Sliding Mode Variable Research Articles

Fractional finite-time control for robust tracking of nonlinear systems subject to Hölder disturbances with application to UAVs

The aim of the present article is to design a robust fractional-order (FO) finite-time (FnT) control able to tackle Hölder disturbances of second-order nonlinear systems. First, a novel sliding manifold with Arc-Tangent function is suggested for second nonlinear systems. It has been proven that the system states globally converge to the origin in FnT using the proposed sliding mode variable. To ensure a FnT stability of the sliding variable, a robust control is developed. By using fractional operators, a uniformly continuous control law is designed to tackle Hölder disturbances. Furthermore, the suggested approach is shown to be resistant to matched Hölder disturbances and uncertainties that are continuous but not necessarily differentiable. Moreover, the FnT stability of quadrotors using the proposed control, that is our second result. The quadrotor simulations analysis demonstrates the practicality of the proposed FnT controller in the presence of Hölder disturbances.

Trajectory tracking control of wearable upper limb rehabilitation robot based on Laguerre model predictive control

Wearable rehabilitation robots have become an important auxiliary tool in rehabilitation therapy, providing effective rehabilitation training and helping to recover damaged muscles and joints. In response to the difficulty of traditional control methods in solving various constraints in the trajectory tracking process of the Upper Limb Rehabilitation Robot (ULRR), this study uses model predictive control to study the trajectory tracking problem of the upper limb rehabilitation robot. Firstly, based on the Lagrangian dynamic model of wearable rehabilitation robots, an extended state space model with pseudo linearization of the system was established. Given the performance indicators and various constraints of the system, a corresponding model predictive controller is designed based on the Laguerre model to ensure system performance while greatly reducing the computational complexity of predictive control. Secondly, the stability of the model predictive controller is demonstrated, and a disturbance observer is introduced into the controller to achieve compensation for slow-varying perturbations; a joint space sliding mode variable is also introduced to achieve simultaneous tracking of the joint’s desired position and desired velocity. Finally, taking a planar two bar robot as an example, comparative simulation verification was conducted on unconstrained joint trajectory tracking and constrained joint trajectory tracking. The simulation results show that the model predictive controller can achieve simultaneous tracking of joint expected trajectory and expected speed while meeting various constraints. It has good effects in improving patient motion control ability and reducing patient fatigue, providing new research ideas and methods for the field of rehabilitation therapy.

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.

Tracking control of a flexible‐link manipulator based on an improved barrier function adaptive sliding mode

AbstractIn this paper, a novel controller designed for robust tracking control of a flexible‐link manipulator operating in the presence of parameter uncertainties and external disturbances within the joint space is introduced. The proposed controller employs an adaptive sliding mode control approach, incorporating an improved barrier function, to ensure that trajectory errors remain within predefined performance bounds. This design enhances the tracking performance without overestimating control‐switching gains. Additionally, a fixed‐time adaptive sliding mode control, featuring a rapid nonsingular terminal sliding mode variable, is introduced to expedite the convergence rate of the system state during the initial stages. The efficacy of the proposed control scheme is established through the Lyapunov method, demonstrating finite‐time convergence of the trajectory error to a specified neighborhood of zero. Experimental validation on a flexible‐link system supports the effectiveness and advantages of the proposed control strategy, as evidenced via comparisons with two existing adaptive control schemes.

Recursive integral terminal sliding mode control with combined extended state observer and adaptive Kalman filter for MEMS gyroscopes

AbstractThe recursive integral terminal sliding mode control with combined extended state observer (ESO) and adaptive Kalman filter (AKF) is proposed in this article for micromechanical system gyroscopes. To accurately estimate the unmeasured system states in the presence of measurement noises, external disturbances and system uncertainties, the special combination of ESO and AKF is proposed. The AKF is employed to deal with measurement noises and prepare necessary signals for the ESO, while the ESO constantly provides the updated estimate of the lumped disturbance for the AKF. Furthermore, a robust control scheme is designed by using the recursive integral terminal sliding mode variable. Simulation results verify that more accurate unmeasured state estimation and higher tracking accuracy are achieved under the proposed method.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Tracking control for robotic manipulators with prescribed performance and adaptive sliding mode disturbance observer

This paper investigates the finite-time disturbance estimation and tracking control for robotic manipulators subjected to model perturbation and external disturbance. First, an adaptive sliding mode disturbance observer (ASMDO) is raised to estimate the lumped uncertainties, which does not need to consider the upper boundary prior knowledge of lumped uncertainties’ derivative, and excessive gain coefficients are avoided, meanwhile, which decrease the chattering phenomenon. Next, a finite-time prescribed performance control (FPPC) is established to guarantee the system converges within a finite time and promote transient performance. Then, together with the FPPC, a finite-time nonsingular fast terminal sliding mode variable is established, which handles singularity problem in terminal sliding mode. In the meantime, a finite-time adaptive nonsingular fast terminal sliding mode controller (FANFTSMC) is constructed based on ASMDO and FPPC. The Lyapunov theorem is given to clarify that the system can reach the stable state within a finite time. Theoretical analysis and experiments reveal that FANFTSMC has better tracking performance and stronger robustness.

