Higher Order Sliding Mode Control Research Articles

An Adaptive Real-Time Third Order Sliding Mode Control for Nonlinear Systems

As most real world systems are significantly nonlinear in nature, developing robust controllers have attracted many researchers for decades. Robust controllers are the controllers that are able to cope with the inherent uncertainties of the nonlinear systems. Many control methods have been developed for this purpose. Sliding mode control (SMC) is one of the most commonly used methods in developing robust controllers. This paper presents a higher order SMC (HOSMC) approach to mitigate the chattering problem of the traditional SMC techniques. The developed approach combines a third order SMC with an adaptive PID (proportional, integral, derivative) sliding surface to overcome the drawbacks of using PID controller alone. Moreover, the presented approach is capable of adaptively tuning the controller parameters online to best fit the real time applications. The Lyapunov theory is used to validate the stability of the presented approach and its feasibility is tested through a comparison with other conventional SMC approaches.

Design and simulation of fuzzy-based nonlinear-PID and sliding mode controllers for ankle rehabilitation soft wearable robot

Soft robotics has become an active research area due to its compliance with the natural anatomy, volume to weight ratio, and overall compatibility. However, the difficulties in controlling soft robots have remained a challenge for employing soft wearable robots for clinical applications. In this paper, a fuzzy-based nonlinear PID controller and higher-order sliding mode controllers which can maintain robustness in the presence of a disturbance signal have been designed and analysed. A simple innovative way to include pain signals in control design has been developed; the patient is actively involved by feeding the pain signal to the controller. The pain signal will be characterised into predefined categories from the physiotherapist's knowledge; a fuzzy controller is developed to generate reference force output for the controller from pain feedback and rate of change of muscle elongation. The developed models were analysed and simulated in MATLAB Simulink and Simscape's physical modelling environment.

Kinematic and Dynamic Control of Cooperating Underwater Vehicle-Manipulator Systems

Cooperative control of autonomous underwater robots can provide capabilities that exceed those of any single marine robot. In this paper, the cooperation between two different underwater vehicle-manipulator systems is considered. Cooperation is enabled through a control scheme which generates state-dependent reference signals to achieve synchronization of the end-effector positions of the robots. These references are tracked by the individual control systems, which consist of decoupled kinematic and dynamic controllers. Consequently, the control systems do not constrain the choice of cooperation scheme. Due to the kinematic redundancy of the robots, a task-priority inverse kinematics controller is used for velocity-level redundancy resolution, and several tasks are defined for each robot. Furthermore, the dynamics of the robots are controlled by a higher-order sliding mode controller, namely the generalized super-twisting algorithm with adaptive gains. The dynamic control approach provides robustness to model uncertainties and unknown disturbances. The effectiveness of the methods is verified in a simulation study on a heterogeneous pair of UVMSs.

Event-triggered type-2 fuzzy-based sliding mode control for steer-by-wire systems

This paper proposes an event-triggered higher-order sliding mode control for steer-by-wire (SbW) systems subject to limited communication resources and uncertain nonlinearity. First, an interval type-2 fuzzy logic system (IT2 FLS) is adopted to approximate the uncertain nonlinearities. A fuzzy-based state observer is developed to estimate unavailable states of the extended SbW system. Then, to save communication resources and eliminate chattering, an event-triggered higher-order 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. After that, the practical finite-time stability of the closed-loop SbW system is proved in the framework of the Lyapunov theory. Finally, numerical simulations and vehicle experiments are given to evaluate the effectiveness and superiority of the proposed scheme.

Disturbance observer–based fixed-time robust control for constrained air-breathing hypersonic vehicle

This article studies the fixed-time robust control problem for the longitudinal dynamics of hypersonic vehicles in the presence of parametric uncertainties, external disturbances and input constraints. First, the dynamic model is transformed into two fourth-order integral chain subsystems by feedback linearization technology. Four novel fast integrating sliding surfaces are designed for each subsystem to guarantee the fixed time convergence of the errors and the derivatives. The double power reaching law is investigated to accelerate the convergence of sliding surfaces. Furthermore, the fixed-time disturbance observer technique is applied to estimate the lumped disturbance precisely. A novel fixed-time anti-saturation auxiliary system is designed to tackle the saturation caused by constraints of actuators. Then the semi-global uniform boundedness of the closed-loop system in a fixed time is proved by Lyapunov’s stability theory. Finally, comparison simulation experiments with the existing higher order sliding mode control method are carried out to verify the proposed method’s effectiveness and superiority.

