Time-varying Sliding Mode Control Research Articles

Predefined-time fractional-order time-varying sliding mode control for arbitrary order systems with uncertain disturbances

This paper proposes a fractional-order time-varying sliding mode control method with predefined-time convergence for a class of arbitrary-order nonlinear control systems with compound disturbances. The method has global robustness and strongly predefined-time stability. All state errors of the system can converge to zero at a desired time, which can be set arbitrarily with a simple parameter. The strongly predefined-time convergence of the system is clearly demonstrated by the analytic expression of state error, which is obtained by solving fractional-order differential equations corresponding to the sliding mode function. The simulation results show that the proposed method still has good control performance in the presence of input saturation and external interference.

Time-varying sliding mode controller for heat exchanger with dragonfly algorithm

<span lang="EN-US">This article proposes the design of a sliding mode controller with a time-varying sliding surface for the plate heat exchanger. A time-varying sliding mode controller (TVSMC) combines the benefit of the control system’s robustness and convergence rate. Using Lyapunov stability theory, the stability of the designed controller is proved. In addition, the controller parameters of the designed controller are specified optimally via the dragonfly algorithm (DA). The input constraint’s effect is considered in the controller design process by applying the concept of the auxiliary system. The bounded disturbances are applied to investigate the robustness of the proposed techniques. Moreover, the quasi-sliding mode controller (QSMC) is developed as a benchmark to evaluate the convergence behavior of the proposed TVSMC technique. The simulation results demonstrate the proposed TVSMC with the optimal parameters provided by the DA algorithm (TVSMC+DA) can regulate the temperature to the desired level under bounded disturbances. When compared to the QSMC method, the TVSMC+DA performs significantly faster convergence speed and greater reduction in chattering occurrence. The results clearly indicate that the proposed controller can enhance convergence properties while being robust to disturbances.</span>

Design of Adaptive Time-Varying Sliding Mode Controller for Underactuated Overhead Crane Optimized via Improved Honey Badger Algorithm

Design of Adaptive Time-Varying Sliding Mode Controller for Underactuated Overhead Crane Optimized via Improved Honey Badger Algorithm

Predefined-time fractional-order time-varying sliding mode control and its application in hypersonic vehicle guidance law

Predefined-time fractional-order time-varying sliding mode control and its application in hypersonic vehicle guidance law

Nonlinear Uncertainty Estimator-Based Robust Control for PMSM Servo Mechanisms With Prescribed Performance

Active nonlinear uncertainties compensation is crucial for realizing high-precision servo control. However, the rejection of the unknown uncertainties is still a challenging problem. In view of these issues, this paper proposes a novel nonlinear uncertainty estimator based time-varying sliding mode control scheme for servo systems with prescribed performance. A nonlinear uncertainty estimator, which employs first-order low-pass filter operations with only one tuning parameter, is constructed to deal with unknown nonlinearities, while the NDE estimation error and uncertainties of the servo system are handled by the robust integral of the sign of the error (RISE) feedbacks. Meanwhile, a modified prescribed performance function (PPF) with a faster convergence rate is incorporated into the control design to restricted the tracking errors within the predefined asymptotic boundaries. By combining PPF and NDE, a time-varying sliding mode controller is developed to eliminate the reaching phase and improve the control performance. The validity and feasibility of the presented control scheme are verified with simulations and experiments based on a motor driving system.

A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper

For the multi-rope structure of the container crane system and its large mass payload anti-swing positioning problem, an equivalent double-swing model based on radial spring-dampers is established and a time-varying PD sliding mode controller (TVPD-SMC) with improved transient performance is proposed. In particular, the dynamics of the container crane system are first analyzed using the Lagrange method, and an equivalent double pendulum dynamics model of the crane is established. Compared with the traditional double pendulum model, this model ensures the accuracy of modeling without measuring the second pendulum angle. On this basis, an enhanced coupled time-varying sliding mode control method is designed to eliminate the sliding mode control method’s reaching phase and improves the robustness of the controller. Finally, the convergence and stability of the closed-loop system are proved using the Lyapunov technique and the Lasalle invariance theorem, and the simulation results demonstrate the effectiveness of the method.

