Terminal Sliding Mode Control Research Articles

CORRIGENDUM to “Novel anti-disturbance fast terminal sliding mode control with improved quick reaching law for DC-DC buck converter”

CORRIGENDUM to “Novel anti-disturbance fast terminal sliding mode control with improved quick reaching law for DC-DC buck converter”

Experimental design and analysis of advanced three phase converter for PV application with WCO-P&O MPPT controller

Photovoltaic (PV)-based power generation systems are becoming increasingly popular as a due to its high performance and cleanliness. Several factors influence the performance of a PV system, including shadowing effects. PV systems employ MPPT methodologies to obtain the power from PV array. Conventional MPPTs works well under normal conditions when there is no shadow effects or partial shading. The presence of partial shading affects the system performance and generates several power peaks. This complicates the process of finding out of the global peak (GMPP) with improved tracking efficiency and reduced settling time including conversion efficiency. This work proposes three hybrid MPPT techniques: Water Cycle Optimisation-Perturb and Observe (WCO-PO), Artificial Neural Network Supported Adaptable Stepped-Scaled Perturb and Observe (ANN-ASSPO), Grey Wolf Optimisation-Modified Fast Terminal Sliding Mode Controller (GWO-MFTSMC), and two conventional MPPT techniques WCO and P&O have been implemented. The proposed system utilizes interleaved boost converter with three phase. The performances of proposed hybrid MPPTs strategies were compared in terms of output voltage, output current and extracted power. The comparison also includes conversion efficiency and average settling time. To analyse the performances, four different cases have been used to test the efficacy of hybrid MPPTs under changing climatic conditions. The MATLAB/Simulink tool has been used to analyze the PV system performances. In the three hybrid MPPT techniques, WCO-PO has performed better when compared to other two hybrid MPPTs in terms of conversion efficiency (99.56%) and settling time (1.4 m).

Integral terminal sliding mode fault tolerant control of quadcopter UAV systems

The article presents an active fault-tolerant control scheme with an integral terminal sliding mode controller for the UAV systems. This scheme effectively addresses saturation issues, disturbances, and sensor and actuator faults. Initially, the quadcopter UAV's model is represented in state space form. Subsequently, an augmented system incorporating auxiliary states from sensor faults is developed. An adaptive sliding mode observer is proposed for estimating the actuator and sensor faults. The integral terminal sliding mode fault-tolerant control, designed for altitude and attitude regulation, relies on fault estimation data. In contrast, a cascade proportional-integral-derivative (PID) controller is employed for position control. Simulation results demonstrate the superiority of the proposed method over existing control algorithms.

Identification and Control of Flexible Joint Robots Based on a Composite-Learning Optimal Bounded Ellipsoid Algorithm and Prescribe Performance Control Technique

This paper presents an indirect adaptive neural network (NN) control algorithm tailored for flexible joint robots (FJRs), aimed at achieving desired transient and steady-state performance. To simplify the controller design process, the original higher-order system is decomposed into two lower-order subsystems using the singular perturbation technique (SPT). NNs are then employed to reconstruct the aggregated uncertainties. An adaptive prescribed performance control (PPC) strategy and a continuous terminal sliding mode control strategy are introduced for the reduced slow subsystem and fast subsystem, respectively, to guarantee a specified convergence speed and steady-state accuracy for the closed-loop system. Additionally, a composite-learning optimal bounded ellipsoid algorithm (OBE)-based identification scheme is proposed to update the NN weights, where the tracking errors of the reduced slow and fast subsystems are integrated into the learning algorithm to enhance the identification and tracking performance. The stability of the closed-loop system is rigorously established using the Lyapunov approach. Simulations demonstrate the effectiveness of the proposed identification and control schemes.

Nonlinear behaviors and chaos control of a fluid-conveying piezoelectric pipe in supercritical regime

The study investigated the steady state response of a piezoelectric pipe conveying fluid under external and internal resonances in the supercritical regime of fluid velocity. Internal resonance conditions between the first and second frequency modes were studied at a specific flow velocity in the supercritical regime. The Galerkin method and the multiple scale method were used to extract the vibration amplitude versus the excitation frequency and amplitude. The steady state solutions lost stability through saddle-node and Hopf bifurcations, leading to periodic, double periodic, multi-periodic, and chaotic behaviors in the forced and frequency response curves. Time response, FFT, phase portrait, and Lyapunov exponents were presented to predict the unstable regions of the piezo-pipe system between the Hopf points. The Wolf algorithm was utilized to evaluate the Lyapunov exponents. Additionally, a fuzzy terminal sliding mode controller was designed in the chaotic region of the piezoelectric pipe conveying fluid, and its parameters were optimized using the genetic algorithm. The controller effectively stabilized the chaotic motion of the system, demonstrating better performance than the sliding mode control in numerical results.

