Hierarchical Sliding Mode Control Research Articles

Fixed-time stabilization of underactuated cart-pendulum system based on hierarchical sliding mode control method

Fixed-time stabilization of underactuated cart-pendulum system based on hierarchical sliding mode control method

Adaptive neural predefined-time hierarchical sliding mode control of switched under-actuated nonlinear systems subject to bouc-wen hysteresis

For switched under-actuated systems subject to bouc-wen hysteresis, an adaptive neural predefined-time control scheme is presented first time in this paper. To improve the robustness and response rate of the system under consideration, a hierarchical sliding mode control technique is introduced. Based on a predefined-time stability criterion, the stabilization time of the system can be directly preset under the designed controller. Besides, the convergence time depends only on the preset value and is independent of all other parameters. The projection algorithm is introduced to avoid the singularity problem in the controller design process. Meanwhile, it is proved that all signals of the closed-loop system are bounded after a preset time through the Lyapunov stability theory. Finally, a simulation example and a comparison example are given to further illustrate the effectiveness and superiority of developed control approach.

Time‐optimal trajectory generation and observer‐based hierarchical sliding mode control for ballbots with system constraints

AbstractThis paper introduces a comprehensive motion planning–tracking–safety constraint scheme for a 3D ballbot system. A nonlinear control for the 3D ballbot system is designed based on three separate planes by utilizing extended state observer (ESO) to estimate coupling mechanisms. Three virtual control signals are generated from these distinct planes and can be used for formulating actual control signals. To overcome the complexity of nonlinear motion equations, flatness theory is used to construct the time‐optimal trajectory through an optimization problem, facilitating smooth movement of the ballbot, and obstacle avoidance based on RRT* waypoints. Furthermore, our work manipulates the hierarchical sliding mode controller (HSMC) as the nominal controller to ensure that the ballbot tracks to the optimal trajectory, unifying with the exponential control barrier function (ECBF) to address safety constraints in the body's deflection angle. Through extensive simulations and comparative analysis, the system demonstrates its effectiveness and safe operation in various working conditions.

Adaptive Hierarchical Fractional-Order Sliding Mode Control Strategy for Multi-terminal VSC-HVDC System with Wind Farm

In this paper, an adaptive hierarchical fractional-order sliding mode controller (AHFSMC) for a multi-terminal Voltage Source Converter (VSC) based High Voltage Direct Current (HVDC) Integrated with a wind farm (WF) system is designed. Multi-terminal VSC-HVDC (MtVDC) connected to wind farms has received several attentions in the power sector because of its numerous benefits. The effectiveness of MtVDC, on the other hand, is dependent on the control scheme used. To achieve this goal, a hierarchical sliding mode control method by fractional-order calculus is used. The controller parameters are adjusted according to a suitable adaptation method to enhance the proposed controller's robustness compared to the system uncertainties coefficient. An appropriate Lyapunov-based approach is used to achieve the adaptation rule. This paper discusses a scheme to design additional controllers in MtVDC systems to damp electromechanical oscillations, one of several features of HVDC presently under active study. Numerical simulations validate the proposed control strategy's feasibility and efficiency. This novel approach is employed for the upgrading of system stability with the dynamic properties of the MtVDC in a variety of operative conditions.

Dynamics-Informed hierarchical sliding mode control for libration of partial space elevators in cargo transportation

This study presents an original analysis of out-of-plane libration dynamics and its control in partial space elevator cargo transportation. A comprehensive three-dimensional dynamic model of the partial space elevator has been derived to examine the effects of out-of-plane libration. To ensure a stable in-plane configuration, a coupling-free analytical speed function is developed that cancels out the coupling effects stemming from out-of-plane libration. A novel approach is developed to introduce a thrust control strategy for the elimination of out-of-plane libration using a virtual dynamic-based hierarchical sliding mode control law. By employing a new combined channel implementation mode, it is demonstrated that in and out-of-plane libration can be controlled with a single thruster, resulting in reduced fuel consumption. The stability of the proposed control strategy is proven within the Lyapunov framework. Numerical simulations validate the effectiveness of the control strategy and highlight its significance. Results show that out-of-plane libration increases the magnitude of in-plane libration, while climber movement amplifies out-of-plane libration. The control strategy successfully eliminates out-of-plane libration using limited control input, ensuring stable cargo transportation in the partial space elevator.