Fault‐tolerant finite‐time adaptive higher order sliding mode control with optimized parameters for attitude stabilization of spacecraft

AbstractThis article considers the problem of attitude regulation of rigid spacecraft under the effect of inertial ambiguity, exogenous disturbances, input saturation, and actuator uncertainties. In this regard, an adaptive second‐order sliding mode control (ASOSMC) is designed to provide robustness against the lumped disturbances (the combination of uncertainties and faults). The ASOSMC presents a two‐fold advantage over conventional SMC. The use of adaptive law eliminates the assumption of a priori knowledge on the upper bounds of the disturbances. Further, the SOSMC methodology alleviates the high‐frequency chattering in the input without compromising robustness. The theoretical analysis under the proposed strategy guarantees the convergence of sliding surface and system states to the origin in a finite‐time. Besides, this work also resolves the inbuilt problem of unwinding in the quaternion‐based attitude representation. Further, the nominal parameters of the proposed control law are optimized offline using an ant lion optimization method. The numerical simulation validates the effectiveness of the proposed controller by comparing its performance with the other existing controllers.

Fixed-time HOSM controller design for constrained sliding mode systems with mismatched terms

The current study has systematically presented a strategy of designing the fixed-time high-order sliding mode (HOSM) controller with asymmetric output constraints. This constructive method is accomplished by three crucial mechanisms. First of all, some nonlinear terms satisfying homogeneous growth conditions are implanted into the mismatched channels of the traditional HOSM system. Based on this, a HOSM system with mismatched terms is built to weaken the uncertainties in control input channels. Secondly, a barrier Lyapunov function (BLF) is developed to resolve the constraints. Thirdly, by integrating the BLF with a backstepping-like method, a fixed-time HOSM controller is explicitly proposed to handle the HOSM dynamics with mismatched terms and asymmetric output constraints. It is shown via the strict Lyapunov analysis that under the constructed controller, the closed-loop system is fixed-time stabilized and the realization of prescribed constraints is insured. The investigations of two cases are provided to validate the established theoretical results.

Quad-rotor adaptive sliding mode control using only position and yaw sensors: Generalized relative degree approach

An output tracking controller design is proposed for perturbed Quad-Rotor Unmanned Aerial Vehicles (QR-UAV) using a generalized relative degree approach that allows employing only four measurements of the QR-UAV states, position (x,y,z) and yaw angle (ψ), instead of the traditional six variables. Adaptive Super-Twisting (ASTW) control is applied for controlling the yaw angle (ψ) in the presence of perturbations with bounded derivatives and unknown bounds. The relative degree approach allows the application of Adaptive Continuous High Order Sliding Mode (ACHOSM) control for controlling the position states (x,y,z), in a single loop, in the presence of smooth perturbations with bounded derivatives and unknown bounds. The proposed single loop ASTW and the ACHOSM controllers, with non-overestimated control gains, drive the position trajectory and yaw tracking errors to zero asymptotically in the absence of dynamics of actuators and sensors. Finite convergent time Filtering HOSM differentiators are used to facilitate the ACHOSM controllers in the presence of the noisy measurements. The proposed single loop sliding mode controllers have been validated via simulations.

