Discrete time integral sliding mode control for overhead crane with uncertainties

This paper describes a novel 3D four-leaf chaotic system and details its qualitative properties. The novel chaotic system is a polynomial system with three quadratic nonlinearities. The phase portraits of the novel four-leaf chaotic system are illustrated. We show that the novel chaotic system has three unstable equilibrium points. The Lyapunov exponents of the novel chaotic system are calculated as L1 = 1.0299, L2 = 0 and L3 = −7.0268. The Lyapunov dimension of the novel chaotic system is found as DL = 2.1466. Next, we apply integral sliding mode control method to find a feedback control law that globally stabilises the novel four-leaf chaotic system. Furthermore, we apply integral sliding mode control method to find a feedback control law that globally synchronises two identical four-leaf chaotic systems. The global control and synchronisation results are proved using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the sliding mode control results derived in this work.

To improve the control performance of linear motors with external perturbations and input saturation, this paper designs an anti-saturation fixed-time integral sliding mode control strategy based on a fixed-time disturbance observer (FxITSMC-FxDO). First, the parameter uncertainties and external disturbances are viewed as composite disturbances. A fixed-time disturbance observer is designed to estimate and compensate for them in real-time, which effectively suppresses chattering by estimating the lumped disturbances. Second, by combined-time theory and integral sliding-modetrol, a fixed-time integral sliding-mode controller is designed to accelerate the convergence speed. Moreover, a non-linear anti-saturation compensator is designed based on the actuator saturation effect parameter to enable the system to exit the saturation region quickly. The fixed-time convergence property of the closed-loop system is proved based on the Lyapunov stability theorem. The experimental results show that the proposed control method effectively improves the control accuracy, response speed, and robustness of linear motors. The step response time of the direct drive permanent magnet linear motor is improved by 16.0% compared to the integral sliding mode control method and 12.5% compared to the finite-time sliding mode control method. In sine target tracking, steady-state accuracy is enhanced by 31.3% over ITSMC and 24.1% over FITSMC-FDO. Furthermore, as the sinusoidal tracking frequency increased from 0.5 to 4 Hz, the proposed control strategy maintained relatively low increases in ITAE and ISE.

Conventional sliding mode controllers have been successfully applied to control various types systems including the Stewart platform manipulator. But chattering, lack of robustness in the reaching phase and sensitivity to unmatched uncertainty are the basic problems which delayed their practical implementations. To avoid the non robust reaching phase to compensate unmatched uncertainties, integral sliding mode controllers have been proposed but only SISO system examples have been tested. Hence in this paper, MIMO implementation of integral sliding mode controller is tested using a 6 DOF Stewart platform manipulator. The integral sliding mode controller is implemented using MATLAB simulation and the result is compared with PD and conventional sliding mode controller. It was found that the integral sliding mode controller performs better in avoiding uncertainties due to load variation and actuator friction.

This article studies the observer‐based integral sliding mode control (ISMC) problem for continuously uncertain neutral semi‐Markovian jumping systems with time‐varying delays (TDs). Firstly, based on the designed state observer, an ISMC method is proposed for the first time. Then, building an appropriate stochastic Lyapunov–Krasovskii functional by taking into account more information about TDs, a novel sufficient condition is established for the robustly stochastic stability of the overall system made up of the error system and the sliding mode dynamics system. Furthermore, an ISMC law is devised to ensure the reachability of the integral sliding surface in a finite time. Additionally, the proposed method can be reduced to the known state case, thus, the ISMC problem for continuously uncertain neutral semi‐Markovian jumping systems with TDs is also investigated in this article. Finally, three numerical examples explain the effectiveness of the results obtained.

This paper analyzes the dynamics of overhead cranes suffering from uncertain disturbances, and then proposes a novel adaptive dynamic integral sliding mode control law for the underactuated overhead cranes with uncertainties. This method solve the problem of the tradeoff between the steady-state error and the chattering effect by employing the dynamic sliding mode technique, moreover, the self-tuning laws for the switching controller are developed to eliminate unknown disturbances exerted on the overhead crane systems. None of the prior information about the upper bound of uncertainties is needed in the sliding mode controller design. The global stability of the proposed controller is proven. Simulation study shows the good performance of the suggested method.

Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator

In this paper, sliding mode controller (SMC) and integral sliding mode controller (ISMC) are designed for a variable speed wind turbine. The main objective of the controller is to optimize the energy captured from the wind at below rated power. To overcome the steady state error, the ISMC is introduced. However, in the presence of large uncertainties, ISMC control approach produces oscillatory phenomenon due to the higher needed gain. To eliminate the tradeoffs between the ISMC tracking performance and the high gain at the control input, we have introduced a new method based on the modification of the output tracking error through the use of the exponential function in order to eliminate the reaching phase. The stability of the proposed ISMC is analyzed by Lyapunov theory and the control action didn't show any chattering. The simulation results of ISMC are presented and the control performance is compared with conventional SMC.

This article proposes a control scheme for formation of maneuvers of a team of mobile robots. The control scheme integrates the integral sliding mode control method with the nonlinear disturbance observer technique. The leader–follower formation dynamics suffer from uncertainties originated from the individual robots. The uncertainties challenge the formation control of such robots. Assuming that the uncertainties are unknown but bounded, an nonlinear disturbance observer-based observer is utilized to approximate them. The observer outputs feed on an integral sliding mode control-based controller. The controller and observer are integrated into the control scheme to realize formation maneuvers despite uncertainties. The formation stability is analyzed by means of the Lyapunov’s theorem. In the sense of Lyapunov, not only the convergence of the approximation errors is guaranteed but also such a control scheme can asymptotically stabilize the formation system. Compared to the results by the sole integral sliding mode control, some simulations are presented to demonstrate the feasibility and performance of the control scheme.