Adaptive Hierarchical Sliding Mode Control Based on Extended State Observer for Underactuated Robotic System

Adaptive Hierarchical Sliding Mode Control Based on Extended State Observer for Underactuated Robotic System

Hierarchical Sliding Mode Control for Underactuated Multicopters With Time-Scale Separation Enforcement

Hierarchical Sliding Mode Control for Underactuated Multicopters With Time-Scale Separation Enforcement

A Novel Hierarchical Recursive Nonsingular Terminal Sliding Mode Control for Inverted Pendulum

This paper aims to develop a novel hierarchical recursive nonsingular terminal sliding mode controller (HRNTSMC), which is designed to stabilize the inverted pendulum (IP). In contrast to existing hierarchical sliding mode controllers (HSMC), the HRNTSMC significantly reduces the chattering problem in control input and improves the convergence speed of errors. In the HRNTSMC design, the IP system is first decoupled into pendulum and cart subsystems. Subsequently, a recursive nonsingular terminal sliding mode controller (RNTSMC) surface is devised for each subsystem to enhance the error convergence rate and attenuate chattering effects. Following this design, the HRNTSMC surface is constructed by the linear combination of the RNTSMC surfaces. Ultimately, the control law of the HRNTSMC is synthesized using the Lyapunov theorem to ensure that the system states converge to zero within a finite time. By invoking disturbances estimation, a linear extended state observer (LESO) is developed for the IP system. To validate the effectiveness, simulation results, including comparison with a conventional hierarchical sliding mode control (CHSMC) and a hierarchical nonsingular terminal sliding mode control (HNTSMC) are presented. These results clearly showcase the excellent performance of this approach, which is characterized by its strong robustness, fast convergence, high tracking accuracy, and reduced chattering in control input.

S Trajectory Based on Sliding Mode Control for Unmanned Aerial Vehicle Slung-load System

For unmanned aerial vehicles (UAVs) slung-load systems, the payload of UAVs may suffer swing caused by inertia and external disturbances during the delivery process, posing a threat to system safety. Simultaneously tracking the trajectory and suppressing the payload swing is a challenging task. In this paper, a control design method is presented for trajectory tracking and swing suppression for a UAV delivery system. A feedforward design with the S-shaped trajectory is employed to suppress the payload swing, and a feedback hierarchical sliding mode control is utilized for trajectory tracking. Furthermore, stability analysis of the control system is conducted using the Lyapunov function, and simulation experiments are performed in MATLAB to validate the performance of the controller.

Hierarchical sliding mode control and disturbance observer for the double inverted pendulum on a cart

Hierarchical sliding mode control and disturbance observer for the double inverted pendulum on a cart

Detumbling of Underactuated Tethered Satellite System Based on Hierarchical Sliding Mode Control

Millions of space debris pose a significant risk to operational spacecraft, making active debris removal (ADR) missions an urgent priority. Net capturing is a promising method to remove space debris objects due to its multiple advantages. However, once a target has been captured, a combined tethered system comprising the chaser, the target, and the tethers is formed, which requires effective stabilization. In this paper, stabilization of the entire postcapture system is realized by solely controlling the active chaser satellite. Such a control strategy can attenuate system hardware facilities compared with those by applying additional tether control such as using a winding mechanism, which were mostly discussed in the literature. Further, for the first time, considering the uncertainties during the capture process, including inaccurate target parameters, initial attitude error of the target, and external disturbances, a hierarchical sliding mode controller (HSMC) with two sublayers is developed to detumble this underactuated system. Additionally, a hybrid position controller is proposed to eliminate the undesired swing motion within the system. Numerical simulations demonstrate that HSMC method delivers better performance over the proportional-derivative controller in efficiency and robustness for postcapture stabilization of the combined tethered system. Overall, our proposed control strategy offers a promising solution for future ADR missions, contributing to a safer and more sustainable space environment.

