Extensive simulations are conducted to validate the theoretical results and show the relationship between the control force and reaching and sliding probabilities. [ABSTRACT FROM AUTHOR]

This paper proposes a terminal sliding-mode (TSM) observer for estimating the immeasurable mechanical parameters of permanent-magnet synchronous motors (PMSMs) used for complex mechanical systems. The observer can track the system states in finite time with high steady-state precision. A TSM control strategy is designed to guarantee the global finite-time stability of the observer and, meanwhile, to estimate the mechanical parameters of the PMSM. A novel second-order sliding-mode algorithm is designed to soften the switching control signal of the observer. The effect of the equivalent low-pass filter can be properly controlled in the algorithm based on requirements. The smooth signal of the TSM observer is directly used for the parameter estimation. The experimental results in a practical CNC machine tool are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

The quantization behaviors of a sliding-mode control system with state feedback when the measurement of the state is quantized are studied. Some inherent dynamical properties for the quantized SMC systems are analyzed. The definition and the occurrence condition of "quantized sliding mode" are proposed. Theoretical results are illustrated with simulation examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a method to overcome the singularity problem of terminal sliding-mode control systems. The system behaviors in both the reaching phase and the ideal sliding-mode are analyzed. A global nonsingular terminal sliding-mode control strategy for nonlinear systems is developed and it is shown that the proposed control strategy can eliminate the singularity, while guaranteeing the finite-time reachability of the systems to the terminal sliding-mode surface and the finite-time convergence of the systems towards the origin along the terminal sliding-mode surface. [Copyright &y& Elsevier]

Abstract: This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, discretization behaviors of equivalent control based sliding mode control systems with matched uncertainties are studied. Upper bounds for system steady states are established. Some inherent dynamical periodic properties of the systems subject to matched constant and periodic uncertainties are explored. Simulations are presented to verify the theoretical results. [Copyright &y& Elsevier]

Abstract: A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method. [Copyright &y& Elsevier]

This paper presents a global non-singular terminal sliding mode controller for rigid manipulators. A new terminal sliding mode manifold is first proposed for the second-order system to enable the elimination of the singularity problem associated with conventional terminal sliding mode control. The time taken to reach the equilibrium point from any initial state is guaranteed to be finite time. The proposed terminal sliding mode controller is then applied to the control of n-link rigid manipulators. Simulation results are presented to validate the analysis. [Copyright &y& Elsevier]

In this paper the design of adaptive sliding mode control for fuzzy systems is discussed. For a complex physical system represented by an amalgamated fuzzy global model that compromises a set of linear models, conditions for the adaptive sliding mode control to stabilize the global fuzzy model are given. The advantage of the control structure is that a priori knowledge of the upper bounds of bounded uncertainties and internal parameters is not required. Numerical simulations are presented to show the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper aims to improve the performance of the permanent magnet synchronous motor (PMSM) speed regulation system by combining a novel disturbance observer (DOB) with the super-twisting sliding mode (STSM) technique. First, a STSM controller is constructed to eliminate the adverse effects of the lumped disturbance in the PMSM speed regulation system. A novel DOB is introduced to estimate and compensate the lumped unknown disturbance, which constitutes a composite controller with a feedforward compensation term and a state-feedback control. As a result, the gain of the composite sliding mode controller can be significantly reduced, which will improve the performance of the closed-loop PMSM speed regulation system. The validity and robustness of the proposed composite control scheme are fully verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the stability of an uncertain system with quantization by using super-twisting controller. Both uniform and logarithmic quantization schemes are considered. Our main discovery is that the trajectories are always bounded with static uniform quantization scheme and are globally finite-time stable with logarithmic quantization scheme. Furthermore, a dynamic uniform quantization scheme is proposed to eliminate quantization errors. Simulation examples are given to shown the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

In this study, a novel idea is proposed for fixed‐time recursive surface structure design for arbitrary‐order system. The stability of controller design methodology is verified by using Lyapunov analysis. The primary benefit behind formulating the proposed surface structure is in achieving fixed‐time convergence during sliding. Moreover, the control structure is designed to get fixed‐time convergence during reaching as well. The approximate convergence time has been calculated mathematically and is verified using simulations. The sliding mode control is formulated for single‐input‐single–output non‐linear dynamical systems. The proposed control scheme is robust and the singularity is avoided. The conditions to ensure stability during reaching phase are derived and are shown to depend only on the design of surface parameters. The detailed simulation results of a general third‐order dynamic system show the efficacy of the proposed scheme. Finally, the proposed method is implemented for automatic generation control (AGC) of a multi‐area interconnected power system while considering the non‐linearity in the dynamic system. For the first time, fixed‐time convergence is assured for AGC. To the best of the authors' knowledge, no such structure is proposed yet for AGC. The results are also compared with the traditional proportional–integral controller. [ABSTRACT FROM AUTHOR]

