Conventional Sliding Mode Research Articles

Adaptive SMC based on the dynamic containment of the sliding variable

Conventional Sliding Mode Controllers (SMCs) exhibit a robust performance against matched bounded uncertainties and disturbances by containing them under a fixed controller’s effort. Consequently, the controller is commonly found excessive, leading to chattering and straining the actuator. As a solution, the variable-gain SMCs adapt to the instantaneous system requirements, thus attenuating the aforesaid effects and keeping the SMC’s benefits. However, the reported adaptive laws underlying such behavior commonly require arbitrary design considerations and do not consider practical implementation. Unlikely, in this work, a hysteresis-based adaptability law to drive the sliding variable to a boundary layer around zero is proposed. The sliding boundary—hysteresis’ width—will consistently “bounce” over the sliding variable, trying to shrink against it while preserving the sliding mode. This behavior finds its steady-state once the sliding variable and the sliding boundary’s dynamics are synchronized, with no need of subjective or arbitrary adjustments. The close-loop tuning can be derived from the system’s parameters alone, and its steady-state performance can be quantitatively predicted. Furthermore, a method to adjust the sliding surface parameters according to the system’s desired behavior is provided, all in a closed, analytical way. Finally, the physical actuator limits are taken into account and never exceeded, and the discrete nature of the devices normally used for SMC implementation is incorporated throughout. Two examples are studied to portray the proposal’s advantages.

Terminal sliding mode control on autonomous underwater vehicle in diving motion control

<p>In this study, mechanism for reducing chattering in discrete conventional Sliding Mode Controller (DSMC) for Autonomous Underwater Vehicle (AUV) was designed in discrete time domain. The combination of reaching law approach and discrete Terminal Sliding Mode Control (DTSMC) scheme was employed to alleviate chattering effect caused by Quasi Sliding Mode (QSM). First, 6 DOF NPS AUV II equation of motion is linearized to diving mode subsystem. Second, linear sliding surface in discrete time domain is designed and Reaching Law Based (RLB) is employed to the control law. Thirdly, discrete nonlinear sliding surface, specifically DTSMC is designed to reduce chattering phenomena and improved precision control simultaneously. Finally, comparative experimental results are presented to illustrate the effectiveness and advantages of the nonlinear sliding surface. (9 pt).</p>

Conventional and Second Order Sliding Mode Control of Permanent Magnet Synchronous Motor Fed by Direct Matrix Converter: Comparative Study

The main objective of this work revolves around the design of second order sliding mode controllers (SOSMC) based on the super twisting algorithm (STA) for asynchronous permanent magnet motor (PMSM) fed by a direct matrix converter (DMC), in order to improve the effectiveness of the considered drive system. The SOSMC was selected to minimize the chattering phenomenon caused by the conventional sliding mode controller (SMC), as well to decrease the level of total harmonic distortion (THD) produced by the drive system. In addition, the literature has taken a great interest in the STA due to its robustness to modeling errors and to external disturbances. Furthermore, due to its low conduction losses, the space vector approach was designated as a switching law to control the DMC. In addition, the topology and design method of the damped passive filter, which allows improvement of the waveform and attenuation of the harmonics of the input current, have been detailed. Finally, to discover the strengths and weaknesses of the proposed control approach based on SOSMC, a comparative study between the latter and that using the conventional SMC was executed. The results obtained confirm the effectiveness of SOSMC over the conventional SMC under different operating conditions.

Path-following control of Mecanum-wheels omnidirectional mobile robots using nonsingular terminal sliding mode

Due to the superior mobility and maneuverability to move toward any position and attain any orientation simultaneously, Mecanum-wheels omnidirectional mobile robot (MWOMR) is playing a significant role in autonomous transportation and service. This paper proposes a robust nonsingular terminal sliding mode (NTSM) control scheme for the path-following problem of an MWOMR. First, a plant model is identified as a second-order state-space equation with four inputs and three outputs to describe the MWOMR’s path-tracking kinematics and dynamics. Afterwards, a multi–input–multi–output NTSM controller is designed for the MWOMR, and the stability of the NTSM control system is verified by means of Lyapunov function. In addition, the setting guideline of control parameters is elaborated in detail, and a Runge–Kutta formula-based dead-reckoning algorithm is employed to calculate the position and yaw angle information of the robot in real time. Lastly, experiments are carried out to test the control performance in the scenarios of lateral movement and circular movement with initial offset. Experimental results demonstrate that the presented NTSM control strategy owns evident superiority in terms of higher tracking accuracy and stronger robustness against different movements in comparison with a conventional sliding mode (CSM) controller.