Effective Control Strategies for Rotary Inverted Pendulum System: Energy-Based, Linear Quadratic Regulator, and Hierarchical Sliding Mode Control Techniques

This work presents a comprehensive study of control problem for the rotary inverted pendulum (RIP), a challenging underactuated system with potential applications in robotics and aerospace. The paper develops effective swing-up energy-based control and stabilization task. It also presents two controllers, linear quadratic regulator (LQR) and hierarchical sliding mode control (HSMC), that effectively handle the stabilization problem. System modelling is based on Lagrangian mechanics, and the control strategies are evaluated using simulations and compared in terms of performance and robustness. The results demonstrate that energy-based control is effective for swing-up, while linear quadratic regulator and hierarchical sliding mode control are effective for stabilization. The proposed controllers show promising results and contribute to the development of robust and efficient control strategies for the rotary inverted pendulum system. The study has implications for the development of control strategies for other underactuated systems and can potentially lead to advancements in the field of robotics and aerospace.

Hierarchical sliding mode-based adaptive fuzzy control for uncertain switched under-actuated nonlinear systems with input saturation and dead-zone

PurposeThis paper aims to study the issues of adaptive fuzzy control for a category of switched under-actuated systems with input nonlinearities and external disturbances.Design/methodology/approachA control scheme based on sliding mode surface with a hierarchical structure is introduced to enhance the responsiveness and robustness of the studied systems. An equivalent control and switching control rules are co-designed in a hierarchical sliding mode control (HSMC) framework to ensure that the system state reaches a given sliding surface and remains sliding on the surface, finally stabilizing at the equilibrium point. Besides, the input nonlinearities consist of non-symmetric saturation and dead-zone, which are estimated by an unknown bounded function and a known affine function.FindingsBased on fuzzy logic systems and the hierarchical sliding mode control method, an adaptive fuzzy control method for uncertain switched under-actuated systems is put forward.Originality/valueThe “cause and effect” problems often existing in conventional backstepping designs can be prevented. Furthermore, the presented adaptive laws can eliminate the influence of external disturbances and approximation errors. Besides, in contrast to arbitrary switching strategies, the authors consider a switching rule with average dwell time, which resolves control problems that cannot be resolved with arbitrary switching signals and reduces conservatism.

Stabilization of Double Inverted Pendulum Systems Based on Hierarchical Sliding Mode Control Techniques

The double rotary inverted pendulum (DRIP) system belongs to the class of under-actuated mechanical systems, and it is a highly nonlinear, unstable, and benchmark system to test the different control techniques. This paper successfully designed the nonlinear hierarchical sliding mode control (HSMC) techniques to stabilize the DRIP system. We compare the performance of these techniques numerically with each other and with the previously designed control technique. We propose an aggregated HSMC technique as it has a much shorter stabilization time than other designed techniques.

Research on Anti-swing of Container Gantry Crane as Hierarchical Sliding Mode Control

Research on Anti-swing of Container Gantry Crane as Hierarchical Sliding Mode Control

Control of a Double-Pendulum Overhead Crane System Based on Hierarchical Sliding Mode Control Techniques

The double-pendulum overhead crane system belongs to a class of underactuated mechanical systems, which is challenging to control due to its strong nonlinearities. This study deals with the nonlinear controller design for a double-pendulum overhead crane based on hierarchical sliding mode control with state-dependent switching gain. The equivalent and switching controls are obtained with the aid of first-level and second-level sliding surfaces. The asymptotic stability of sliding surfaces is proved theoretically and also shown graphically. Numerical simulations show that the proposed controller performs better than conventional hierarchical sliding mode control. The proposed controller effectively suppresses the load and hook swing and precisely controls the trolley’s displacement. It has strong robustness to the payload displacement and the change of the crane parameters.