A novel adaptive-gain higher-order sliding mode controller and its parameters tuning

A novel adaptive-gain higher-order sliding mode controller and its parameters tuning

Improved Super Twisting Based High Order Direct Power Sliding Mode Control of a Connected DFIG Variable Speed Wind Turbine

This work presents the theoretical and practical comparison of linear and nonlinear control laws for the direct power control of a grid-connected double fed induction generator (DFIG), based wind energy conversion system (WECS) under different operating modes. We will show the improvement brought by the super twisting based high order sliding mode control to mitigate the chattering phenomenon, due to the high switching frequency. It will also avoid the hyperlink of the controller settings to the system’s mathematical model and will reduce the sensibility to external disturbances. The overall structure of the proposed control requires the use of the DFIG simplified model with field-oriented control (FOC). This last allows an instantaneous decoupled control of the DFIG stator active and reactive power by acting on dq rotor currents (Iqr , Idr ) respectively. In the preliminary tests, a comparative study is conducted to verify the superior performance of the proposed WECS control scheme during various operating modes including the maximum power point tracking MPPT mode. The study reveals the effectiveness of each implemented control law with its advantages and drawbacks.

Photovoltaic Energy Conversion Systems with Sliding Mode Control

A new sliding-mode-control-based power conversion scheme is proposed for photovoltaic energy conversion systems. The perturbation and observation (P&O) maximum power-point tracking (MPPT) approach is adopted for optimizing the power generation capabilities from solar panels. Due to the inherent nonlinear dynamics of power converters, we need to adopt a nonlinear control approach to optimize the energy conversion efficiency and tolerate the fluctuations and changes of load and sunlight irradiance. In this manuscript, novel first-and higher-order sliding mode control approaches are proposed, aiming to provide a systematic approach for the robust and optimal control of solar energy conversion, which guarantees Lyapunov stability and consistent performance in the face of external perturbations and disturbances. Moreover, to eliminate the chattering phenomenon inherent in the first-order approach, super-twisting second-order sliding mode control is developed for the buck-boost converter. Furthermore, the output of DC–DC converter supplies a voltage-oriented-control (VOC)-based space-vector pulse-width-modulated inverter to generate three-phase AC power to the grid. To demonstrate the robustness and effectiveness of the proposed scheme, computer simulations and dSPACE hardware-in-the-loop platform have been carried on for examining the proposed sliding-mode-control-based solar energy conversion system.

SPMSM Sliding Mode Control Based on the New Super Twisting Algorithm

To achieve the high-performance control of the surface-mounted permanent magnet synchronous motor (SPMSM) speed control system, this paper proposes a high-order sliding mode control strategy based on a new super twisting algorithm (NSTA). This strategy introduces an adaptive term in its proportional term based on the original super twisting algorithm, which solves low reaching speed and poor antidisturbance ability due to the square root calculation of proportional term in the original super twisting algorithm. The simulation results show that the proposed strategy can effectively improve the system’s response speed and antidisturbance and greatly suppress the chattering phenomenon of traditional sliding mode control.

Investigation of Reusable Launch Vehicle Landing Guidance Control with Multiple Sliding Surface Technique

This paper proposes an autonomous approach and landing guidance law for a reusable launch vehicle (RLV) at the specified runway touchdown. With the full nonlinear point-mass dynamics, the multiple sliding surfaces guidance (MSSG) technique is developed for the closed-loop guidance law to guarantee a successful approach and landing (A&L) movement, which has the same advantage in the finite time convergent property as higher order sliding mode control. Its global stability is proved using Lyapunov theory. The resultant guidance law has features in on-line trajectories calculation without any off-line analysis only using the boundary conditions of the A&L phase and instantaneous states of the RLV. Therefore, it is capable of targeting different touchdown points on the runway and overcoming large initial condition errors. Simulations are provided to verify the effectiveness of the proposed law.

Design of high‐order sliding mode controller under asymmetric output constraints

AbstractThis article is devoted to the design issue of high‐order sliding mode (HOSM) controller subject to asymmetric output constraints. A barrier Lyapunov function (BLF) is first developed to deal with the constraints. Subsequently, by implanting the BLF into the modified adding a power integrator technique, a HOSM control algorithm, which is able to handle the closed‐loop system simultaneously with and without asymmetric output constraints, has been presented. It has been shown on the basis of the rigorous mathematical proof that under the proposed control strategy, the finite‐time stability of the considered system with the asymmetric output constraints is ensured. Meanwhile, the proposed algorithm also satisfies the requirement of the preset asymmetric output constraint. At last, an illustrative example is given to demonstrate the effectiveness of the presented algorithm.

