A quasi-optimal sliding mode control scheme based on control Lyapunov function

In this paper, the sliding mode control (SMC) method is integrated with a nonlinear suboptimal control method based on control Lyapunov function (CLF). According to the system nominal part, a CLF is first constructed in general to facilitate the nonlinear optimal system design and Sontag's formula is used in particular to generate a suboptimal controller. To take system uncertainties into account, the SMC mechanism is designed based on the CLF. By integration, the suboptimal control and SMC are made to function in a complementary manner. When the system state is far away from the equilibrium and the system nominal part is predominant, the nonlinear optimal control part will govern the system response as well as drive the system state approach the equilibrium in an optimal fashion. On the contrary, when approaching the equilibrium such that system perturbations become the main factor, the SMC will take over the control task to warrant the desired robustness property and achieve precise control.     

Robust finite-time sliding mode control for discrete-time singular system with time-varying delays

This paper explores the finite-time bounded issue for discrete-time singular time-varying delay system via sliding mode control method. A suitable discrete-time sliding mode control law is constructed to drive the state trajectories onto the specified sliding surface in a given finite time interval. Meanwhile, sufficient conditions for finite-time bounded to the closed-loop delayed system are provided in both reaching phase and sliding motion phase. In addition, the finite-time sliding mode controller gain matrix can be solved by using the linear matrix inequalities approach. Finally, three numerical examples are illustrated to demonstrate the superiority and practicability of presented results.     

Fuzzy sliding mode control design of Markovian jump systems with time-varying delay

This paper studies the robust stochastic stabilization problem for a class of fuzzy Markovian jump systems with time-varying delay and external disturbances via sliding mode control scheme. Based on the equivalent-input-disturbance (EID) approach, an online disturbance estimator is implemented to reject the unknown disturbance effect on the considered system. Specifically, to obtain exact EID estimation Luenberger fuzzy state observer and a low-pass filter incorporated to the closed-loop system. Moreover, novel fuzzy EID-based sliding mode control law is constructed to ensure the stability of the closed-loop system with satisfactory disturbance rejection performance. By employing Lyapunov stability theory and some integral inequalities, a new set of delay-dependent robust stability conditions is derived in terms of linear matrix inequalities (LMIs). The resulting LMI is used to find the gains of the state-feedback controller and the state observer a for the resulting closed-loop system. At last, numerical simulations based on the single-link arm robot model are provided to illustrate the proposed design technique.     

Data-driven discrete terminal sliding mode decoupling control method with prescribed performance

This paper proposes a data-driven terminal sliding mode decoupling controller with prescribed performance for a class of discrete-time multi-input multi-output systems in the presence of external disturbances and uncertainties. First, utilizing a discrete-time extended state observer and a compact form dynamic linearization data model, we derive a new data-driven mothod and establish the relationship between the input and output signals of controlled plant. Moreover, the disturbances, uncertainties, and couplings are suppressed owing to the application of the terminal sliding mode technique. Combined with the principle of prescribed performance control, the terminal sliding mode law with prescribed performance is derived. With the proposed data-driven method, the tracking error is lower, and the decoupling ability is improved. Furthermore, the stability of the control system is proven. Finally, a simulation is conducted on a three-tank system to demonstrate the effectiveness of the proposed scheme.     

Observer-based finite-time asynchronous sliding mode control for Markov jump systems with time-varying delay

The issue of finite-time sliding mode control (SMC) is studied for a class of Markov jump systems, in which parameter uncertainties, external disturbances and time-varying delay are considered. Firstly, a suitable observer-based SMC law is devised so that state trajectory of the system can reach the designed sliding mode surface in finite-time, the gain of the controller is asynchronous to the mode of original system. Meanwhile, the sufficient conditions of finite-time boundedness in the sliding phase and reaching phase are derived by the time partition strategy. Moreover, the gains of the observer and the observer-based controller will be acquired by using the linear matrix inequalities tool. In fine, emulation products are used to confirm the merits of the SMC strategy.     

Dual terminal sliding mode control design for rigid robotic manipulator

This paper proposes a dual terminal sliding mode control scheme for tracking tasks of rigid robotic manipulators. As a significant novelty, the presented design technique integrates the individual sliding mode surfaces to achieve the finite time convergence of tracking errors utilizing specially designed construct, and accordingly the convergence time is easily obtained due to the integral design. The underactuated issue and input limitation are specially considered in this paper, i.e., the underactuated issue is solved by introducing the hierarchical methodology into the basic dual sliding mode controller. The proposed method can easily combine with the adaptive technique to eliminate the negative effect caused by the input limitation in the rigorous stability analysis. These newly proposed methods also have the characteristics of nonsingularity and chattering suppression, and the effectiveness and high efficiency are verified by stabilizing the motions of the overhead crane and the tracking tasks of the rigid robotic manipulator. Simulation results validate the theoretical analyses about the proposed method.     