Adaptive backstepping sliding mode compensation control for electro‐hydraulic load simulator with backlash links

AbstractWhen a mechanical backlash between the loading piston rod and the steering gear piston rod connection of the electro‐hydraulic load simulator (EHLS), it will lead to poor loading accuracy. To solve this problem, an adaptive backstepping sliding mode controller based on the backlash feedforward compensation and state observer is proposed. First, the mechanism of surplus force generation in the EHLS is analyzed, and a mathematical model containing position disturbance and backlash nonlinearity is established based on the analysis results. Second, a state observer is designed to estimate the system state and the parameter adaptive law is designed to estimate the system parameters. Third, the adaptive backstepping method is combined with the non‐singular terminal sliding mode control (NTSMC) strategy to deal with the position disturbance and parameter uncertainty and to enhance the system's dynamic performance. Finally, a backlash feed‐forward compensator is engineered to restrain the detrimental effects caused by the backlash nonlinearity, and the simulation experimental results show that the designed new method can realize the precise loading of the EHLS under different working conditions, and the surplus force is suppressed better at the same time.

A novel adaptive fast sliding mode control method based on fuzzy algorithm for the air management system of fuel cell stack

Proton exchange membrane fuel cells (PEMFCs) offer advantages, such as, cleanliness, high efficiency, and environmental friendliness. To achieve optimal control of the PEMFC stack's air supply and management system under complex operating conditions, a novel non-singular terminal sliding mode controller based on fuzzy algorithm is proposed. Compared with the conventional sliding mode control, the terminal sliding mode control exhibits further performance improvements. However, it still has limitations. The proposed innovative sliding mode structure would ensure finite-time convergence and avoid the issue of singularity associated with terminal sliding mode control. Moreover, fuzzy logic makes sliding mode gain adapt to the system and further enhances the performance and stability, which is benefited from a stronger sliding surface. Results indicate that, compared with the other controllers, the designed controller could reduce delay further and provide faster response to sudden changes. The overshoot of sliding surface has decreased by 70% compared to its previous level. This novel control approach significantly enhances the efficiency and reliability of the PEMFC system.

Synchronization of angular velocities of chaotic leader-follower satellites using a novel integral terminal sliding mode controller

Synchronization of satellite systems offers numerous advantages, including cost-effectiveness, flexibility, and extended area coverage. However, the presence of chaotic behavior in such systems poses substantial challenges. This paper investigates chaos in satellite systems and proposes a novel approach - the Novel Integral Terminal Sliding Mode (NITSM) controller - specifically designed for synchronizing the angular velocities of chaotic Leader-Follower satellite systems. The NITSM controller leverages limited-time features to eliminate chattering and exhibits remarkable robustness against external disturbances such as cosmic rays and solar storms. MATLAB simulations are conducted to validate the effectiveness of the proposed method, comparing the synchronization error of the NITSM controller with a common approach. The results demonstrate the superior performance of the Novel Integral Terminal Sliding Mode controller, showcasing reduced response time, robust behavior, and a substantial six-fold reduction in angular velocity synchronization error.

A Novel Faster Fixed-Time Adaptive Control for Robotic Systems With Input Saturation

In this paper, an adaptive anti-saturation fixed-time control method with a faster convergence rate is studied for uncertain robotic systems. Firstly, a new segmental sliding variable is constructed to solve the singularity problem brought by the terminal sliding mode control (TSMC) and achieve a faster convergence rate. Secondly, to approximate and compensate for the model uncertainty and the viscous friction parameter, an adaptive neural network (ANN) is employed. Then, a novel auxiliary system is constructed to mitigate the effects of input saturation. Based on this, a novel non-singular TSMC algorithm integrated with the ANN and the auxiliary system is designed, so that the trajectory tracking errors of the robotic system can converge within a faster fixed time with actuator saturation. Finally, the superiority and practicability of the present method are verified by comparative experiments.

