Sliding Mode Controller Design for a Class of Nonlinear System

A sliding mode control methodology is presented for nonlinear systems represented by input output models, which does not depend on the state variables. There are two parts in the controller design, one is the sliding controller design and the other is the design of linear feedback system. Simulation results demonstrate the validity of the control scheme.

Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

Marine Predator Algorithm-based Sliding Mode Control of a Novel Motion Simulator for High Column Sloshing Experiments

Sloshing experiment is crucial to determine the reaction performance of regeneration columns on an offshore floating platform.A novel type of column motion simulating device and a Marine Predator Algorithm-based Sliding Mode Controller(MPA-SMC)are proposed for such sloshing experiments.The simulator consists of a Stewart platform and a steel framework.The Stewart platform is located at the column's center of gravity(CoG)and supported by the steel framework.The platform's hydraulic servo system is controlled by a sliding mode controller with parameters optimized by MPA to improve robustness and precision.A numerical sloshing experiment is conducted using the proposed device and controller.The results show that the novel motion simulator has lower torque during the column sloshes,and the proposed controller performs better than a well-tuned PID controller in terms of target tracking precision and anti-interference capability.

Asynchronous Learning-Based Output Feedback Sliding Mode Control for Semi-Markov Jump Systems: A Descriptor Approach

This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of system state and mode information,an asynchronous output-feedback sliding sur-face is adopted in the case of incompletely available state and non-synchronization phenomenon.The holonomic dynamics of the sliding mode are characterized by a descriptor system in which the switching surface is regarded as the fast subsystem and the system dynamics are viewed as the slow subsystem.Based upon the co-occurrence of two subsystems,the sufficient stochastic admissibility criterion of the holonomic dynamics is derived by utilizing the characteristics of cumulative distribution functions.Furthermore,a recursive learning controller is formulated to guarantee the reachability of the sliding manifold and realize the chattering reduction of the asynchronous switching and sliding motion.Finally,the proposed theoretical method is substantia-ted through two numerical simulations with the practical contin-uous stirred tank reactor and F-404 aircraft engine model,respectively.

Fixed-Time Sliding Mode Control With Varying Exponent Coefficient for Modular Reconfigurable Flight Arrays

The modular system can change its physical structure by self-assembly and self-disassembly between modules to dynamically adapt to task and environmental requirements. Recognizing the adaptive capability of modular systems, we introduce a modular reconfigurable flight array(MRFA) to pursue a multifunction aircraft fitting for diverse tasks and requirements,and investigate the attitude control and the control allocation problem by using the modular reconfigurable flight array as a platform. First, considering the variable and irregular topological configuration of the modular array, a center-of-mass-independent flight array dynamics model is proposed to allow control allocation under over-actuated situations. Secondly, in order to meet the stable, fast and accurate attitude tracking performance of the MRFA, a fixed-time convergent sliding mode controller with state-dependent variable exponent coefficients is proposed to ensure fast convergence rate both away from and near the system equilibrium point without encountering the singularity. It is shown that the controller also has fixed-time convergent characteristics even in the presence of external disturbances. Finally,simulation results are provided to demonstrate the effectiveness of the proposed modeling and control strategies.

Control system design for a pressure-tube-type supercritical water-cooled nuclear reactor via a higher order sliding mode method

Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.

Adaptive Predefined-Time Attitude Tracking Control for Quadrotor Using a Novel Terminal Sliding Mode Approach

This paper proposes an adaptive predefined-time terminal sliding mode control(APTSMC)scheme for attitude tracking control of a quadrotor.To create this,an adaptive predefined-time stability controller based on a terminal sliding mode is constructed.The upper bound of convergence time in the proposed scheme can be adjusted by the explicit parameters during the design process of the controller.In addition,it is proved that the attitude tracking error will converge within two periods of the preset time.These two periods are set between two ranges:From the initial values to the sliding mode surface and from the sliding mode surface to the region near the origin.Furthermore,an adaptive law is adopted to eliminate unknown external disturbances and the effects of the uncertainties in the quadrotor model,so it is unnecessary to require the prior knowledge of the upper bound of the perturbations.Simulation results are produced and comparative case studies are carried out to demonstrate that the proposed scheme has faster convergence speed and smaller tracking errors.

Adaptive Super‑Twisting Sliding Mode Fault‑Tolerant Control of Launch Vehicles with Actuator Faults

A fault-tolerant control law based on adaptive super-twisting sliding mode control(SMC)is designed for the attitude command tracking problem of a launch vehicle with actuator faults,considering the uncertainties arising from unknown external disturbances,fuel consumption of the launch vehicle,and the perturbation due to the change in rotational inertia caused by tank sloshing,as well as the potential system model changes due to actuator fault and unmodeled dynamics.This control algorithm integrates the super-twisting SMC,the fuzzy logic control,and the adaptive control.First,a super-twisting sliding surface is selected to mitigate the“chattering”phenomenon inherent in SMC,ensuring that the system tracking error converges to zero within a finite time.Second,building upon this sliding surface,the fuzzy logic control is used to approximate the unknown system function,which includes fault information.Adaptive parameters are used to approach the system parameters and enhance disturbance rejection.The stability and finite-time convergence of the launch vehicle attitude tracking control system are verified by the Lyapunov method.Numerical simulations demonstrate the effectiveness and robustness of the proposed adaptive super-twisting SMC algorithm.