In this paper, we propose the periodic event-triggering based design of sliding mode control (SMC) for the linear time-invariant (LTI) systems. In this technique, the triggering instants are generated by a triggering mechanism which is evaluated periodically at those time instants when the state measurements are available. So, the continuous state measurement, as it is usually needed in the continuous event-triggering strategy, is no longer required in this proposed triggering strategy. The main advantages of this triggering mechanism are: (1) a uniform positive lower bound for the inter event time is guaranteed and (2) this technique is more economical and realistic than its continuous counterpart due to the relaxation of continuous measurements. In this work, we use SMC to design the periodic event-triggering condition where SMC is designed in such a way that it allows periodic evaluation of triggering rule while guaranteeing the robust performance of the system. Moreover, an upper bound of the sampling period for the periodic measurements is also obtained in this design. Finally, the simulation results are given to demonstrate the design methodology and performance of the system with the proposed event-triggering strategy. [ABSTRACT FROM AUTHOR]

This article’s primary motivation is to propose a nonsingular and continuous terminal sliding-mode (TSM) control with reduced chattering, which is able to rapidly stabilize the second-order plant with high precision. To this end, a novel sliding-mode manifold, coined as practical TSM (PTSM) one, is first constructed. Once the proposed sliding surface is reached, a Lipschitz-continuous but slope-steep generalized velocity will be established at the origin such that the global nonsingularity of the equivalent control is ensured. The fast dynamic response with local high gain characterizes the sliding behavior inside the unit neighborhood of the origin. Importantly, the analytical solution of the proposed sliding-mode reduced-order system is deduced, which indicates that the finite time taken to slide into a preset small neighborhood of the origin can be calculated. The above designability of convergence time is necessary for control practices with accurate time sequence planning. Further, the corresponding globally singular-free PTSM reaching law with reduced chattering is designed based on the super-twisting algorithm. Finally, several groups of linear-motor-based control experiments verify the superiorities of proposed controllers. [ABSTRACT FROM AUTHOR]

In this paper, the Euler’s discretization of the second order sliding mode control system with the twisting algorithm is studied. It shows that, for all values of discretization steps, initial conditions and allowable parameter setting, the system trajectories are always bounded. It also shows that for the uncertain systems, under a mild condition, the system trajectories are also bounded. Further, the periodic behaviors and limit cycles of the system trajectories are explored with conditions for the existence of periodic orbits formulated. Extensive simulation examples are given to show typical trajectories, and comparison between the first order and second order sliding mode control systems. [ABSTRACT FROM AUTHOR]

Abstract: In conventional sliding-mode control systems, the sliding-mode motion is of reduced order. Two main problems hindering the application of the sliding-mode control are the singularity in terminal sliding-mode control systems and the chattering in both the conventional linear sliding-mode and the terminal sliding-mode control systems. This paper proposes a chattering-free full-order terminal-sliding-mode control scheme. Since the derivatives of terms with fractional powers do not appear in the control law, the control singularities are avoided. A continuous control strategy is developed to achieve the chattering free sliding-mode control. During the ideal sliding-mode motion, the systems behave as a desirable full-order dynamics rather than a desirable reduced-order dynamics. A systematic design method of full-order sliding-mode control for nonlinear systems is presented, which allows both the chattering and singularity problems to be resolved. Simulations validate the proposed chattering free full-order sliding-mode control. [Copyright &y& Elsevier]

This paper develops a sliding-mode control (SMC) approach for systems with mismatched uncertainties via a nonlinear disturbance observer (DOB). By designing a novel sliding surface based on the disturbance estimation, a DOB-based SMC method is developed in this paper to counteract the mismatched disturbance. The newly proposed method exhibits the following two attractive features. First, the switching gain is only required to be designed greater than the bound of the disturbance estimation error rather than that of the disturbance; thus, the chattering problem is substantially alleviated. Second, the proposed method retains its nominal performance, which means the proposed method acts the same as the baseline sliding-mode controller in the absence of uncertainties. Simulation results of both the numerical and application examples show that the proposed method exhibits much better control performance than the baseline SMC and the integral SMC (I-SMC) methods, such as reduced chattering and nominal performance recovery. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the problem of designing a control strategy to guarantee stability in probability for high-order stochastic systems. The control hinges on the sliding-mode scheme. We first prove that the control design can stabilize a fast terminal sliding-mode function. We further show that the stable sliding mode is able to assure the stability in probability for the high-order stochastic system. The resulting system may account nonvanishing diffusion terms, which is regarded as a novelty. The derived control strategy has implications for applications—experiments are carried out to control the pitch angle of a one-degree-of-freedom aerial device. The corresponding experimental results demonstrate the benefits and effectiveness of our approach. [ABSTRACT FROM AUTHOR]