Collision-avoidance steering control for autonomous vehicles using neural network-based adaptive integral terminal sliding mode

Due to the complex driving conditions confronted by an autonomous vehicle, it is significant for the vehicle to possess a robust control system to achieve effective collision-avoidance performance. This paper proposes a neural network-based adaptive integral terminal sliding mode (NNAITSM) control scheme for the collision-avoidance steering control of an autonomous vehicle. In order to describe the vehicle’s lateral dynamics and path tracking characteristics, a two-degrees-of-freedom (2DOF) dynamic model and a kinematic model are adopted. Then, an NNAITSM controller is designed, where a radial basis function neural network (RBFNN) scheme is utilized to online approximate the optimal upper bound of lumped system uncertainties such that prior knowledge about the uncertainties is not required. The stability of the control system is proved via Lyapunov, and the selection guideline of control parameters is provided. Last, Matlab-Carsim co-simulations are executed to test the performance of the designed controller under different road conditions and vehicle velocities. Simulation results show that compared with conventional sliding mode (CSM) and nonsingular terminal sliding mode (NTSM) control, the proposed NNAITSM control scheme owns evident superiority in not only higher tracking precision but also stronger robustness against various road surfaces and vehicle velocities.

A Novel Fault-Tolerant Control Method for Robot Manipulators Based on Non-Singular Fast Terminal Sliding Mode Control and Disturbance Observer

In this study, a novel Fault-Tolerant Control Methodology (FTCM) is developed for robot manipulators. First, to overcome singularity glitch and to enhance convergence time of conventional Terminal Sliding Mode Control (TSMC), a new Fast Terminal Sliding Mode Surface (FTSMS) is constructed. Next, to reduce the computation complexity and to provide requirements about undefined nonlinear functions for the control system, a Disturbance Observer (DO) to estimate uncertain dynamics, external disturbances, or faults. Besides, a Super-Twisting Reaching Control Law (STRCL) is designed to compensate for the estimated error of disturbance observer with chattering rejection. Final, a novel, robust, FTCM was developed for robot manipulators to obtain the stability goal of the system, to reach the prescribed performance, and to overcome the effects of disturbances, nonlinearities, or faults. Accordingly, the proposed FTCM has remarkable features, such as fast convergence speeds, robust precision, high tracking performance, significant alleviation of chattering behavior, and finite-time convergence. The position tracking computer simulations were implemented to exhibit the effectiveness and feasibility of the suggested FTCM compared with other control algorithms.

Adaptive fuzzy sliding mode control design for vehicle steer-by-wire systems

This paper presents a novel adaptive fuzzy sliding mode (AFSM) control scheme for a vehicle steer-by-wire (SbW) system. Initially, the dynamics of the SbW system are described by a second-order differential equation where the Coulomb friction and the self-aligning torque are treated as external disturbances. Furthermore, an AFSM controller is designed for the SbW system, which utilizes an adaptive law to estimate both the Coulomb friction and the self-aligning torque, a sliding mode control component to deal with the parametric uncertainties and unmodeled dynamics, and a fuzzy strategy to strike a good balance between the chattering-alleviation and the tracking precision. The stability of the control system is verified in the sense of Lyapunov, and the selection of control parameters is provided in detail. Lastly, experiments are carried out under various road conditions. The experimental results demonstrate that the developed AFSM controller possesses superiority in terms of higher tracking accuracy, stronger robustness and a better balance between the control precision and smoothness in comparison with a conventional sliding mode (CSM) controller and a boundary layer-based adaptive sliding mode (BLASM) controller.