Enhanced Fuzzy Logic Control Model and Sliding Mode Based on Field Oriented Control of Induction Motor

In the context of induction motor control, there are various control strategies used to separately control torque and flux. One common approach is known as Field-Oriented Control (FOC). This technique involves transforming the three-phase currents and voltages into a rotating reference frame, commonly referred to as the “dq” frame. In this frame, the torque/speed and flux components are decoupled, allowing for independent control, by doing so, the motor’s speed can be regulated accurately and maintain a constant flux which is crucial to ensure optimal motor performance and efficiency. The research focused on studying and simulating a field-oriented control system using fuzzy control techniques for an induction motor. The aim was to address the issue of parameter variations, particularly the change in rotor resistance during motor operation, which causes the control system to deviate from the desired direction. This deviation implies to an increase in the magnetic flux value, specifically the flux component on the q-axis. By employing fuzzy logic techniques to regulate flux vector’s components in the dq frame, this problem was successfully resolved, ensuring that the magnetic flux value remains within the nominal limits. To enhance the control system’s performance, response speed, and efficiency of the motor, sliding mode controllers were implemented to regulate the current in the inner loop. The simulation results demonstrated the proficiency of the proposed methodology.

Sliding Mode Controller Design for Position and Speed Control of Flight Simulator Servo System with Large Friction

Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in the flight simulator servo system, especially in a low-speed state. Based on the description of dynamic and static models of a nonlinear Stribeck friction model, this paper puts forward sliding mode controller to overcome the friction, whose stability is

High-order sliding mode attitude controller design for reentry flight

A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and accurate tracking of the aerodynamic angle commands with the finite time convergence. The proposed control strategy is developed on the basis of integral sliding mode philosophy, which combines conventional sliding mode control and a linear quadratic regulator over a finite time interval with a free-final-state and allows the finite-time establishment of a high-order sliding mode. Firstly, a second-order sliding mode attitude controller is designed in the proposed high-order siding mode control framework. Then, to address the control chattering problem, a virtual control is introduced in the control design and hence a third-order sliding mode attitude controller is developed, leading to the chattering reduction as well as the control accuracy improvement. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.

Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.

Landslide distribution and sliding mode control along the Anninghe fault zone at the eastern edge of the Tibetan Plateau

Tibetan Plateau is known as the roof of the world.Due to the continuous uplift of the Tibetan Plateau,many active fault zones are present.These active fault zones such as the Anninghe fault zone have a significant influence on the formation of special geomorphology and the distribution of geological hazards at the eastern edge of the Tibetan Plateau.The Anninghe fault zone is a key part of the Y-shaped fault pattern in the Sichuan-Yunnan block of China.In this paper,high-resolution topographic data,multitemporal remote sensing images,numerical calculations,seismic records,and comprehensive field investigations were employed to study the landslide distribution along the active part of the Anninghe.The influence of active faults on the lithology,rock mass structures and slope stress fields were also studied.The results show that the faults within the Anninghe fault zone have damaged the structure and integrity of the slope rock mass,reduced the mechanical strength of the rock mass and controlled the slope failure modes.The faults have also controlled the stress field,the distribution of the plastic strain zone and the maximum shear strain zone of the slope,thus have promoted the formation and evolution of landslides.We find that the studied landslides are linearly distributed along the Anninghe fault zone,and more than 80%of these landslides are within 2–3 km of the fault rupture zone.Moreover,the Anninghe fault zone provides abundant substance for landslides or debris flows.This paper presents four types of sliding mode control of the Anninghe fault zone,e.g.,constituting the whole landslide body,controlling the lateral boundary of the landslide,controlling the crown of the landslide,and constituting the toe of the landslide.The results presented merit close attention as a valuable reference source for local infrastructure planning and engineering projects.

Some Remarks on the Boundedness and Convergence Properties of Smooth Sliding Mode Controllers

Conventional sliding mode controllers are based on the assumption of switching control, but a well-known drawback of such controllers is the chattering phenomenon. To overcome the undesirable chattering effects, the discontinuity in the control law can be smoothed out in a thin boundary layer neighboring the switching surface. In this paper, rigorous proofs of the boundedness and convergence properties of smooth sliding mode controllers are presented. This result corrects flawed conclusions previously reached in the literature. An illustrative example is also presented in order to confirm the convergence of the tracking error vector to the defined bounded region.

Simulation and Design of Fuzzy Sliding-mode Controller for Ship Heading-tracking

In considering the characteristic of a rudder,the maneuvers of a ship were described by an unmatched uncertain nonlinear mathematic model with unknown virtual control coefficient and parameter uncertainties.In order to solve the uncertainties in the ship heading control,specifically the controller singular and paramount re-estimation problem,a new multiple sliding-mode adaptive fuzzy control algorithm was proposed by combining Nussbaum gain technology,the approximation property of fuzzy logic systems,and a multiple sliding-mode control algorithm.Based on the Lyapunov function,it was proven in theory that the controller made all signals in the nonlinear system of unmatched uncertain ship motion uniformly bounded,with tracking errors converging to zero.Simulation results show that the demonstrated controller design can track a desired course fast and accurately.It also exhibits strong robustness peculiarity in relation to system uncertainties and disturbances.

Designing and Optimization of Fuzzy Sliding Mode Controller for Nonlinear Systems

For enhancing the control effectiveness,we firstly design a fuzzy logic based sliding mode controller(FSMC)for nonlinear crane systems.On basis of overhead crane dynamic characteristic,the sliding mode function with regard to trolley position and payload angle.Additionally,in order to eliminate the chattering problem of sliding mode control,the fuzzy logic theory is adopted to soften the control performance.Moreover,aiming at the FSMC parameter setting problem,a DE algorithm based optimization scheme is proposed for enhancing the control performance.Finally,by implementing the computer simulation,the DE based FSMC can effectively tackle the overhead crane sway problem and avoid unexpected accident greatly.