Adaptive Backstepping Hierarchical Sliding Mode Control for 3-Wheeled Mobile Robots Based on RBF Neural Networks

This paper proposes a new adaptive controller for three-wheeled mobile robots (3WMRs) called the ABHSMC controller. This ABHSMC controller is developed through a cooperative approach, combining a backstepping controller and a Radial Basis Function (RBF) neural network-based Hierarchical Sliding Mode Controller (HSMC). Notably, the RBF neural network exhibits the remarkable capability to estimate both the uncertainty components of the model and systematically adapt its parameters, leading to enhanced output trajectory responses. A novel navigational model, constructed by the connection to the adaptive BHSMC controller, Timed Elastic Band (TEB) Local Planner, and A-star (A*) Global Planner, is called ABHSMC navigation stack, and it is applied to effectively solve the tracking issue and obstacle avoidance for the 3-Wheeled Mobile Robot (3WMR). The simulation results implemented in the Matlab/Simulink platform demonstrate that the 3WMRs can precisely follow the desired trajectory, even in the presence of disturbances and changes in model parameters. Furthermore, the controller’s reliability is endorsed on our constructed self-driving car model. The achieved experimental results indicate that the proposed navigational structure can effectively control the actual vehicle model to track the desired trajectory with a small enough error and avoid a sudden obstacle simultaneously.

Fractional-order robust fixed-time sliding mode control for deployment of tethered satellite

Tether deployment of the space tether system is the first step of related on-orbit experiments, which requires an advanced and reliable control scheme to realize rapid deployment without overshoot. In this paper, we propose a fractional-order fixed-time controller based on hierarchical sliding mode control to be applied to the deployment process of the tether system. The application of fractional calculus improves the local effect of the controller. Through strict mathematical derivation, we prove that the proposed control law satisfies the global fixed-time stability. So the closed-loop system has the performance of fixed-time convergence. Part of the simulation uses a fractional sliding mode control law for comparison, which further illustrates the superiority of the control law proposed in this paper. In view of the uniqueness of tether system dynamics, the research ideas in this paper are also of reference value to similar under-actuated systems.

Hierarchical Sliding Mode Control Combined with Nonlinear Disturbance Observer for Wheeled Inverted Pendulum Robot Trajectory Tracking

A proposed optimized model for the trajectory tracking control of a wheeled inverted pendulum robot (WIPR) system is presented in this study, which addresses the problem of poor trajectory tracking performance in the presence of unknown disturbances due to the nonlinear and underactuated characteristics of the system. First, a kinematic controller was used to track a reference trajectory and generate a control law that specifies the desired forward and rotation speeds of the system. Next, a nonlinear disturbance observer (NDO) was designed to enhance the system’s robustness to external disturbances and improve its tracking performance. Then, the coupled system state variables were decoupled into two subsystems: a forward rotation subsystem and a tilt angle velocity subsystem. An improved hierarchical sliding mode controller was designed to control these subsystems separately. Finally, simulation experiments were conducted to compare the proposed method with a common sliding mode control approach. The simulation results demonstrate that the proposed method achieves better tracking performance in the presence of unknown disturbances.

Fixed time robust control for tower cranes with unmatched disturbances and input saturation

SummaryTo address the challenging problem of fixed‐time anti‐sway and positioning control for tower cranes with uncertain disturbances and input saturation, a novel fixed‐time anti‐saturation robust algorithm is proposed. First, on the basis of a newly designed fixed‐time convergence system, a fixed‐time disturbance observer (FTDO) is developed to estimate the matched and unmatched disturbances. Then, an anti‐saturation compensator is employed to deal with the input saturation and make the control input leave the saturated region rapidly. Upon which, a novel non‐singular fast terminal sliding mode surface is presented. Furthermore, in order to ensure the stability of each subsystem, a hierarchical sliding mode surface taking into account unmatched disturbances and input saturation is designed. Finally, the FTDO based hierarchical sliding mode control law is introduced to improve the transient control performance and robustness of tower cranes. The fixed‐time convergence of the closed‐loop system is proved by Lyapunov technique. Numerical simulations for four scenarios demonstrate the validity of the presented control scheme and fastest convergence speed in comparison to the recently proposed fixed‐time control methods.