Three-dimensional integrated guidance and control with input saturation and impact angle constraints

Considering the problem of a skid-to-turn (STT) interceptor attacking maneuvering targets in the three-dimensional space, a new integrated guidance and control (IGC) law with the constraints of impact angles and input saturation is developed. To achieve the finite-time convergence and satisfactory input characteristics, a time-varying sliding mode control (TVSMC) method is presented based on a time base generator function. To this end, the IGC scheme is developed based on the TVSMC and the back-stepping. At each step, the derivative of the virtual signal is approximated by a tracking differentiator. Meanwhile, an auxiliary compensation system is designed to reduce the adverse effect raised from the saturation error. Moreover, the modeling uncertainties and disturbances are attenuated effectively by using fractional power extended state observers to estimate them. The closed-loop system states are proved to be uniformly ultimately bounded and the controlled states are proved to converge into small neighborhoods of the origin at the interception time. Finally, the performance of the presented IGC law is verified through numerical simulations.

The Tracking Control of the Variable-Order Fractional Differential Systems by Time-Varying Sliding-Mode Control Approach

This paper is concerned with the problem of tracking control for a class of variable-order fractional uncertain system. In order to realize the global robustness of systems, two types of controllers are designed by the global sliding-mode control method. The first one is based on a full-order global sliding-mode surface with variable-order fractional type, and the control law is continuous, which is free of chattering. The other one is a novel time-varying control law, which drives the error signals to stay on the proposed reduced-order sliding-mode surface and then converges to the origin. The stability of the controllers proposed is proved by the use of the variable-order fractional type Lyapunov stability theorem and the numerical simulation is given to validate the effectiveness of the theoretical results.

Finite-time observer-based model-free time-varying sliding-mode control of disturbed surface vessels

In this study, the model-free robust tracking control problem of a surface vessel in the presence of unknown dynamics and disturbances is solved by creating an innovative finite-time observer-based time-varying sliding-mode control approach. By developing a trend data model and a regulation index function, an efficient time-varying sliding-mode surface is devised such that the asymptotic convergence of the plant’s outputs with small overshoots can be guaranteed. With the aid of data-driven strategy and finite-time control technique, a data-driven finite-time observer is further proposed to quickly estimate the total unknowns including unknown dynamics, external disturbances and couplings, and whereby a model-free time-varying sliding mode controller is thereafter synthesized such that these unknowns can be accommodated well since sliding mode can be exactly reached. Finally, the efficiency of the developed approach is evaluated via theoretical analysis and simulation studies on a benchmarked surface vessel.

Field-of-View Constrained Impact Time Control Guidance via Time-Varying Sliding Mode Control

The problem of impact time control guidance with field-of-view constraint is addressed based on time-varying sliding mode control. The kinematic conditions that satisfy the impact time control with field-of-view constraint are defined, and then a novel time-varying sliding surface is constructed to achieve the defined conditions. The sliding surface contains two unknown coefficients: one is tuned to achieve the global sliding surface to satisfy the impact time constraint and zero miss distance, and the other is tuned to guarantee the field-of-view constraint. The guidance law is designed to ensure the realization of the global sliding mode. On this basis, the guidance law is modified to a closed-loop structure, and the maximum detection capability of the seeker is utilized to a greater extent. Under the proposed guidance law, neither the small angle assumption nor time-to-go estimation is needed. The guidance command is continuous and converges to 0 at the desired impact time. Simulation results demonstrate the effectiveness and superiority of the proposed guidance law.

Sensor-Based Robust Incremental Three-Dimensional Guidance Law with Terminal Angle Constraint

In this work, a robust incremental three-dimensional (3D) guidance law is proposed considering terminal angle constraint against maneuvering targets. As a stepping stone, the line-of-sight (LOS) tracking error dynamics is employed for the 3D guidance law design. A sliding variable is constructed such that its first-order derivative excludes the relative range in the perturbation, which avoids the unboundedness of system perturbation induced by target maneuvers near collision. A time-varying version of the sliding variable is designed to accelerate convergence of the LOS tracking errors and avoid large initial sliding variables. Then, two guidance laws are derived as a benchmark via the nonlinear dynamic inversion (NDI)-based sliding mode control (NDI-SMC) and NDI-based time-varying sliding mode control (NDI-TVSMC), respectively. To further improve guidance robustness with reduced system perturbation, the sensor-based incremental nonlinear dynamic inversion (INDI) control is used to design the INDI-SMC-based and INDI-TVSMC-based guidance laws. The sensor-based guidance laws exploit the LOS angular acceleration and guidance command output at the latest step, which result in smaller guidance gains to reject the perturbation than the NDI guidance laws. Numerical simulations in various cases and comparison studies are conducted to verify the effectiveness and robustness of the proposed method.

