Discrete-time Sliding Mode Control Research Articles

A compressive study on discrete time sliding mode control with advances and applications

In this paper, a compressive study on state space approach of discrete time sliding mode control (DTSMC) for various applications has been discussed. The design of the robust DTSMC reaching/sliding manifold is a key steps which is studied in this paper, and performance of each of the approaches have been included. The aim of this paper is in two folds. First, compressive studies of DTSMC reaching laws and control strategies are included. Second, advances in the development of DTSMC techniques are discussed. The reaching laws and control laws formulation as well as advantages and applications of DTSMC in various fields are also included. The comparative study and simulation of a typical system are carried out with prevalent DTSMC techniques and its modified laws to analyse the effects on the system states and control signal.

A compressive study on discrete time sliding mode control with advances and applications

A compressive study on discrete time sliding mode control with advances and applications

A Nonlinear Discrete-Time Sliding Mode Controller for Autonomous Navigation of an Aerial Vehicle Using Hector SLAM

In this paper, a discrete-time sliding mode controller (DTSMC) is designed for full position and attitude control of a quadrotor UAV. The aim of this study is to design a controller suitable for practical implementation on an autonomous quadrotor for remote sensing in the hostile nuclear environments. A nested DTSMC is developed and compared against two continuous-time sliding mode control methods; classical SMC as well as a chattering-free SMC (CFSMC) studied in the previous works. The performance of the controllers are evaluated in combination with the Hector SLAM algorithm for localisation in GPS denied environments. For this purpose, MATLAB in combination with the Robotic Operating System (ROS) are used to develop the controllers. Control signals are sent from MATLAB to the Gazebo simulation environment in ROS, which simulates the quadrotor and runs the Hector SLAM algorithm.

Robust Formation Control and Trajectory Tracking of Multiple Quadrotors Using a Discrete-Time Sliding Mode Control Technique

In this paper, a centralised robust discrete-time sliding mode controller is proposed for the formation control of a multi-quadrotor system in the presence of disturbances. The control system, based on consensus control, is designed around the full, nonlinear, under actuated dynamics of the quadrotor. Graph theory is used to define the communication topology of the multi-agent system. Results obtained through simulation in MATLAB and Simulink are used to verify the control system.

Disturbance Compensation Based Discrete-time Sliding Mode Control with a Reference Trajectory Generator

Disturbance Compensation Based Discrete-time Sliding Mode Control with a Reference Trajectory Generator

Discrete-time sliding mode controller based on backstepping disturbance compensation for robust current control of PMSM drives

A robust current control approach with disturbance cross-coupling compensation for permanent magnet synchronous motor drives (PMSM) is proposed in this paper. The proposed approach can enhance the reference tracking and provides a robust option for current control of PMSM drives. A discrete-time sliding mode current controller is proposed. The PMSM model includes the digital implementation delay, present due to the discrete-time algorithm execution. A discrete-time backstepping disturbance observer is developed, being combined to the sliding mode controller as a means to improve the robustness and tracking capability. The effects of coupling, parametric uncertainties and load disturbances are compensated by the backstepping disturbance observer. The stability analysis of the combined system is presented and the limits for overall system stability are discussed. Simulations and experimental results validate the combined scheme and demonstrate the good performance of the proposal.

Control of a Digital Galvanometer Scanner Using a Discrete-Time Sliding-Mode Variable-Structure Controller Based on a Decoupled Disturbance Compensator

Laser processing plays an important role in industrial manufacturing, in which a galvanometer scanner (GS) functions as the core component of the laser processing equipment. With the development of the digital system, the GS based on the digital system finds a broader range of potential application. In order to address the slow step-responses of a GS with disturbance and parameter perturbation, the mathematical model of the motor of the GS is derived and a discrete-time sliding-mode variable-structure controller (DSVC) based on a decoupled disturbance compensator (DDC) (DSVC+DDC) is designed. The step-response performance of a GS is the key factor affecting the quality evaluation of laser processing. Experiments are conducted on the step responses of the motor of the GS on a digital experimental platform. The experiment results show that when guaranteeing a steady-state error within 20 urad and an overshoot of less than 5%, the rise time for step-responses in 1% and 10% of the whole stroke is 1 and 2 ms, decreasing by 23% and 58% compared with the reference performance index, which indicates the effectiveness of the proposed method. The proposed approach can not only compensate for the external disturbance online and improve the step-response speed of the GS, but also relax the traditionally assumed limit of the upper bound of external disturbance to the limit of the change rate of external disturbance, which reduces the difficulty of a practical application. This method has great significance for further applications in high precision machining.