In this study, trajectory tracking control of six–degrees of freedom robotic manipulator has been performed using the proposed fractional-order adaptive integral sliding mode control scheme. The proposed method is first composed by fractional-order and adaptive integral sliding mode control to achieve the finite-time convergence, chattering-free control inputs, better tracking performance and robustness for the robotic manipulator. Furthermore, an adaptive method has been utilized to evaluate and compensate the uncertain and unknown dynamics of the system without relying on the prior knowledge of the upper bounds. To illustrate the efficiency of the proposed fractional-order adaptive integral sliding mode control method, the real-time experimental studies have been performed for the six–degrees of freedom industrial robot manipulator. The experimental outcomes strongly verified that the proposed controller gives quite well trajectory tracking response and faster convergence compared with the classical integral sliding mode control under the external payload.

Starting in the rotating condition is an important technology for induction motor (IM) speed sensorless control. The key of this technology is that the initial speed of the IM in the rotating condition should be estimated quickly and accurately. In this article, an integral sliding mode control method based on the nonlinear model of the rotor back electromotive force is designed to start a speed sensorless controlled IM in the rotating condition. The stability is guaranteed by Lyapunov stability analysis, and the robustness to rotor time constant and disturbance are analyzed. Meanwhile, in comparison with the proposed control method, the existing input–output feedback linearization (IOFL) control method is introduced and the stability and robustness are also analyzed. Compared with the existing IOFL control method, the proposed control method can estimate the initial speed in the rotating condition without overshoot and has better dynamic performance and robustness. In addition, the proposed control method can be applied not only to the restart operation but also to the normal operation. Only a single control strategy is required from the restart operation to the normal operation. The proposed method is verified by simulation and experiments using a 7.5 kW IM.

A fault tolerant control (FTC) scheme for tracking control is proposed for nonlinear uncertain systems affected by actuator faults and matched uncertainties with unknown upper bound. The proposed controller utilizes backstepping control which is integrated with integral sliding mode control method. For designing the integral sliding mode controller, an adaptive law is used to estimate the unknown upper bounds of faults and uncertainties. The proposed FTC ensures satisfactory transient and steady state performances with a chattering free control input. Asymptotic stability in presence of matched uncertainties and partial loss of actuator effectiveness is guaranteed in the proposed control system. The efficiency of the proposed fault tolerant control scheme is demonstrated by simulation results.

In order to weaken the influences of system uncertainties on the coordinated tracking control performance of the speed and tension system of the reversible cold strip rolling mill, a backstepping sliding model control strategy is proposed based on the extended state observers (ESOs). First, the ESOs are constructed to dynamically observe the system's unmatched uncertainties, which effectively improve the system's tracking control precision. Next, based on the backstepping control and the tracking differentiators (TDs), the integral sliding mode controllers (ISMCs) for the speed and tension system of the reversible cold strip rolling mill are designed, which solve the "differential explosion" problem of conventional backstepping control, and improve the robust stability of the system, Finally, simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill by using actual data, and the results show the validity of the proposed control strategy.

This paper proposes a tracking control method for a three-wheeled omnidirectional manipulator system (OMMS) with disturbance and friction. The OMMS is separated into two subsystems, a three-wheeled omnidirectional mobile platform (OMP) and a selective compliant articulated robot for assembly (SCARA) type of manipulator. Therefore, two controllers are designed to control the OMP and the manipulator system. Firstly, based on a kinematic modeling of the manipulator, a kinematic controller (KC), combined with an integral sliding mode controller (ISMC), is designed for the end-effector of the manipulator to track a desired trajectory with the desired angular velocity vector of links. Secondly, a differential sliding mode controller (DSMC) based on a dynamic modeling of the OMP with force external disturbances is proposed to obtain control inputs moving the OMP so that the manipulator tracks the desired posture without singularity. The system stability is proven using Lyapunov stability theory. The simulation and experimental results are presented to illustrate the effectiveness of the proposed controllers in the presence of disturbance and friction.

This study addresses the challenge of attitude tracking control for a rigid‐flexible spacecraft with high‐inertia rotating appendages. The Lagrange method was used to establish the kinematic and dynamic models of the spacecraft. The translation and rotation of the spacecraft, vibrations of solar panels, and imbalance caused by the rotating appendages, which cause a complex control problem, were considered. To address the complex control problem, a novel, fast nonsingular integral sliding mode control method is proposed to perform the attitude tracking function of spacecraft. A sliding mode control law was established for the high‐inertia appendages to maintain an appropriate angular velocity during rotation. Finally, the effectiveness of the proposed attitude control law was verified by numerical simulations for a spacecraft with high‐inertia rotating appendages and symmetrical flexible solar panels.

In previous researches, an operator-based sliding mode control design to achieve high power transfer efficiency of a wireless power transfer (WPT) system via magnetic resonance coupling were shown. However, it is difficult to reduce the steady-state error by using SMC-based tracking controller. In this paper, an operator-based integral sliding mode control method is adopted to reduce the steady-state error in the WPT system. Moreover, high power efficiency should be achieved in the WPT system by using an impedance matching control. The effectiveness of the proposed method is verified by simulation results.