Robust compound control for wheeled inverted pendulum in an uncertain and disturbed environment

This paper proposes a robust control for wheeled inverted pendulum (WIP) taking into account the wheel position and pendulum angle in the presence of uncertain disturbances. The proposed control algorithm is a combination of time-varying sliding mode control (TVSMC), exponential reaching law (ERL), and nonlinear feedback control (NFC) to eliminate the chattering phenomenon and arrive at better stability and tracking performance. For consistency, the nonlinear dynamic model of WIP is derived using Lagrangian and Newtonian approaches. The convergence and stability of the proposed control scheme are proved using Lyapunov theorem. The study also presents a comparative analysis of linear and nonlinear control strategies based on investigation of time response, tracking error, and control energy. The WIP system has been subjected to various rigorous initial conditions and disturbances to characterize the stability and tracking performance of the implemented controllers. The simulation results demonstrate the promising performance of the proposed control scheme in eliminating the chattering phenomenon, suppressing the uncertain disturbances effect, and improving the stability and tracking performance.

Time-varying sliding mode control of missile based on suboptimal method

This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory. The analytical solution of suboptimal time-varying sliding surface and the corresponding suboptimal control law are obtained by solving the state-dependent Riccati equation analytically. Then, the Lyapunov method is used to analyze the motion trend in sliding surface and the asymptotic stability of the closed-loop system is validated. The suboptimal control law is transformed to the form of pseudo-angle-of-attack feedback. The simulation results indicate that the satisfactory performance can be obtained and the control law can overcome the influence of parameter errors.

Robust Adaptive Global Time-varying Sliding-mode Control for Finite-time Tracker Design of Quadrotor Drone Subjected to Gaussian Random Parametric Uncertainties and Disturbances

The quadrotor has many potential applications such as infrastructure predictive maintenance in mining tunnels of the railway. In order to navigate through those environments by using the quadrotor drone, there are many challenges such as aerodynamics disturbances, parametric uncertainties, and noise measurements. A robust adaptive global time-varying sliding-mode controller (RAGTVSMC) is proposed to address the quadrotor path in the presence of the random disturbances and uncertainties. In order to eliminate the reaching phase and reduce the initial control effort, a novel time-varying sliding mode (TVSM) surface is presented for the quadrotor system. Moreover, the TVSM surface is designed to meet the impact time requirement with a global sliding mode. Adaptive laws are developed to address the upper bound of the additives disturbances on the quadrotor dynamics using only the error position and velocity. The convergence with specific time is assured and the quadrotor stability is proved according to Lyapunov’s theory. Finally, to demonstrate the effectiveness of the proposed controller in this work, simulations are conducted.

A Time-Varying Sliding Mode Control Method for Distributed-Mass Double Pendulum Bridge Crane With Variable Parameters

This paper aims to explain the design of a novel time-varying sliding mode control of variable parameter (VP-TVSMC), which can effectively solve the anti-swing and positioning problem of distributed-mass double pendulum bridge crane system with its quick responsiveness and strong robustness to external interference. More specifically, this model initiates with the establishment of the dynamic equation of double pendulum crane model based on distributed-mass, then followed by the design of a time-varying parameter to realize the dynamic adjustment of the sliding mode surface and enhance the adjustment ability of the sliding mode surface, which is conducive to the global robustness of the double pendulum crane system under VP-TVSMC. With Lyapunov method and LaSalle’s invariance principle, the asymptotic stability of the system can be sufficiently proved. Finally, the adoption of three kinds of external interference signals and uncertain system parameters successfully verified the preeminent control performance and global robustness against external interference of the proposed controller. The simulation results indicate that compared with the conventional CSMC and PDSMC, the proposed control method can reduce the driving force of the trolley, ensure the rapid and precise positioning of the trolley, as well as restrain the load swing angle within 5° in an effective manner. In addition, compared with the symbolic function sgn( $S$ ), the designed continuous function th( $S$ ) possesses a better anti-chattering effect, thus strengthening of the control performance of VP-TVSMC.

Time-Varying Second-Order Sliding Mode Control for Systems Subject to External Disturbance

In this article, the design problem of a class of novel second-order sliding mode controller for systems subject to external disturbance is investigated, where the sliding variable is affected by a time-varying regulation. On the one hand, for the unmatched disturbance bounded by positive functions, a second-order sliding mode controller is proposed to prove the finite-time stability of aforementioned system through the backstepping-like method and virtual control strategy. On the other hand, for the non-vanishing bounded disturbance, a non-singular terminal sliding mode surface containing disturbance observations is designed via a finite-time disturbance observation method and the finite-time stability of the system controlled output is realized. The claimed performances of the proposed methods are validated by two simulation examples.