A Fast Converging Hybrid MPPT Algorithm Based on ABC and P&O Techniques for a Partially Shaded PV System

Among all the conventional maximum power point tracking (MPPT) techniques for a photovoltaic (PV) system that have been proposed, incremental conductance (INC) and perturb and observe (P&O) are the most popular because of their simplicity and ease of implementation. However, under partial shading conditions (PSCs), these MPPT algorithms fail to track the global maximum power point (GMPP) and instead converge into local maximum power points (LMPPs), resulting in considerable PV power loss. This paper presents a new hybrid MPPT technique combining the artificial bee colony (ABC) and P&O algorithms named ABC-P&O. The P&O technique is used to track the MPP under uniform irradiance, and only during irradiance variations is the ABC algorithm employed. The effectiveness of the proposed hybrid algorithm at tracking the GMPP, under both uniform and nonuniform irradiance conditions, was assessed by hardware-in-the-loop (HIL) tests employed by a dc–dc boost converter. Then, the ABC-P&O strategy was applied to obtain the voltage reference for the outer PI control loop, which provided the current reference to the discrete-time sliding-mode current control. The ABC-P&O algorithm has a reasonable computational cost, allowing the use of a commercial, low-priced digital signal controller (DSC) with outer voltage and inner current control loops. Many challenging tests validated that the proposed ABC-P&O technique converges fast to the GMPP with high efficiency and superior performance under different PSCs.

Observer-based discrete-time sliding mode control for systems with unmatched uncertainties

This paper addresses an observer-based sliding mode control (SMC) approach for discrete-time systems with unmatched uncertainties. A modified sliding surface based on disturbance estimation and a sliding mode controller are designed to counteract with the unmatched disturbance. The proposed method exhibits the following three features. First, the hyperplane matrix is designed in a simple way based on the discrete-time Riccati equation. Second, a chattering-free SMC method is utilized. Third, the proposed approach retains the nominal performance of the system. The stability of the overall system is achieved and simulation results are presented to verify the effectiveness of the proposed method.

Input-decoupled discrete-time sliding mode control algorithm for servo multi-field multi-armature DC machine

The multivariable modeling of a servo actuating system consisting of multi-field multi-armature direct current (MFMADC) machine is extracted and a novel discrete time nonlinear algorithm is proposed for the corresponding system. The proposed control algorithm demonstrates robustness against modeling uncertainty and by utilizing its novel mathematical structure, decouples the dynamical interactions of the connected motors. The main contribution of this paper is the proposition of a new decoupling control algorithm that in which, the driving (commanding) voltages of the connected driving motors are extracted separately and independently using the Lyapunov principle in discrete time. In fact, the obtained coupled stabilizing convex inequalities of the controlling voltages, resulting from the evaluation of the Lyapunov functions, are analytically decoupled using elementary matrix operations. Consequently, each motor now has the capability to perform its controlling task (position control or torque control) with asymptotic stability and robustness against uncertainty. To assess the performance of the proposed controlling algorithm and its verification, a MFMADC machine is attached to a harmonic drive reducer (HDR) whose flex spline and circular spline are fabricated using viscoelastic polyesters PLA and thermoplastic PLA, respectively. A number of experiments are conducted where in the first test, the MFMADC is controlled in only-position mode while in the second test, the MFMADC is controlled in simultaneous position-torque control mode. Comparative assessments confirm that the MFMADC technology is needed when a high precision tracking of position, under high frequency disturbances, is desired.