This paper presents a novel cascade proportional-integral (PI) continuous second-order sliding mode control (SMC) for induction motor in the presence of operational constraints. The inner-loop SMC is designed to control the current dynamics of the motor, while the outer-loop control is the PI control of speed. The main advantage of the proposed method is that the PI control provides reference to the inner-loop SMC with constraints according to the system requirements in terms of maximum current and speed limits. Moreover, because the inner-loop dynamics of the motor are nonlinear, SMC design has more importance in terms of robustness and disturbance rejection capability. The proposed control is a continuous-time design strategy with fixed-time convergence, while its discretization is performed at the implementation stage. The performance of the developed controller is validated by carrying out real-time experimental studies on an industrial size induction machine. Experimental results demonstrate remarkable robust tracking performance of the controller in terms of transient speed response and steady-state accuracy. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time attitude tracking control problem for rigid spacecraft with input quantization and external disturbances. A novel fixed-time disturbance observer is designed to estimate unknown disturbances. By using adding a power integrator technique, a fixed-time controller is constructed, which can guarantee system states converge to a neighborhood of origin in fixed time. The parameter of quantizer can be coarsely chosen. Finally, simulation results are employed to demonstrate the effectiveness of the developed control scheme. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to solve the position tracking control problem for the permanent magnet linear motor by using the discrete-time fast terminal sliding mode control (SMC) method. Specifically, based on Euler's discretization technique, the approximate discrete-time model is first obtained and analyzed. Then, by introducing a new type of discrete-time fast terminal sliding surface, an improved discrete-time fast SMC method is developed and an equivalent-control-based fast terminal SMC law is subsequently designed. Rigorous analysis is provided to demonstrate that the fast terminal SMC law can offer a higher accuracy than the traditional linear SMC law. Numerical simulations and experimental results are finally performed to demonstrate the effectiveness of the proposed approach and show the advantages of the present discrete-time fast terminal SMC approach over some existing approaches, such as discrete-time linear sliding mode control approach and the PID control method. [ABSTRACT FROM AUTHOR]

This paper investigates the fuzzy control issue for uncertain active suspension systems via dynamic sliding-mode method. The Takagi–Sugeno fuzzy approach is adopted on the background of the varying masses to describe the prescribed nonlinear system in order to achieve the design targets via the method of sector nonlinearity. This paper employs the dynamic sliding-mode scheme to control nonlinear active suspension systems. In the proposed sliding-mode control scheme, the sliding surface function is formed linearly with the system states and control inputs. Then, a fuzzy dynamic term is utilized to construct the sliding-mode feedback controller. In existing results, the sliding mode is achieved and maintained with no consideration of the system perturbations. Thus, sufficient conditions are proposed to make the sliding surface reachable with the existence of the system perturbations to make the augmented system stable. Finally, simulation results are presented to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Abstract: A continuous nonsingular terminal sliding mode control approach is proposed for mismatched disturbance attenuation. A novel nonlinear dynamic sliding mode surface is designed based on a finite-time disturbance observer. The time taken to reach the desired setpoint from any initial states under mismatched disturbance is guaranteed to be finite time. In addition, the proposed method exhibits the fine properties of nominal performance recovery as well as chattering alleviation. [Copyright &y& Elsevier]

Abstract: This paper is concerned with robust integral sliding mode control for an offshore steel jacket platforms subject to nonlinear wave-induced force and parameter perturbations. A robust integral sliding mode controller is designed to stabilize the dynamic model of the offshore steel jacket platform. It is shown through simulation results that the robust integral sliding mode control scheme can reduce the internal oscillations of the offshore steel jacket platform dramatically; and the performance of the offshore steel jacket platform under the robust integral sliding mode control scheme is better than the ones under the nonlinear control scheme and the dynamic output feedback control scheme. [Copyright &y& Elsevier]

This brief paper proposes a method for tuning the parameters of a variable structure controller. The approach presented extracts the error at the output of the controller and applies a nonlinear tuning law using this error measure. The adaptation mechanism drives the state tracking error vector to the sliding hypersurface and maintains the sliding mode. In the simulations, the approach presented has been tested on the control of Duffing oscillator and the analytical claims have been justified under the existence of measurement noise, uncertainty and large nonzero initial errors. [Copyright &y& Elsevier]