Multiloop state-dependent nonlinear time-varying sliding mode control of unmanned small-scale helicopter

Time delays, parameter uncertainties, and disturbances are the fundamental problems that hinder the stability and reduce dramatically the tracking performance of dynamical systems. In this paper, a new state-dependent nonlinear time-varying sliding mode control autopilot structure is proposed to cope with these dynamical and environmental complexities for an unmanned helicopter. The presented technique is based on freezing the nonlinear system equations on each time step and designing a controller using the frozen system model at this time step. The proposed method offers an improved performance in the presence of major disturbances and parameter uncertainties by adapting itself to possible dynamical varieties without a need of trimming the system on different operating conditions. Unlike the existing linear cascade autopilot structure, this study also proposes a nonlinear cascade state-dependent coefficient helicopter autopilot structure consisting of four separate nonlinear sub-systems. The proposed method is tested through the real time and PC-based simulations. To show the performance of the proposed robust method, it is also bench-marked against a linear sliding control control in PC-based simulations.

A global time-varying sliding-mode control for the tracking problem of uncertain dynamical systems

In this paper, a global time-varying sliding-mode control scheme with prespecified convergence time is proposed for the tracking problem of a class of uncertain nonlinear systems under parameters uncertainties and external disturbances. Firstly, a novel time-varying sliding manifold with appropriate coefficients is presented. These coefficients are tuned to eliminate the reaching phase and to drive the system states to the equilibrium in a specified time. Hence, the system states are constrained to the sliding surface from the beginning of the motion which enables the global robustness, the reduction of the initial control effort, and the meet of the convergence time requirement. Moreover, in order to address the more practical case that the upper bound of the system uncertainties and disturbances is unavailable, an adaptive time-varying sliding mode control algorithm is derived, by which the tracking error vanish as time tends to infinity. The stability of the system has been proved by the Lyapunov stability theorem, and simulation studies are conducted to show the effectiveness of the suggested control schemes.

Analysis and Design of a Multi-Channel Time-Varying Sliding Mode Controller and its Application in Unmanned Aerial Vehicles

Abstract This study introduces a new multi-channel robust nonlinear control algorithm based on the theory of the time-varying sliding mode control (TVSMC) strategy to stabilize the attitude of an unmanned aerial vehicle (UAV) for nuclear decommissioning applications. Since the UAV is imposed by constant radiations, its parameters are always time-varying and uncertain. This is particularly important in designing sliding mode control because the motion of the control system in the reaching phase can be influenced by environmental disturbances and parameter uncertainties. In this study, a time-varying sliding manifold is proposed to eliminate the reaching phase and to enhance the robust performance. Therefore, a novel type of time-varying sliding surface is introduced based on the initial condition as a slope-varying manifold. Then, a procedure for determining the control parameters is investigated. Furthermore, chattering phenomenon can be avoided using two techniques known as boundary layer and continuous SMC. Finally, to highlight the robust performance of the proposed methods, a quadrotor UAV subject to external disturbances and uncertainties is simulated.

Parameter Estimation-Based Time-Varying Sliding Mode Control for Multimotor Driving Servo Systems

This paper presents a parameter estimation-based time-varying sliding mode controller for the multimotor driving servo systems with the unknown parameters and actuator saturation, such that the finite-time coupling control of load output tracking and motors synchronization is achieved. First, the parameter estimation scheme employs the filtered representation of the load system dynamics to obtain the parameter estimation error, which is utilized to design the adaptive parameter law with dynamic gain to attain the finite-time parameter estimation with the prescribed transient and steady-state performances. Then, the generalized coupling error (GCE) is designed based on the estimation results to transform the complicated coupling control problem into the GCE convergence, which would extremely simplify the controller design. By incorporating the fuzzy echo state network (FESN), a time-varying sliding mode controller is presented to successfully eliminate the reaching phase and guarantee the finite-time GCE convergence with $L_2$ norm performance. For the FESN compensation, a novel learning law is derived based on the norm of FESN weight vector to reduce the computational cost where only a scalar weight needs to be updated online. Finally, the comparative experiments illustrate the benefits and reliability of the proposed algorithms.