A Bidirectional Versatile Buck-Boost Converter Driver for Electric Vehicle Applications.

This work presents a novel dc-dc bidirectional buck–boost converter between a battery pack and the inverter to regulate the dc-bus in an electric vehicle (EV) powertrain. The converter is based on the versatile buck–boost converter, which has shown an excellent performance in different fuel cell systems operating in low-voltage and hard-switching applications. Therefore, extending this converter to higher voltage applications such as the EV is a challenging task reported in this work. A high-efficiency step-up/step-down versatile converter can improve the EV powertrain efficiency for an extended range of electric motor (EM) speeds, comprising urban and highway driving cycles while allowing the operation under motoring and regeneration (regenerative brake) conditions. DC-bus voltage regulation is implemented using a digital two-loop control strategy. The inner feedback loop is based on the discrete-time sliding-mode current control (DSMCC) strategy, and for the outer feedback loop, a proportional-integral (PI) control is employed. Both digital control loops and the necessary transition mode strategy are implemented using a digital signal controller TMS320F28377S. The theoretical analysis has been validated on a 400 V kW prototype and tested through simulation and an EV powertrain system testing.

Dynamics of the Vibration System Driven by Three Homodromy Eccentric Rotors Using Control Synchronization

To solve the limitation of vibration synchronization, this paper investigates the dynamics of a vibration system driven by three homodromy eccentric rotors (ERs) using control synchronization. According to the synchronous condition and the stability condition, the changes of the phase differences of the three-ERs system and the two-third ERs system are obtained. Based on the electromechanical mathematic model of the vibration system and the master-slave control strategy, the synchronous target that three ERs achieve the same phase motion is converted into velocity and phase tracking of ERs. Considering the coupling characteristic of the self-adjusting of the system in the state of vibration synchronization, the velocity and phase controllers are designed by employing discrete-time sliding mode control. An experimental system for control synchronization is designed, including hardware composition and software programming. For the feedback signal used to match control targets, a method of calculating velocity and the phase difference is proposed from engineering. Recording the rotational velocities, phase differences, and system response, three group experiments with different control schemes are achieved. According to the experimental data, the coupling characteristic of the vibration system adopting control synchronization is analyzed, which can provide the basis for designing vibration machines using control synchronization.

Discrete-Time Sliding Mode Control Coupled with Asynchronous Sensor Fusion for Rigid-Link Flexible-Joint Manipulators

This paper proposes a novel discrete-time terminal sliding mode controller (DTSMC) coupled with an asynchronous multirate sensor fusion estimator for rigid-link flexible-joint (RLFJ) manipulator tracking control. A camera is employed as external sensors to observe the RLFJ manipulator’s state which cannot be directly obtained from the encoders since gear mechanisms or flexible joints exist. The extended Kalman filter- (EKF-) based asynchronous multirate sensor fusion method deals with the slow sampling rate and the latency of camera by using motor encoders to cover the missing information between two visual samples. In the proposed control scheme, a novel sliding mode surface is presented by taking advantage of both the estimation error and tracking error. It is proved that the proposed controller achieves convergence results for tracking control in the theoretical derivation. Simulation and experimental studies are included to validate the effectiveness of the proposed approach.

A Novel Variable Exponential Discrete Time Sliding Mode Reaching Law

A new variable exponential discrete-time sliding mode control (DSMC) reaching law is proposed to suppress the chattering phenomenon and accelerate the reaching speed for the switching function. The variable exponential reaching law consists of two-phase different exponential term. The main effect of the first phase exponential reaching law is to reduce reaching steps. The second phase exponential reaching law can decrease the magnitude of quasi-sliding-mode domain (QSMD). Otherwise, the disturbance term is restrained by second order difference function which can also significantly diminish the range of QSMD. The reaching steps of the reaching law to converge to QSMD are derived from this new reaching law. Meanwhile, the dynamic analysis of the DSMC system based on new reaching law is presented. Finally, the mathematical simulations are conducted to preliminarily verify the results of theoretical analysis.

