Chattering-free Control Research Articles

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

In this technical note, a combined discrete-time controller, consisting of a partial feedback linearization controller and a backstepping controller, is proposed to manage the stabilization for a class of underactuated nonlinear mechanical systems. The traditional backstepping control method is impracticable to directly apply it to underactuated systems since they are generally not in the lower triangular form. First, a feedback controller that partially linearizes the underactuated mechanical systems is derived to facilitate the backstepping controller design. In the design, discrete-time system dynamics obtained utilizing the Euler approximation are considered. Afterward, a novel coordinate transformation is introduced for a class of underactuated systems that transform the mathematical model of the partially linearized underactuated mechanical systems into the strict-feedback form. After these steps, the conventional backstepping approach is structured in discrete-time setting. The stability of the closed-loop system dynamics with the proposed combined discrete-time controller is shown utilizing Lyapunov theory. Several computer-based simulations are executed to depict the performance and the applicability of the proposed method on the Cart–Pole system and the Inertia Wheel Pendulum. Moreover, the effectiveness of the proposed nonlinear controller is verified by numerical simulation results in comparison with a discrete-time chattering-free sliding-mode controller.

A Robust Backstepping Sliding Mode Controller with Chattering-Free Strategy for a Swarm of Drones

This paper presents a robust controller for a swarm of drones that are subjected to external disturbances. Integrating a fuzzy-based system in the sliding mode control technique, a chattering-free controller is proposed for the trajectory tracking of a drone. Furthermore, the formation controller for a group of drones is developed using the Backstepping control design technique. The integration of a fuzzy rule-based system in the sliding mode tracking controller enables overcoming the inherent chattering problem due to discontinuous switching function in the sliding mode control technique and provides smooth and chattering-free control signals. The asymptotic stability of the overall system is shown using the Lyapunov stability theory. Finally, the control design performance is evaluated using numerical simulations.

A time-varying observer design for synchronization with an uncertain target and its applications in coordinated mission rendezvous

Coordinated mission rendezvous is the most fundamental and crucial issue in the application of cooperative search and rescue, forest fire fighting, and target hunting even tactical simulation and drill. The biggest challenge is how to schedule the limited resource to carry out cooperative mission rendezvous against uncertain targets with unknown external inputs and heterogeneous system dynamics. Three fundamental challenges are addressed: (1) how to accurately estimate the motion trajectory of an uncertain target; (2) how to design a pre-action mission rendezvous framework to create the rendezvous region; and (3) how to enhance the difficulty of interception but improve the accuracy of rendezvous. To do this, this paper first proposes a time-varying observer design for synchronization with an uncertain target over a dual design framework. By introducing proper assumptions, a novel condition of dwell time of switching communication topologies can be constructed, from which a synchronization algorithm is developed to achieve the cooperative behaviors between the trackers and distributed observers such that they eventually synchronize to their target signal. With the application of multi-missile systems, the time-varying formation techniques will be further developed for an uncertain mission rendezvoustarget. Specifically, this paper proposes a novel multi-stage cooperative mission rendezvous strategy that includes preparation and execution phases. In the preparation stage, the trackers will maintain a specified altitude to pre-construct the mission rendezvous region. In the execution stage, the trackers are in time-varying formation attitudes to approach the uncertain target over time-varying observers to accomplish the cooperative mission rendezvous. Specifically, the cases of chattering reduction and synchronization for general heterogeneous systems are discussed, respectively. At last, two simulations with uncertain moving targets, i.e., the ground vehicle and robotic with unknown input signals, are presented to demonstrate the proposed theories and chattering-free controllers.

Outer synchronization of two different multi-links complex networks by chattering-free control

This paper investigates the outer synchronization problem of two different multi-links complex networks (MLCNs) by chattering-free control. In comparison to the existing works, node dynamics, internal coupling, sub-networks numbers, and node numbers in response networks are not required to be the same as the ones in drive networks. The model proposed is more general. In order to reduce chattering in the synchronization process, some novel chattering-free control schemes are designed to address the synchronization phenomenon of networks. Based on Lyapunov stability theory and Linear matrix inequality, synchronization criteria are established by strict theoretical proof. Numerical simulations and comparison are presented to demonstrate the effectiveness and superiority of the proposed theoretical results.