An improved sliding mode speed controller for PMSM based on new terminal reaching law with generalized proportional integral observer

A compound sliding mode controller for permanent magnet synchronous motor (PMSM) based on an adaptive terminal sliding mode reaching law with generalized proportional integral observer is proposed. First, an adaptive terminal reaching law is proposed to solve the defects of large chattering in commonly used sliding mode control, which consists of a piecewise function and a terminal term of state variables. The reaching law could adjust the gain according to the distance between the system state and the equilibrium point. On the premise of reducing chattering, a higher reaching speed is guaranteed. The convergence time has an upper bound and is not concerned with the initial value of the sliding mode variable. Based on the reaching law, an adaptive sliding mode controller is established. Second, to reduce the sliding mode gain and enhance the antidisturbance ability of the PMSM, a generalized proportional integral observer is established to evaluate the perturbations in PMSM and compensate them to the speed controller in real time. Simulations and experiments verify that the new compound control method has a faster-approaching speed, smaller chattering, and stronger antidisturbance ability than other methods.

Attack-tolerant control for Markovian jump systems with stochastic sampling: A sliding mode scheme

This work discusses the sampled-data sliding mode control problem for Markovian jump systems in the presence of Denial-of-Service (DoS) attacks, where the state signals are sampled stochastically and transmitted via vulnerable communication networks. The successful transmitted sequence with double randomness is established, and the probability distribution on both the attacked signals and stochastic delays are given. With the aid of the coordinate transformation, a linear sliding surface is constructed and the mode-dependent sliding mode controller is designed by means of only successfully transmitted state signals. Moreover, the resultant closed-loop systems composed of partial state and sliding mode variable are described as a continuous time-delay system with double randomness depending on the probability distribution characteristics of both the sampling periods and DoS attacks. Both the mean-square exponential ultimate boundedness of the closed-loop system and the reachability of the sliding surface are analyzed and the corresponding sufficient conditions are derived. Meanwhile, an optimization problem with genetic algorithm is formulated for achieving fast convergence of the state trajectory, small ultimate bound of the system state and small sliding bound. Finally, the simulation results via the numerical example are provided to illustrate the proposed sampled-data sliding mode control scheme.

Adaptive sliding mode control of the motor shaft rotation angle

An adaptive integral control law in sliding mode, the purpose of which is to solve the problem of controlling the angle of rotation of the motor shaft in a nonlinear formulation, is considered. The region of the integral sliding mode, which ensures convergence in finite time, is determined, and the law of fast convergence is developed. An adaptive law for estimating the upper limit of interference and a control law are received. Using finite-time theory, the convergence properties of the closed-loop system are confirmed and the areas of convergence of sliding mode variables are determined. Numerical modeling confirming the noise immunity and efficiency of the presented control system is carried out. Keywords engine control, automatic control system, integral sliding mode method, law of fast convergence, adaptive control, finite time convergence

Distributed sliding mode control strategy for intelligent connected vehicle platoon in complex media

This study examines the performance of a nonlinear sliding mode controller in cooperative control of the intelligent connected vehicles systems. The study begins by proposing a vehicle-to-vehicle car-following model that takes into account the impacts of disturbances both external and within in the system. Subsequently, an adaptive exponential reaching sliding mode controller based on a non-singular terminal sliding mode variable is proposed. It is analyzed theoretically using Lyapunov method, differential method and difference method and the results show that using the new controller, the system can converge in finite time with enhance dynamic performance. Finally, to verify the effectiveness of the controller proposed in this study, numerical experiments in MATLAB and simulation experiments in the ROS-Gazebo environment are conducted, and the results show that the controller proposed in this study enables the intelligent vehicle system to maintain stable operation in the face of interferences. Experiment results are in accordance with theoretical analysis.