Reduced-order disturbance observer-based adaptive reaching law control for discretized MIMO systems with unmatched uncertainties

In this paper, an adaptive discrete-time sliding mode control based on reduced-order disturbance observer is proposed for discretized multi-input multi-output systems subjected to unmatching condition. By using the designed discrete reduced-order disturbance observer, a new sliding surface is constructed to counteract the unmatched uncertainties. Then, to guarantee a smaller width of the quasi-sliding mode domain, an adaptive reaching law is developed, whose switching gain is adaptively tuned to prevent overestimation of disturbance on the premise of ensuring the reaching condition of sliding surface; meanwhile, the ranges of the quasi-sliding mode band and attractiveness region are deduced. The proposed control algorithm has low computational complexity and needs no information about the upper bound of unmatched uncertainty. The simulations on the control of a bank-to-turn missile demonstrates that the proposed method can effectively reject unmatched disturbance and provide higher accuracy in comparison with traditional methods.

A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties

This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (lmis). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (auv). The simulation results demonstrate the effectiveness of the proposed controller.

Unified Approach for Robust Stability Analysis of Buck Converters with Discrete-Time Sliding Mode Control

This paper proposes a novel discrete-time sliding mode (DTSM) control approach to address the robust stability problem of buck converters with multiple disturbances. The contributions lie in the “unified” modelling and controller design. In modelling, all the possible model uncertainties and external disturbances are considered and further classified into two cases. It can also be extended to the situations with individual/several disturbances. While for the controller design, differing from the traditional DTSM based on the nominal model, the disturbances are directly introduced in the process, giving the robust stability condition and four new regulation subranges. It is suitable for both nominal and perturbed systems. Finally, the influences of the sampling time and disturbances on the control performance are investigated. Simulations and experiments confirm the benefits of the unified approach with greater accuracy and wider applications.

Composite chattering-free discrete-time sliding mode controller design for active front steering system of electric vehicles

Composite chattering-free discrete-time sliding mode controller design for active front steering system of electric vehicles

Hybrid H-infinity synchronization for uncertain continuous chaotic systems based on digital redesign approach

In this paper, the design of hybrid H-infinity synchronization control for continuous chaotic systems based on sliding mode control (SMC) is considered. H-infinity discrete sliding mode controllers integrated with the digital redesign approach are newly designed to achieve robust chaos synchronization. By the proposed design procedure, an H-infinity discrete-time SMC can be easily obtained to guarantee the robustness of synchronization even if the system is disturbed with unmatched perturbations. Besides, since the saturation function is adopted to eliminate the unexpected chattering phenomenon, this paper also discusses the effect of saturation function in multi-input multi-output (MIMO) SMC and the upper bounds of sliding mode trajectories are obtained which is not indicated in the literature. Finally, we perform the simulation to verify the effectiveness of the proposed controller.

Decoupled error dynamics design for discrete-time sliding mode control in industrial servo systems under control input saturation and disturbance

This paper presents a design framework for the discrete-time Sliding mode control with Decoupled disturbance compensator and Auxiliary state (SDA) method in industrial servo applications. In particular, the discrete-time SDA method is formulated to provide an excellent tracking performance even in the presence of control input saturation and disturbance. Moreover, it preserves the separation principle of the sliding mode dynamics and the disturbance estimation error dynamics of the original discrete-time Sliding Mode Control (SMC) with Decoupled Disturbance Compensator (DDC) method. However, it can be problematic due to the unpredictable transients in the error states under control input saturation. This paper investigates the error dynamics of discrete-time SDA after a transition from a saturated region to an unsaturated region, which is called the decoupled error dynamics. The decoupled error dynamics can be designed by shaping a “hidden” sliding manifold which is activated only after the transition. Based on the analysis, a systematical design methodology for the decoupled error dynamics is proposed, which prevents the recurrence of the control input saturation and provides fast convergence of the error states. The effectiveness of the proposed design methodology is shown experimentally using an industrial linear motor system.