A Modified HOSM Controller Applied to an ABS Laboratory Setup with Adaptive Parameter

The antilock braking system (ABS) is an electromechanical device whose controller is challenging to design because of its nonlinear dynamics and parameter uncertainties. In this paper, an adaptive controller is considered under the assumption that the friction coefficient is unknown. A modified high-order sliding-mode controller is designed to enhance the controller performance. The controller ensures tracking of the desired reference and identifies the unknown parameter, despite parametric variations acting on the real system. The stability proof is done using the Lyapunov approach. Some numerical and experimental tests evaluate the controller on a mechatronic system that represents a quarter-car model.

Sliding Manifold Design for Higher-order Sliding Mode Control of Linear Systems

Sliding Manifold Design for Higher-order Sliding Mode Control of Linear Systems

HOSM Controller Using PI Sliding Manifold for an Integrated Active Control for Wheeled Vehicles

This study considers the design of a modified high-order sliding mode (HOSM) controller using a PI sliding surface to the attitude control of a ground vehicle. A robust-modified HOSM controller is derived, so that the lateral velocity and yaw rate tracks the desired trajectory despite the environment actions acting on the ground vehicle and parameter variations. The stability is guaranteed with Lyapunov’s stability theorem function. The performance of the dynamic controllers is evaluated using the CarSim simulator considering a challenging double steer maneuver.

Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems

A fast self-adapting high-order sliding mode (FSH-OSM) controller is designed for a class of nonlinear systems with unknown uncertainties. As for uncertainty-free nonlinear system, a new switching condition is introduced into the standard geometric homogeneity. Different from the existing geometric homogeneity method, both state variables and their derivatives are considered to bring a reasonable effective switching condition. As a result, a faster convergence rate of state variables is achieved. Furthermore, based on the integral sliding mode (ISM) and above geometric homogeneity, a self-adapting high-order sliding mode (HOSM) control law is proposed for a class of nonlinear systems with uncertainties. The resulting controller allows the closed-loop system to conduct with the expected properties of strong robustness and fast convergence. Stable analysis of the nonlinear system is also proved based on the Lyapunov approach. The effectiveness of the resulting controller is verified by several simulation results.

Finite-Time Adaptive Higher-Order SMC for the Nonlinear Five DOF Active Magnetic Bearing System

The active magnetic bearings (AMB) play an essential role in supporting the shaft of fast rotating machines and controlling the displacements in the rotors due to the deviation in the shaft. In this paper, an adaptive integral third-order sliding mode control (AITOSMC) is proposed. The controller suppresses the deviations in the rotor and rejects the system uncertainties and unknown disturbances present in the five DOF AMB system. The application of AITOSMC alleviates the problem of high-frequency switching called chattering, which would otherwise restrict the practical application of sliding mode control (SMC). Moreover, adaptive laws are also incorporated in the proposed approach for estimating the controller gains. Further, it also prevents the problem of overestimation and avoids the use of a priori assumption about the upper bound knowledge of total disturbance. The Lyapunov and homogeneity theories are exploited for the stability proof, which guarantees the finite-time convergence of closed-loop and output signals. The numerical analysis of the proposed strategy illustrates the effective performance. Furthermore, the comparative analysis with the existing control schemes demonstrates the efficacy of the proposed controller.

Real time observer and control scheme for a wind turbine system based on a high order sliding modes

The introduction of advanced control algorithms may improve considerably the efficiency of wind turbine systems. This work proposes a high order sliding mode (HOSM) control scheme based on the super twisting algorithm for regulating the wind turbine speed in order to obtain the maximum power from the wind. A robust aerodynamic torque observer, also based on the super twisting algorithm, is included in the control scheme in order to avoid the use of wind speed sensors. The presented robust control scheme ensures good performance under system uncertainties avoiding the chattering problem, which may appear in traditional sliding mode control schemes. The stability analysis of the proposed HOSM observer is provided by means of the Lyapunov stability theory. Experimental results show that the proposed control scheme, based on HOSM controller and observer, provides good performance and that this scheme is robust with respect to system uncertainties and external disturbances.