Global fast terminal sliding mode controller for hydraulic turbine regulating system with actuator dead zone

This paper investigates the frequency change problem of hydraulic turbine regulating system based on terminal sliding mode control method. By introducing a novel terminal sliding mode surface, a global fast terminal sliding mode controller is designed for the closed loop. This controller eliminates the slow convergence problem which arises in the terminal sliding mode control when the error signal is not near the equilibrium. Meanwhile, following consideration of the error caused by the actuator dead zone, an adaptive RBF estimator based on sliding mode surface is proposed. Through the dead zone error estimation for feed-forward compensation, the composite terminal sliding mode controller has been verified to possess an excellent performance without sacrificing disturbance rejection robustness and stability. Simulations have been carried out to validate the superiority of our proposed methods in comparison with other two other kinds of sliding mode control methods and the commonly used PID and FOPID controller. It is shown that the simulation results are in good agreement with the theoretical analysis.     

Synchronization of second-order chaotic systems via adaptive terminal sliding mode control with input nonlinearity

In the presence of system uncertainties, external disturbances and input nonlinearity, this paper is concerned with the adaptive terminal sliding mode controller to achieve synchronization between two identical attractors which belong to a class of second-order chaotic system. The proposed controller with adaptive feedback gains can compensate nonlinear dynamics of the synchronous error system without calculating the magnitudes of them. Meanwhile, these feedback gains are updated by the novel adaptive rules without required that the bounds of system uncertainties and external disturbances have to be known in advance. Some sufficient conditions for stability are provided based on the Lyapunov theorem and numerical studies are performed to verify the effectiveness of presented scheme.     

A real-time estimation and control scheme for induction motors based on sliding mode theory

In this paper a sliding mode position control for high-performance real-time applications of induction motors is developed. The design also incorporates a sliding mode rotor flux estimator in order to avoid the flux sensors. The proposed control scheme presents a low computational cost and therefore can be implemented easily in a real-time applications using a low cost Digital Signal Processor (DSP). The stability analysis of the observer and the controller, under parameter uncertainties and load torque disturbances, is provided using the Lyapunov stability theory. Finally simulated and experimental results show that the proposed controller with the proposed observer provides a good trajectory tracking and that this scheme is robust with respect to plant parameter variations and external load disturbances.     

Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.     

Chaos control of the permanent magnet synchronous motor with time-varying delay by using adaptive sliding mode control based on DSC

This paper focuses on the problem of chaos control for the permanent magnet synchronous motor with chaotic oscillation, unknown dynamics and time-varying delay by using adaptive sliding mode control based on dynamic surface control. To reveal the mechanism of motor system and facilitate controller design, the dynamic behavior of the system is investigated. Nonlinear items of system model, upper bounds of time delays and their derivatives are taken as unknown in the overall process. A RBF neural network with an adaptive law, which eliminates restrictions on accurate model and parameters, is employed to cope with unknown dynamics. In order to solve issues such as chaotic oscillation, ‘explosion of complexity’ of backstepping, and chattering associated with sliding mode control, a sliding mode controller is developed within the framework of dynamic surface control by the hybrid of adaptive technology and RBF neural network. In addition, an appropriate Lyapunov function is employed to demonstrate the system stability. Finally, the feasibility of the proposed scheme is testified by simulation.     

Fault-tolerant adaptive control for uncertain switched systems with time-varying delay and actuator faults based on sliding mode technique

This paper utilizes the sliding mode approach to tackle the issue of adaptive control for uncertain switched systems with time-varying delay and actuator faults. Firstly, a kind of mathematical model of switched time-varying delay systems under sudden actuator faults is defined. Then, a linear sliding manifold is constructed, followed by some adequate conditions for exponential stability of the switched systems running on the sliding phase. Furthermore, an adaptive fault-tolerant controller for handling the actuator degradation is designed and the reachability of the established sliding manifold is proved. At last, a series of simulation examples are provided to demonstrate the efficiency of the proposed solution.     