Improved higher order adaptive sliding mode control for increased efficiency of grid connected hybrid systems

Abstract This paper proposes a hybrid learning algorithm based super twisting sliding mode control (STSMC) of a hybrid wind/photovoltaic (PV) power system for grid connected applications. The gating pulses of the voltage source converter (VSC) are generated by employing adaptive reweighted zero attracting least mean square (RZA-LMS) algorithm. The control law acquiring the super-twisting algorithm generates a continuous and saturated control signal to regulate a hybrid system influenced by disturbances. The proposed control injects sinusoidal currents into the grid with low total harmonic distortion (THD) which improves the steady state & dynamic performance of the system by mitigating power system problems like harmonic injections besides giving satisfactory results under dynamic loading, varying wind speeds and solar insolation. It is a chattering free control which enhances the quality of disturbance rejection and sensitivity to parameter variation. It also caters to abnormal conditions like voltage distortions, DC link variations and reduces the latter by a factor of 80 V besides reducing switch stress by a factor of 5 V. This control exhibits robustness against model uncertainties and external disturbances. Also, the loss component is reduced which decreases the unmodelled losses. It also ensures efficient power flow between the grid, hybrid source and the load. The efficacy of the system is verified in MATLAB/Simulink. Improvements are also observed during dynamic conditions in terms of reduced fluctuations, steady state error and peak overshoot.

Robust model reference adaptive backstepping sliding-mode control for quadrotor attitude with disturbance observer

Purpose The purpose of this research paper is to design a disturbance observer-based control based on the robust model reference adaptive backstepping sliding-mode control for attitude quadrotor model subject to uncertainties and disturbances. Design/methodology/approach To estimate and reject the disturbance, a disturbance observer is designed for the exogenous disturbances with perturbation while a control criterion is developed for the tracking of desired output. To achieve the control performance, backstepping and sliding-mode control techniques are patched together to obtain robust chattering-free controller. Furthermore, a model reference adaptive control criterion is also combined with the design of robust control for the estimation and rejection of uncertainties and unmodeled dynamics of the attitude quadrotor. Findings The findings of this research work includes the design of a disturbance observer-based control for uncertain attitude quadrotor system with the ability of achieving tracking control objective in the presence of nonlinear exogenous disturbance with and without perturbation. Practical implications In practice, the quadrotor flight is opposed by different kinds of the disturbances. In addition, being an underactuated system, it is difficult to obtain an accurate mathematical model of quadrotor for the control design. Thus, a quadrotor model with uncertainties and disturbances is inevitable. Hence, it is necessary to design a control system with the ability to achieve the control objectives in the presence of uncertainties and disturbances. Originality/value Designing the control methods for quadrotor control without uncertainties and disturbances is a common practice. However, investigating the uncertain quadrotor plant in the presence of nonlinear disturbances is rarely taken into consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the uncertainties and disturbances as well as investigate a control algorithm to achieve tracking performance.

A Robust Noise-Free Linear Control Design for Robot Manipulator with Uncertain System Parameters

In robot control, the sliding mode control is known for its robustness against external disturbances and system uncertainties. However, it has the disadvantage of control chattering, which can damage the actuator and degrade system performance. With a new stability proof, this paper presents an alternative simple linear feedback control that can cope with large system uncertainties and suppress large external disturbances, doing so as effectively as sliding mode control does. The advantage of using linear control is that the control law is simple and control chattering can be avoided. Moreover, a noise-free control scheme is proposed as an improvement of the feedback control; the modified design preserves the advantages of linear control and generates a chattering-free control signal even in a noisy environment.