Robust Sliding Mode H∞ Controller of DFIG Based on Variable Speed Wind Energy Conversion System

In this study, a Sliding Mode (SM) methodology combined with a robust H∞ control scheme (SM-H∞) was proposed to control the stator active and reactive power generated by the Doubly Fed Induction Generator (DFIG). The purpose of the proposed controller is to improve the DFIG stator active and reactive power tracking performances by reducing chattering phenomena under variable wind speed, which provides major drawbacks of conventional SM controllers. The H∞ technique was used to define the SM attractive control part, which helps to reduce chattering phenomena and improves robustness in the presence of parameter variations and wind speed changing. The DFIG stator was directly connected to the grid and, its rotor was linked to the grid through a back-to-back converter. The proposed approach was tested using Matlab/Simulink and a comparison with the conventional SM and the SM fuzzy logic controllers was carried out. The results of simulation illustrated an effectiveness of the proposed SM-H∞ controller even in the presence of the DFIG parameter variations and speed changing compared with the other techniques.

Smooth super-twisting sliding mode control for the class of underactuated systems.

In this article, Smooth Super-twisting Sliding Mode Control (SSTWSMC) is investigated for the class of underactuated system. In underactuated systems, the control design is not directly applicable as for other systems (known as fully actuated systems). Therefore, at initial step, a nonlinear uncertain model of systems is transformed into the controllable canonical form, and then Smooth Super Twisting (SSTW) based Sliding Mode Control (SMC) is devised for the control design purpose for the considered class. In addition, closed loop stability of the proposed technique is presented in a fascinating way. The effectiveness and supremacy of the proposed control technique is proven by extensive analysis between conventional Sliding Mode Control (SMC), Super twisting (STW) sliding mode control and Smooth Super-twisting Sliding Mode Control (SSTWSMC). The comprehensive analysis evaluates the attributes like robustness enhancement, settling time, control effort, chattering reduction, overshoot, sliding mode convergence, etc. and is supported by simulations as well as practical implementation on ball and beam balancer (which is considered as application example).

Adaptive Integral Terminal Sliding Mode Control for Automobile Electronic Throttle via an Uncertainty Observer and Experimental Validation

A robust adaptive integral terminal sliding mode (AITSM) control scheme with an uncertainty observer (UO) is developed for automobile electronic throttle (AET) systems. Distinguished from the ordinary sliding mode (SM)-based AET control systems, by using a novel integral terminal sliding surface (SS) to force the closed-loop system to start on the SS at the very beginning, an excellent error convergence and tracking accuracy as well as robustness of the closed-loop system against uncertainties and nonlinearities including transmission friction, return spring limp-home, and gear backlash can be assured. Also, in order to achieve a stably excellent performance for different tracking commands, the sliding parameters are updated by the designed adaptive laws in Lyapunov sense. Moreover, for reducing the control chattering caused by the large switching gain in conventional SM control, an SM-based UO is introduced to provide with the online estimation for the system lumped uncertainty and conduct the feed-forward compensation in the control design. In addition, model-free robust exact differentiators (MRED) are presented to obtain the accurate angular velocity and acceleration information from the unique angle sensors with measurement noises. Not only the comparative experimental results from a real-time digital signal processor (DSP)-based AET plant but also the quantitive root mean square (RMS) values and the maximum (MAX) values of the sampled tracking errors are demonstrated to validate the superior performance of the proposed control. In particular, in the disturbance rejection test by combining trapezium and sinusoidal reference commands, the proposed control exhibits the smallest RMS error values of 0.6832 deg (37% and 27% of the ones of the nonsingular terminal sliding mode and the proportional-integral-derivative controllers), and the smallest MAX values of 2.9352 deg (67% and 35% of the ones of the comparative controllers, respectively).

Comparative study of three types of controllers for DFIG in wind energy conversion system

This paper presents an enhanced control strategy for Wind Energy Conversion System (WECS) using Doubly-Fed Induction Generator (DFIG). A robust Super-Twisting (STW) sliding mode control for variable speed wind turbine is developed to produce the optimal aerodynamic torque and improve the dynamic performance of the WECS. The electromagnetic torque of the DFIG is directly tracked using the proposed control to achieve maximum power extraction. The performance and the effectiveness of the STW control strategy are compared to conventional Sliding Mode (SM) and Proportional-Integral (PI) controllers. The proposed STW algorithm shows interesting features in terms of chattering reduction, finite convergence time and robustness against parameters variations and system disturbances.