Integral Sliding Mode Control-Based Robust Bidirectional Platoon Control of Vehicles With the Unknown Acceleration and Mismatched Disturbance

This paper proposes integral sliding mode control (ISMC)-based robust bidirectional platoon control methods in the longitudinal platoon for vehicles with unknown acceleration and mismatched disturbance. A finite time robust estimator (FTRE) is presented to estimate the practically unknown acceleration and mismatched disturbance of adjacent vehicles. In addition, the matched disturbance in the vehicle is also compensated for to further ensure the robustness of the platoon control. A modified constant time headway (MCTH) policy that removes the influence of the initial spacing and velocity error is defined to improve the transient response of the platoon control. Two robust platoon control methods, a nonlinear disturbance observer (DOB)-based ISMC and an adaptive dual-layer super-twisting ISMC (STISMC), are proposed. The proposed methods based on the nonlinear DOB and ISMC are more effective against highly nonlinear disturbances than the existing linear DOB-based methods and the disturbances can be compensated at all times by eliminating the reaching mode, unlike the exiting SMC-based methods. Furthermore, the proposed adaptive dual-layer STISMC provides a continuous control input that guarantees the finite time convergence of the sliding mode variables to zero without requiring an upper bound on disturbance. Both simulation and experimental results are provided to demonstrate the superior platoon control performance of the adaptive dual-layer STISMC method compared to both the existing linear DOB-based robust platoon control method using ISMC and the nonlinear DOB-based ISMC method.

Fixed time prescribed performance dynamic positioning control design for surface vessels

This paper addresses the problem of fixed time dynamic positioning (DP) control for surface vessels under the influence of external disturbances, while considering input and output constraints. Using the hyperbolic tangent function, a saturation handling method with an auxiliary control system is constructed, which can handle the saturation constraints of both the control input and its rate of change within a same control framework. By incorporating an auxiliary sliding mode variable, a fixed time disturbance observer (FTDO) is developed to estimate external disturbances. This FTDO ensures that the estimation error converges within a fixed time and provides users with the flexibility to determine the desired convergence time. Moreover, a nonlinear function is introduced in the FTDO to reduce the possibility of singular problems in the control system. Combining the developed FTDO, prescribed performance control strategy and backstepping control technique, a novel DP control strategy is proposed, which not only ensures that the positioning error satisfies the output constraint requirements within a fixed time but also guarantees the fixed time stability of the closed-loop system. Finally, to validate the effectiveness of the proposed DP control law, numerical simulation analysis is carried out on a supply vessel.

Distributed “End-Edge-Cloud” structural car-following control system for intelligent connected vehicle using sliding mode strategy

This paper proposes a new car-following model to describe the characteristics of the urban Internet of vehicle (IoV) of the “End-Edge-Cloud” architecture. The stability of the proposed CF model is analyzed using the perturbation method. Furtherly, in order to overcome the disturbances in the operation of the newly proposed system in this paper, a sliding mode controller is designed based on non-homogeneous terminal sliding mode variables, and after setting up the controller, the dynamic performance of the system is analyzed by solving the linear inhomogeneous differential equation and the Lyapunov method, and it is proved that the system can converge in finite time. Finally, the rationality of the model proposed in this paper and the significant improvement in the dynamic performance of the system under the action of the controller are effectively demonstrated through numerical experiments conducted in MATLAB and simulation experiment carried out in the ROS-Gazebo environment.

Fault-tolerant attitude tracking control for carrier-based aircraft using RBFNN-based adaptive second-order sliding mode control

This paper proposes a fault-tolerant attitude tracking control for carrier-based aircraft with external disturbances and actuator faults, which is based on backstepping control, second-order sliding mode control (SOSMC) and the radial basis function neural network (RBFNN) adaptation algorithm. First, the generic attitude dynamic model of carrier-based aircraft is presented. Based on backstepping method, the attitude control system is divided into two simple and low-order subsystems. Then, the basic SOSMC using the type of proportional integral (PI) sliding mode variable are designed respectively for two subsystems, which can guarantee the system stable with no chattering in the finite time. To compensate for disturbances and faults more accurately, we design RBFNN-based adaptive second-order sliding mode control (RASOSMC) where RBFNN algorithm is utilized to approximate the lumped perturbation, which attenuates the impact of disturbances and faults more effectively and improves attitude tracking performance. Furthermore, the adaptive online algorithms for the RBFNN weights are proposed based on Lyapunov theory. Finally, numerical simulation results are given to indicate the effectiveness and robustness of the SOSMC scheme and RASOSMC scheme.

Fixed-time disturbance observer based robust tracking control of wheeled mobile robot with multiple disturbances

In this article, the problem of robust tracking control for wheeled mobile robot (WMR) with skidding, slipping, and parameter uncertainties is addressed. Through designing double sliding mode variables, a fixed time disturbance observer is developed to estimate the multiple disturbances within a fixed time, and the convergence time is regardless of the initial estimation error of the system. Based on the fixed-time disturbance observer (FTDOB) and the novel power reaching law sliding mode technique, a robust tracking controller is synthesized. The proposed control method eliminates the chattering problem existing in the traditional sliding mode control, and can guarantee the high-precision tracking control performance even in the presence of skidding, slipping and parameter uncertainties. The closed-loop system stability analysis is verified by the Lyapunov stability theory. Meanwhile, simulation comparative results are carried out to illustrate the effectiveness of the proposed control method.