An intelligent sliding mode controller based on LAMDA for a class of SISO uncertain systems

This paper presents a new intelligent sliding mode controller based on LAMDA (Learning Algorithm for Multivariate Data Analysis), a fuzzy method used for supervised and unsupervised learning applicable to the detection of functional systemic states. LAMDA computes the Global Adequacy Degree (GAD) of an object to a class or functional state to determine its degree of similarity. An inference stage has been added to LAMDA to make it work as a controller, in combination with the basic features of a sliding mode control (SMC) and Lyapunov stability theory. The novelty of this proposal is that we have used the LAMDA algorithm to compute the SMC continuous and discontinuous control actions to obtain a chattering-free controller, which can then be applied to a class of SISO systems with variable dynamics and model uncertainties. Simulations on two nonlinear chemical processes have validated the proposal: 1) control of a continuous stirred tank reactor (CSTR) under bounded disturbances and reference changes, and 2) regulation of a mixing tank with variable parameters (variable dynamics). The experiments are compared with other control techniques, demonstrating that the proposed method can accurately control the tanks, improving the results in performance, robustness, and disturbance rejection.

Gained switching-based fuzzy sliding mode control for a discrete-time underactuated robotic system with uncertainties

This study proposes a gained switching-based discrete-time sliding mode control method to address the chattering issue in disturbed discrete-time systems, which suffer from various unknown uncertainties. Through the new structure of the designed reaching law, the proposed method can effectively increase the convergence speed while guaranteeing chattering-free control. The performance of controlling underactuated robotic systems can be further improved by the adoption of fuzzy logic to perform adaptive online hyper-parameter tuning. In addition, an underactuated robotic system with uncertainties is studied to validate the effectiveness of the proposed reaching law. Results reveal the dynamic performance and robustness of the proposed reaching law in the studied system and prove the proposed method’s superiority over other state-of-the-art methods.

Observer-based adaptive sliding mode control for steer-by-wire systems with event-triggered communication

This paper proposes an event-triggered adaptive sliding mode control for the steer-by-wire (SbW) system subject to unavailable state, time-varying disturbance, and limited communication resources. Firstly, an adaptive state observer is proposed to estimate the unmeasured state of the SbW system. The uncertain nonlinearity and the time-varying can be estimated by the adaptive fuzzy logic system and the disturbance observer, respectively. Then, considering the limited communication resources, an even-triggered adaptive sliding mode control is proposed for the SbW system. The key advantage is that the proposed control scheme can offset the observation error and the event-triggering error. Much importantly, the high-frequency switching function is nested in the control input without increasing the input–output relative degree of the controlled system, such that the chattering-free control input can be obtained. Finally, theoretical analysis shows that the practical finite-time stability of the closed-loop SbW system can be saved, and communication resources in the controller-to-actuator channel can be saved while avoiding the Zeno-behavior. Numerical simulations and experiments are given to evaluate the effectiveness of the proposed scheme.

A Fuzzy Sliding-Mode Control Based on Z-Numbers and LAMDA

Z-Numbers is a recent concept related to fuzzy logic where the restriction and reliability criteria are characterized as fuzzy sets. Due to the potential of Z-numbers, this paper presents the development of a fuzzy controller that combines the fundamentals of LAMDA (Learning Algorithm for Multivariate Data Analysis) with the concepts of the Total Utility of Z-numbers, to establish an inference method to improve the performance in a control system. The controller uses criteria from the sliding mode control (SMC) and the Lyapunov concepts to guarantee robustness and stability respectively. The LAMDA method is applied to compute a chattering-free control action which is applied to systems with model uncertainties and variable dynamics. The fuzzy controller has been tested by simulation in two different tasks: 1) Control of a process that consists of a mixing tank with variable dynamics, and 2) Trajectory tracking of a mobile robot. The proposed approach provides suitable results at runtime and outperforms the results of the other tested controllers in terms of performance, minimizing the deviation between the current system output and the reference. Finally, a complexity analysis is presented to evaluate the feasibility in the implementation of the proposal. The obtained results prove the suitability of using a LAMDA Z-number-based controller in the tested systems.