Sliding Mode Control with Nonlinear Disturbance Observer based on Genetic Algorithm for Inverted Pendulum with Mismatched Disturbances

Objective: This study proposes the application of optimized Sliding Mode Control (SMC) with Nonlinear Disturbance Observer (NDO) for the Inverted pendulum, which is subjected to mismatched disturbances. Methods/Statistical Analysis: Sliding Mode Control (SMC) with Nonlinear Disturbance Observer (NDO) solves the main problem of chattering present in traditional sliding mode controllers while retaining the nominal performance even with mismatched disturbances. Chattering defines the presence of finite frequency and finite amplitude oscillations in the control input. Genetic Algorithm is used for searching the optimal controller parameters, which includes switching function coefficient, switching gain and observer gain. Findings: Simulation results shows the advantages of NDO based SMC and proves that NDOSMC can observe the mismatched disturbances very effectively. The conventional SMC method is also used in the control design the Inverted pendulum for comparison studies. The two main issues to be tackled in conventional Sliding Mode Control (SMC) are convergence time and chattering. Chattering and convergence time can be reduced in SMC by getting the optimal values of controller parameters using intelligent optimization techniques such as Genetic Algorithm (GA). In the present study convergence time and chattering of the controlled system are considered as the performance index of objective function. Application/Improvements: This study can further be extended for Multi-Input Multi-Output (MIMO) systems subjected to mismatched disturbances and parametric uncertainties.

Sliding Mode Control of Hydrogen Fuel Cell and Ultracapacitor Based Electric Power System: Electric Vehicle Application

The paper deals with controlling an electric power system comprised of a Hydrogen Fuel Cell (HFC), boost and boost/buck DC-DC power converters and the Ultracapacitor (UC) for an auxiliary power supply in order to control servomotor speed within a vehicle application. Relative degree approach is applied for direct control of the servomotor input voltage and speed, as well as the HFC and UC currents in the presence of the model uncertainties. The non-minimum phase property of the DC-DC boost converter is eliminated by controlling HFC and UC currents based on the power balance approach. The adaptive-gain second order sliding mode controllers (2-ASMC) control the current in HFC and the servomotor speed. The conventional Sliding Mode Controllers (SMC) are designed for controlling the output voltage of the converter and the load current of the UC. The efficiency and robustness of the proposed SMC and 2-ASMC are confirmed via computer simulations.

Time-Varying Sliding Mode Control for ABS Control of an Electric Car

Controller design for the Anti-Lock Braking System (ABS) of a wheeled vehicle is a challenging task because of the complex and nonlinear nature of the tyre-road interaction. An efficient ABS controller should be capable of maintaining the wheel slip at an optimal value, which is suitable for the particular road conditions experienced at a given instant in time, preventing the wheel from locking while braking. Many controller designs in the literature track either an optimal slip which is assumed constant or are not supported by experimental validation or simulation testing with higher order models. This paper first presents an ABS system based on a conventional Sliding Mode Control (SMC). The performance of this controller is tested on an experimental vehicle. The results are compared with simulation results obtained with both a quarter car model and a full-car model built in the Matlab/Simulink environment. The performance of this controller is improved by effective state estimation using a Sliding Mode Differentiator (SMD) where the results are benchmarked with an implementation using an Extended Kalman Filter (EKF). The paper then presents a controller based on Time-Varying Sliding Mode Control (TV-SMC) which tracks an optimal slip trajectory.

Free chattering hybrid sliding mode control for a class of non‐linear systems: electric vehicles as a case study

In current study, in order to find the control of general uncertain nonlinear systems, a new optimal hybrid control approach called Optimal General Type II Fuzzy Sliding Mode (OGT2FSM) is presented. In order to estimate unknown nonlinear activities in monitoring dynamic uncertainties, the benefits of general type-2 fuzzy logic systems (GT2FLS) is utilized by the suggested controller. The suggested controller not only warranties the constancy and hardiness against uncertainties of the lumped resulted by external disturbances and un-modeled dynamics, but also considerably decreases the control chattering inherent in traditional sliding mode control. Moreover, the Modified Backtracking Search Algorithm (MBSA), which is a new heuristic algorithm, is used in the offered controller. A comparison is performed between the results of current study and the results of some of the most recent studies on the same topic, which are an Adaptive Interval Type-2 Fuzzy Logic Controller (AGT2FLC) and Conventional Sliding Mode Controller (CSMC), to assess the efficiency of the suggested controller. The suggested control scheme is finally used to the Electric Vehicles type as a case study. Results of simulation confirm the good performance the suggested controller.