Extended State Observer-Based Continuous Finite Time Control for a Fixed-Wing Vertical Take-Off and Landing Unmanned Aerial Vehicle

Dual system Vertical Take-Off and Landing (VTOL) fixed-wing Unmanned Aerial Vehicles (UAVs) combine the advantages of both the rotorcraft and fixed-wing UAV, characterizing horizontal and vertical flight capabilities. However, they face challenges such as aerodynamic coupling between propulsion systems, model uncertainty, and external disturbances, significantly deteriorating the tracking accuracy and robustness. This paper proposes an Extended State Observer based Continuous Finite-Time Control (ESO-CFTC) scheme to solve the attitude and trajectory tracking problem of such a VTOL fixed-wing UAV. Initially, the Nonsingular Fast Terminal Sliding Mode (NFTSM) controller guarantees the tracking errors reach a prescribed manifold in finite time with a continuous reaching law, then converge to the origin in finite time while avoiding singularities. To suppress the inherent chattering problem of the sliding mode control, an ESO technique is incorporated into the ESO-CFTC scheme, which is completely decoupled with the basic NFTSM controller. The supremum of the estimation residual set is derivated theoretically. The scheme forces the tracking errors to converge into the neighborhood of the origin in finite time without requiring prior knowledge of lumped disturbance supremum values. Finally, the numerical simulation results in a Matlab/Simulink environment demonstrate that the presented method outperforms existing benchmark in terms of disturbance estimation, tracking accuracy, convergence rate, and robustness.

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

Adaptive fractional-order nonsingular terminal sliding mode control and sequential quadratic programming torque distribution for lateral stability of FWID-EVs with actuator constraints

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

Ultralocal Model-Free Adaptive Supertwisting Nonsingular Terminal Sliding Mode Control for Magnetic Levitation System

The magnetic levitation technology has attracted blooming attention from all walks of life thanks to its superiorities such as non-contact and active control. While the intrinsic features of open-loop instability and strong nonlinearity, along with the uncertain external disturbance make the levitation control particularly significant and difficult. For speeding up the convergence and obtaining a better stability and disturbance robustness, this paper proposes an ultra-local model-free adaptive super-twisting nonsingular terminal sliding mode control (ULMF-ASTNTSMC) strategy for the magnetic levitation system. Different from the conventional model-based control, ultra-local model-free control breaks the constraint of a precise system model. Therefore, an improved second-order ultra-local model is established for the magnetic levitation system. For the benefit of finite time convergence and non-singularity, the nonsingular terminal sliding mode surface is chosen. As a second-order algorithm, super-twisting (ST) algorithm can fundamentally suppress the chattering effect of the sliding mode control (SMC). An adaptive super-twisting algorithm is designed for the further improvement of the system dynamic response. The stability of the proposed scheme is strictly verified based on the Lyapunov stability theory. Simulation and experimental comparisons with the existing control methods validate the exceeding performance of the proposed strategy under various operating conditions.

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

Disturbance‐observer‐based fault‐tolerant control of robotic manipulator: A fixed‐time adaptive approach

AbstractThe concurrent existence of model uncertainties, external disturbances, and actuator faults in a nonlinear system such as a robotic manipulator can significantly affect the trajectory tracking performance of these systems. Therefore this study is devoted to proposing a control approach based on fixed‐time control theory to improve the trajectory tracking performance of the robotic manipulator in the presence of lumped disturbance, including uncertainties, external disturbances, and actuator faults. The control approach in this paper is designed based on the integration of a fixed‐time adaptive sliding mode observer and a fixed‐time non‐singular fast terminal sliding mode control design strategy. Firstly, a new fixed‐time adaptive sliding mode observer is designed based on fixed‐time theory and adaptive control theory to estimate the lumped disturbance present in the system. Then, using the information from the disturbance observer, the fixed‐time non‐singular fast terminal sliding mode control is devised based on a non‐singular fixed‐time sliding surface and a fixed‐time reaching approach. Furthermore, in the sense of the Lyapunov theorem, through rigorous analysis, it is demonstrated that the tracking errors of the closed‐loop system converge to a small neighbourhood within a fixed time, regardless of the information about the initial conditions of the states of the system. Finally, extensive comparative simulations are performed using the PUMA560 robot to manifest the feasibility and validity of the proposed control strategy in terms of trajectory tracking accuracy and fast convergence in the presence of uncertainties, disturbances, and actuator faults.

Adaptive fast trajectory tracking control for the airship based on prescribed performance

A fast trajectory tracking controller is designed for the airship, involving dynamic uncertainties of parameters, capable of guaranteeing the prescribed performance of tracking errors, and fast response of the closed-loop system. To achieve the decoupling of velocity control and attitude control of the airship, a new guidance and control integration framework is proposed first. Then, based on the dynamics model established by the spinor method, the lumped disturbance, caused by unknown aerodynamic parameter uncertainties and exogenous disturbances, is estimated online using a high-order finite-time observer. The control performance, namely, overshoot and steady-state performance of tracking errors, is significantly improved by utilizing the prescribed output performance constraints, while the convergence rate is further enhanced by combining the finite-time convergence property of the fast terminal sliding mode control. Simulation results attest to the effectiveness of the strategy in this paper. Compared with the adaptive fast terminal sliding mode control, the strategy effectively utilizes the capability of the actuator within the allowed range and reduces the convergence time by more than half with similar control inputs.