Fault-tolerant control for turbocharged diesel engine air path via disturbance observer

ABSTRACT This paper investigates fault-tolerant control algorithm for diesel engine air path system with consideration of system parametric uncertainties, external disturbances and actuator faults. Initially, a finite-time disturbance observer is developed for estimating the synchronised uncertainties including parametric uncertainties and external disturbances. Based on the reconstructed information from the observer, a fault-tolerant control law is designed by using sliding mode control incorporated adaptive method. Furthermore, to attenuate the chattering problem caused by conventional sliding mode control method, the hyperbolic tangent function is utilised. A novel sliding variable is employed for improving the performance of the modified chattering-free control approach. The proposed fault-tolerant control algorithm is feasible for implementing and unnecessary caculations can be avoided, because the synchronised uncertainties and the actuator faults are tackled separately. Besides, the observer does not require the priori knowledge of the upper bounds of the synchronised uncertainties. Finally, simulation results and comparison are carried out and analysed for illustrating the effectiveness and validness of the proposed control schemes.

Continuous integral sliding mode control for space manipulator with actuator uncertainties

This paper studies the trajectory tracking control of space manipulator in the presence of actuator uncertainties, such as actuator fault, actuator saturation and the bias control torque. In addition, parametric uncertainty and external disturbances are also taken into consideration. A novel continuous adaptive integral sliding mode controller, which is chattering free and singularity free compared to the traditional terminal sliding mode control, is proposed to achieve the finite-time trajectory tracking control for space manipulator with uncertainties. Lyapunov theory is employed to prove the stability of the closed-loop system. The main advantage of the proposed controller is that it is easy to be implemented with continuous chattering-free control command. Numerical simulations are used to verify the effectiveness of the proposed controller.

Robust autonomous flight for quadrotor UAV based on adaptive nonsingular fast terminal sliding mode control

This paper presents a robust adaptive nonlinear controller for a flying machine represented by a quadrotor UAV (Unmanned Aerial Vehicle) in the presence of parasitic dynamics. A hybrid control strategy is used to steer the quadrotor behavior and an online adaptive methodology is introduced to improve the robustness of the adopted control technique against unmodeled dynamics. On the basis of the Newtonian formalism, the system model is formulated and decoupled into two subsystems, a position and attitude subsystems. A new Adaptive Nonsingular Fast Terminal Sliding Mode Control (ANFTSMC) is adopted to steer the quadrotor flight attitude, and a robust Backstepping Sliding Mode Control (BSMC) is used to manage the quadrotor position, contributing fast-accurate tracking despite the impact of external disturbances. The design procedure for both controllers is described thoroughly and the closed-loop stability is proved by means of the lyapunov theory. Multiple flight tests were performed and comparison is done with the backstepping controller (BS), the integral sliding mode control (ISMC), the second order sliding mode control (2-SMC) and the global fast terminal sliding mode control (GFTSMC). Simulation results show marked improvements of the quadrotor behavior with enhanced convergence time, chattering-free control efforts and strong robustness to the parasitic dynamics.

Output Feedback Adaptive Fractional-Order Super-Twisting Sliding Mode Control of Robotic Manipulator

In this study, trajectory tracking of robotic manipulators with uncertainties and external disturbances is obtained by proposing model-free adaptive fractional super-twisting sliding mode control (AOFSTSM). The proposed AOFSTSM method is composed of an adaptive super-twisting sliding mode control integrated with fractional-order (FO) control. An adaptive tuning control is utilized to evaluate the uncertain unknown dynamics of the system without relying on the prior knowledge of the upper bounds. Moreover, FO control and super-twisting sliding mode control are used to achieve the fast finite-time convergence, chatter-free control inputs, better tracking performance and robustness. An output feedback (OF) is proposed and the state estimation is obtained by robust exact differentiator. Furthermore, the stability of the overall system is investigated and derived from the Lyapunov stability criterion. Finally, to validate the effectiveness and robustness of the developed control method, comparative simulations of state-feedback and OF of proposed method with fractional-order nonsingular fast terminal sliding mode control are realized to demonstrate the performance of AOFSTSM.