A Sliding Mode Control Design based on the Reaching Law for Matrix Rectifiers

This paper presents a novel approach for achieving both a tight DC voltage regulation and a power factor control by applying the Reaching Law Sliding Mode Control (RL-SMC) and the conventional Sliding Mode Control (SMC). Applying these strategies on a matrix rectifier (MR) can achieve a unity grid side power factor when the DC load changes widely and it can provide a ripple-free output voltage that is easily affected by distortions of the three-phase ac voltage supply. Furthermore, by employing the reaching law on the SMC can solve the chatting problem of the sliding motion. Comparative Matlab simulations and experimental verifications for these strategies have been presented and discussed in this paper. The results show that by applying the SMC and RL-SMC on a MR can achieve a unity grid side power factor and a regulated ripple-free DC output.

Multi-mode sliding mode control for precision linear stage based on fixed or floating stator

This paper presents the control performance of a linear motion stage driven by Voice Coil Motor (VCM). Unlike the conventional VCM, the stator of this VCM is regulated, which means it can be adjusted as a floating-stator or fixed-stator. A Multi-Mode Sliding Mode Control (MMSMC), including a conventional Sliding Mode Control (SMC) and an Integral Sliding Mode Control (ISMC), is designed to control the linear motion stage. The control is switched between SMC and IMSC based on the error threshold. To eliminate the chattering, a smooth function is adopted instead of a signum function. The experimental results with the floating stator show that the positioning accuracy and tracking performance of the linear motion stage are improved with the MMSMC approach.

Robust and fast non‐singular terminal sliding mode control for piezoelectric actuators

Piezoelectric actuators (PEAs) are essential elements in many systems that require high precision and accuracy. However, the difficulty with the use of PEAs is their actuator uncertainties including the highly non-linear behaviour which is a consequence of the hysteresis property inherently within PEAs. Therefore, a robust control system is essential for such actuators. This study proposes a systematic control method that utilises a fast non-singular terminal sliding mode (FNTSM) for PEAs. Unlike the conventional sliding mode (CSM), the FNTSM control method is characterised by chatter free. Besides, a zero error convergence can be guaranteed in finite time in the presence of disturbance and system uncertainties. The design of the FNTSM control is based on the bounded information of parametric uncertainties. The feedback velocity is provided for the FNTSM controller by using the a model-free velocity estimator. Theoretical analysis and experimental results reveal that the FNTSM controller can achieve faster and higher precision performance in comparison with either a CSM or a linear controller.

Improvement of Conventional Sliding Mode Observer for Full Range Sensorless Control of a PMSM

This paper investigates some strategies to overcome the chattering problem of the conventional sliding mode observer (SMO) and to improve the rotor position estimation performance for full range sensorless control of a PMSM. An adaptive observer gain based on the Lyapunov's stability criterion and a cascade low pass filter with advanced phase delay compensation were proposed to reduce the chattering problem and to strengthen the filtering capability of the SMO. Several cases studies through experiments were carried out to confirm conventional SMO's problems and effectiveness of the proposed strategies. The experimental results show that the proposed method gives precise estimation on speed and rotor position when the motor rotates on 2% of its rated speed.

Control of fuel cell-based electric power system using adaptive sliding mode control and observation techniques

The paper deals with controlling an autonomous electric power system that comprises of a primary source of power supply, Proton Exchange Membrane fuel cell (PEMFC), DC–DC boost power converter as a power conditioner, and the ultracapacitor for an auxiliary power supply. Relative degree approach is applied for direct control of the output load voltage as well as the fuel cell and ultracapacitor current in the presence of the model uncertainties. The zero dynamics of the studied electric power system is analyzed and appeared to be stable. The non-minimum phase property of the DC–DC boost converter is eliminated by controlling the fuel cell current based on the power balance. The adaptive super-twisting sliding mode observer is employed for identification of the load resistance, which estimated value is used for generating the fuel cell current command profile. The adaptive gain second order (2-SM) super-twisting sliding mode controller is proposed for controlling the current in PEMFC. The conventional Sliding Mode Controllers (SMC) is designed for controlling the output voltage of the converter and the load current of the ultracapacitor. The efficacy and robustness of the proposed decentralized three-fold electric power system controller that consists of two SMCs and one 2-SM adaptive-gain controller are confirmed via computer simulations.