Observer-based adaptive tracking control of robotic manipulators with predefined time-guaranteed performance: Theory and experiment

This paper investigates the challenging problem of fixed time trajectory tracking for robotic manipulators under the presence of unavailable model perturbation, external disturbance and from different initial states. Firstly, a novel fixed-time extended state observer (FESO) is designed to estimate and compensate the lumped disturbance, which is analyzed and proved to be stable in the sense of fixed time bounded stability. Secondly, a new type of fixed-time prescribed performance control (FPPC) is constructed to guarantee the system convergences to stable state within a predefined time and enhance transient performance. Furthermore, a novel continuous fixed time nonsingular fast terminal sliding mode variable is established, which addresses singularity obstacle in terminal sliding mode. Together with FESO and FPPC, a new fixed-time adaptive nonsingular fast terminal sliding mode controller (FANFTSMC) is developed. Meanwhile, an adaptive terminal sliding mode reaching law adopted in FANFTSMC promotes the robustness and decreases the chattering phenomenon. Then, the Lyapunov approach is given to clarify the advantages of FANFTSMC in terms of predefined time stabilization and which is demonstrated on a 2-DOF robotic manipulators. Thirdly, theoretical analysis and experiments are presented to illustrate the formulated control strategy owns fine performance and stronger robustness.

Adaptive Optimal Terminal Sliding Mode Control for T-S Fuzzy-Based Nonlinear Systems

This study utilizes the Takagi–Sugeno fuzzy model to represent a subset of nonlinear systems and presents an innovative adaptive approach for optimal dynamic terminal sliding mode control (TSMC). The systems under consideration encompass bounded uncertainties in parameters and actuators, as well as susceptibility to external disturbances. Performance evaluation entails the design of an adaptive terminal sliding surface through a two-step process. Initially, a state feedback gain and controller are developed using Linear Matrix Inequality (LMI) techniques, grounded on H2-performance and partial eigenstructure assignment. Dynamic sliding gain is subsequently attained via convex optimization, leveraging the derived state feedback gain and the designed terminal sliding mode (TSM) controller. This approach diverges from conventional methods by incorporating control effort and estimating actuator uncertainty bounds, while also addressing sliding surface and TSM controller design intricacies. The TSM controller is redefined into a strict feedback form, rendering it suitable for addressing output-tracking challenges in nonlinear systems. Comparative simulations validate the effectiveness of the proposed TSM controller, emphasizing its practical applicability.

Research on switching control based sliding mode coordination strategy of hybrid electric vehicle

The transient mode transition from pure electric driving to hybrid driving in a hybrid electric vehicle (HEV) involves multiple stages, each characterized by different models and control objectives, demanding diverse levels of controller robustness and convergence performance. Addressing the complexities of multi-stage transitions in a parallel HEV, the paper proposes a dynamic coordination strategy based on the switched control system concept. Distinct sliding mode controllers (SMC) are designed for each transition stage, tailored to the specific characteristics of powertrain operation. At the engine starting and speed synchronization stages, the global integral sliding mode control (GISMC) is integrated with a novel anti-saturation reaching law to ensure the system resides in the sliding mode, enhancing global robustness. During the engine speed regulation stage, the nonsingular terminal sliding mode control (NTSMC) facilitates rapid engine speed tracking for reduced mode transition time. By combining GISMC for global robustness and NTSMC for accelerated convergence, the strategy is designed to enhance mode transition quality at different stages. Simulation results demonstrate a 7.3% reduction in mode transition time and a 60.7% decrease in jerk compared to the conventional SMC strategy. In hardware-in-the-loop tests, the proposed control strategy proves effective in improving mode transition quality.

Quadrotor UAV Trajectory Tracking Control Based on Adaptive Non-singular Terminal Sliding Mode

To address the issue of the quadrotor unmanned aerial vehicle (UAV) being susceptible to external disturbances and model uncertainties during flight, an adaptive non-singular terminal sliding mode controller with disturbance compensation is proposed. Firstly, the quadrotor UAV dynamic model considering system disturbances is constructed using the Newton-Euler method. Next, the trajectory tracking problem is transformed into a command tracking control problem for each channel. To enhance the adaptability and robustness of trajectory tracking for the quadrotor UAV, an adaptive law is designed to dynamically adjust the sliding mode surface gain. In addition, a disturbance observer is introduced to estimate and compensate for external disturbances and model uncertainties. Finally, the stability of the designed controller is proven through the Lyapunov function. Simulation results demonstrate that the proposed controller effectively enhances the disturbance resistance and trajectory tracking response speed of the quadrotor UAV.