Neural network adaptive dynamic sliding mode formation control of multi-agent systems

This paper considers the problem of achieving time-varying formation for second-order multi-agent systems with actuator hysteresis, unknown system dynamics and external disturbances. A novel adaptive dynamic sliding mode scheme is developed to control a group of agents to follow desired trajectories. First, a dynamic sliding mode approach based on local formation tracking error is utilised to reject external disturbances and obtain smooth and chattering-free control input. Then, Chebyshev neural network is employed to estimate the nonlinear function related to the system's dynamic equation. A smooth projection law is also applied to regulate the output of the neural network. Moreover, a Bouc–Wen hysteresis compensator has been added to the current control law to offset the known actuator hysteresis effect. Finally, a numerical simulation based on a multiple omni-directional robot system is presented to illustrate the performance of the proposed control law.

Robust Observer-Based Sliding Mode Control for Maximum Power Point Tracking

This paper presents a new observer-based maximum power point tracking technique (MPPT) for the solar panel system. Apart from fulfilling the main objective of MPPT, it is designed to accomplish the task without having the measure solar panel output voltage and with a chatter-free control. The proposed control strategy employs a disturbance observer to do away with the need to sense solar panel output voltage and also to ensure insensitivity of uncertainties. A special state observer enables operating the system even when the converter output voltage is initially zero. The performance of the algorithm is assessed for robustness towards the parasitics and uncertainties. The scheme is validated by simulation as well as experimentation in the laboratory.

Adaptive Integral Terminal Third-Order Finite-Time Sliding-Mode Strategy for Robust Nanopositioning Control

This article proposes a novel adaptive integral terminal third-order finite-time sliding-mode control strategy dedicated to motion tracking control of a piezoelectric-driven nanopositioning system. One uniqueness of the reported controller lies in that it generates finite-time convergence along with an inherent chattering-free control action. The model uncertainty involving the hysteresis nonlinearity and unmodeled dynamics is estimated through the perturbation estimation technique. Adaptive rules are established to update the control gains without acquiring the upper boundary of the estimation error. The stability of the presented third-order adaptive integral terminal sliding-mode control strategy has been proved based upon the Lyapunov analysis. It enables the achievement of third-order sliding-mode precision and prespecification of the tracking error boundary. The controller performance is verified by performing both simulation and experimental investigations. Results reveal the fine robust tracking performance of the developed controller for the nanopositioning system in the presence of model uncertainty and external disturbance.

Adaptive chattering-free terminal sliding-mode control for full-order nonlinear system with unknown disturbances and model uncertainties

This study investigates an adaptive chattering-free sliding-mode control method for n-order nonlinear systems with unknown external disturbances and uncertain models. The proposed method takes the advantage of finite-time fast convergence to avoid singularity problem and ensure its robustness against system uncertainty and unknown disturbance. To achieve fast convergence from any initial condition to system origin, a full-order terminal sliding-mode controller containing differential terms is proposed based on the property of n-order nonlinear systems. Then the continuous and smooth actual control law is obtained by integrating the differential control law containing the discontinuous sign function to realize chattering free. Meanwhile, instead of evaluating the fixed upper bound of system uncertainty and interference in practical implementations, an adaptive method is utilized for its unknown upper bound estimation. The convergence of the adaptive terminal sliding-mode controller in finite time is verified based on Lyapunov stability theory. Finally, two simulation results demonstrate the effectiveness of the proposed control method.

Adaptive finite integral non-singular terminal synergetic control of nth-order nonlinear systems

This paper proposed a novel finite synergetic control scheme. This controller utilizes an integral non-singular terminal attractor technique that guarantees the finite-time convergence of the states, solves the singularity problem of a conventional terminal attractor manifold, and provides a chattering-free control signal. The principles of this controller are introduced and demonstrated for second and nth-order nonlinear systems. The stability of the controller is verified using Lyapunov stability theory. In addition, an interval type-2 fuzzy logic system is implemented to improve the overall performance of the controller. Analysis of a robotic manipulator and a servo-hydraulic actuator is used to illustrate the efficacy of the proposed Adaptive Finite Integral Non-singular Terminal Synergetic Control (AFINTSC).