Adaptive dynamic surface and sliding mode tracking control for uncertain QUAV with time-varying load and appointed-time prescribed performance

In this paper, the appointed-time prescribed performance and finite-time tracking control problem is investigated for quadrotor unmanned aerial vehicle (QUAV) in the presence of time-varying load, unknown external disturbances and unknown system parameters. For the position loop, a novel appointed-time prescribed performance control (ATPPC) strategy is proposed based on adaptive dynamic surface control (DSC) frameworks and a new prescribed performance function to achieve the appointed-time convergence and prescribed transient and steady-state performance. For the attitude loop, a new finite-time control strategy is proposed based on a new designed sliding mode control technique to track the desired attitude in finite time. Some assumptions of knowing system parameters are canceled. Finally, the stability of the closed-loop system is proved via Lyapunov Theory. Simulations are performed to show the effectiveness and superiority of the proposed control scheme.     

Finite-time tracking using sliding mode control

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler–Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. An approach known as the terminal sliding mode control (TSMC) involves non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. The main advantage of this control scheme is in fast converging times without excessive control effort. Such controllers are known to have singularities in some parts of the state space and, in this paper, we propose a method of partitioning the state space into two regions where the TSMC is bounded and its complement. We show that the region of bounded TSMC is invariant and design an auxiliary sliding mode controller predicated on linear smooth sliding surface for the initial conditions outside this region. Furthermore, we extend these results to address TSMC for underactuated systems characterized by the mobile robot dynamics. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader. Finally, we validate our results experimentally using a wheeled mobile robot platform.     

Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer

Over the last decade, considerable interest has been shown from industry, government and academia to the design of Vertical Take-Off and Landing (VTOL) autonomous aerial vehicles. This paper uses the recently developed sliding mode control driven by sliding mode disturbance observer (SMC-SMDO) approach to design a robust flight controller for a small quadrotor vehicle. This technique allows for a continuous control robust to external disturbance and model uncertainties to be computed without the use of high control gain or extensive computational power. The robustness of the control to unknown external disturbances also leads to a reduction of the design cost as less pre-flight analyses are required. The multiple-loop, multiple time-scale SMC-SMDO flight controller is designed to provide robust position and attitude control of the vehicle while relying only on knowledge of the limits of the disturbances. Extensive simulations of a 6 DOF computer model demonstrate the robustness of the control when faced with external disturbances (including wind, collision and actuator failure) as well as model uncertainties.     

N-sigma stability of stochastic systems with sliding mode control

In this paper, sliding mode control for discrete time systems with stochastic noise in their input channel has been discussed. The idea of process control using control charts has influenced this new approach towards dealing with systems with stochastic noise. The new approach approximates the stochastic noise as a bounded uncertainty, similar to having bounds in the control charts for stochastic process control data. For discrete time systems, this results in a bounded stability in probability of the quasi sliding mode, which is referred to as the N-sigma bounded stability. The probability associated with the stability notions is not fixed and the control engineer may desire lower or higher degrees of stability in terms of this probability. Thus one has design flexibility while implementing the theory in practice, where one might have to adjust the desired degree of stability due to hardware limitations.     

Enhanced continuous higher order sliding mode control with adaptation

This paper proposes a new Continuous Adaptive HOSM control algorithm. The key advantage of the adaption scheme is that it does not require knowledge of the bounds on the matched uncertainty, and the gains themselves are not conservatively overestimated by the adaption scheme – which helps mitigate the problem of chattering. Compared with earlier work, two variable parameters are allowed to adapt and this facilitates much better self-tuning capabilities and improved closed-loop performance.     

Load frequency control for wind-integrated multi-area power systems: An area-based event-triggered sliding mode scheme

This paper deals with the load frequency control problem of multi-area power system with doubly-fed-induction-generator-based wind farm. An area-based event-triggered (ET) sliding mode control scheme is proposed to restore the nominal frequency by transmitting less information. The main feature of area-based ET scheme is that each area will transmit its states information to the controller independently via its own triggering mechanism. By flexibly selecting triggering thresholds, the area-based ET scheme can meet the unbalanced network resources among different areas. Meanwhile, the designed sliding mode controller can effectively suppress the fast fluctuation resulting from load and wind generation to achieve frequency restoration and maintain the tie-line power at its scheduled value. The optimization algorithm on the sufficient conditions is given. Finally, the proposed control scheme is illustrated via a three-area power system and IEEE 39-bus system.     

Adaptive second order terminal sliding mode controller for robotic manipulators

In this paper an adaptive second order terminal sliding mode (SOTSM) controller is proposed for controlling robotic manipulators. Instead of the normal control input, its time derivative is used in the proposed controller. The discontinuous sign function is contained in the derivative control and the actual control obtained after integration is continuous and hence chatterless. An adaptive tuning method is utilized to deal with the system uncertainties whose upper bounds are not required to be known in advance. The performance of the proposed control strategy is evaluated through the control of a two-link rigid robotic manipulator. Simulation results demonstrate the effectiveness of the proposed control method.