Chattering-free discrete-time sliding mode control for integrated missile guidance and control system

With the development and validation of flight control devices, electronic equipment is widely used in current flight vehicles, which results in a series of control signals in the discrete-time domain. However, many mature integrated guidance and control schemes are designed in the continuous-time domain, and some results of them may not be preserved in the discrete-time domain especially for the sliding mode control. To address this issue, a chattering-free discrete-time sliding mode control scheme is proposed for the integrated guidance and control systems of missiles. By applying the Euler’s discretization method, an approximated discrete-time model with matched and mismatched disturbances is first derived for integrated guidance and control system. Then, the estimates of the disturbances are obtained by using discrete-time generalized proportion integral observers. Integrating the estimated disturbances into the sliding mode variable, a discrete-time sliding mode controller is established by utilizing a modified chattering-free reaching law. The reachability of quasi-sliding mode band, states boundedness, and output convergence performance are analyzed rigorously. Finally, comparative numerical simulations are conducted to verify the effectiveness of the proposed control scheme in the presence of unknown target maneuvers and parameter uncertainties.

Fixed-Time Filtered Adaptive Parameter Estimation and Attitude Control for Quadrotor UAVs

In this article, a fixed-time filtered adaptive parameter estimation and control scheme is proposed for attitude tracking of quadrotor unmanned aerial vehicles. A nonsingular fixed-time sliding mode surface is constructed to avoid the existence of the singularity issue resulted from the differentiation of the sliding mode variable. Through designing auxiliary filtered matrices, a fixed-time parameter update law is developed to achieve the fixed-time parameter convergence. Then, an adaptive neural controller is designed to ensure the fixed-time convergence of attitude tracking errors in the presence of the model uncertainties. Instead of using any piecewise continuous functions, the possible singularity issue in the conventional fixed-time controller design can be overcome by constructing auxiliary functions, and thus the fixed time stability analysis becomes more concise. The efficiency of the presented scheme is validated through experiments on a practical Quanser quadrotor platform.

Robust Tracking Control for Electrohydraulic System Using an Internal Model-Based Sliding Surface

Abstract An electrohydraulic system, which is widely applied in practice, is a highly nonlinear system with uncertainty. In order to improve the control performance, the nonlinearity and uncertainty should be taken into consideration. In this context, a lot of researches have been carried out, and most of them need the derivatives of the tracking error to construct their controllers. However, the accurate values of the derivatives are difficult to be obtained in practice. What's more, without considering the characteristics of the reference signal, the direct applications of these control methods in the periodic motion tracking problem of electrohydraulic systems are difficult to achieve satisfactory control performances. Therefore, a novel internal model principle (IMP)-based sliding mode control (SMC) is proposed in the paper. First, an ideal driving force for the second-order piston motion dynamics is designed based on the IMP with the measurement of piston position. And then, the deviation between the ideal and measured driving force is selected as the sliding mode variable. At last, the SMC is formed to guarantee the actual driving force can converge to the ideal one in finite time. As the main contribution of this paper, the proposed IMP-based SMC does not need the derivatives of the tracking error and can achieve a better performance by eliminating the reference frequency related component in the tracking error. To verify the control performance of the proposed method, a 20 Hz sinusoidal reference tracking scenario is considered, and the finite-time exact differentiator (FTD)-based SMC and the FTD-based high-order SMC (HOSMC) are selected as comparison methods. A group of simulations are performed on an electrohydraulic system used in the controlled trajectory rapid compression and expansion machine (CT-RCEM). The simulation results show that the 20 Hz component in the tracking error is eliminated under the proposed controller, but the 20 Hz error components are still remaining as 2.58 mm and 0.64 mm under the FTD-based SMC and the FTD-based HOSMC, respectively.

Robust iterative learning control design based on iterative integral sliding mode for nonlinear systems with unrepeatable disturbance

For the repetitive tracking control tasks, the unrepeatable disturbance is an obstruction to learning control schemes. This paper discussed the robust iterative learning control (RILC) design based on the sliding mode control (SMC) technique for a class of nonlinear systems with unrepeatable disturbances. In order to make the tracking error converge to zero in the iteration domain under the sliding mode and eliminate the reaching phase of the SMC, an iterative integral sliding mode (IISM) surface design was proposed. The IISM leads to linear tracking error dynamics in the iteration domain, which guarantees the convergence if the sliding mode parameters meet the given condition. After that, the iterative learning control (ILC) based on the IISM was designed, which drove the sliding mode variable of the closed-loop system to reach the origin with iterations from the initial time instant, despite the effect of the unrepeatable disturbances. The robustness to the unrepeatable disturbance and the fast convergence were achieved. Finally, the proposed IISM method was applied to a one-link robotic manipulator, and the simulation results validated the performance of the proposed control design.