Discrete Sliding Mode Control Research Articles

An Adaptive Discrete Integral Terminal Sliding Mode Control Method for a Two-Joint Manipulator

In response to the trajectory tracking control problem of manipulators under measurement disturbances, a novel multi-input multi-output discrete integral terminal sliding mode control scheme is proposed. Initially, this scheme establishes a dynamic model of a two-joint manipulator based on the Lagrangian dynamics analysis method. Subsequently, a discrete integral terminal sliding mode control law based on the dynamic model of the two joints is designed, incorporating delayed estimation of unknown disturbances and discretization errors in the manipulator system. To enhance the trajectory tracking accuracy of the control scheme and suppress the impact of sliding mode chattering on the manipulator system, an adaptive switching term is introduced into the discrete integral terminal sliding mode control law. The paper derives an adaptive discrete integral terminal sliding mode control scheme and provides stability proof for the proposed approach. Simulation experiments are conducted to compare the proposed adaptive discrete integral terminal sliding mode control scheme with classical discrete sliding mode control schemes and discrete integral terminal sliding mode control schemes. The simulation results demonstrate that the designed adaptive discrete integral terminal sliding mode control scheme maintains trajectory tracking errors within 0.004 radians for each joint of the manipulator, with minimal changes in control torque for each joint. The absolute integral of the control torque variations is calculated at 5.85×103, which is lower than other control schemes, thereby validating the effectiveness and superiority of the proposed approach.

Adaptive Set-Membership Filter Based Discrete Sliding Mode Control for Pneumatic Artificial Muscle Systems With Hardware Experiments

Pneumatic artificial muscle (PAM), featuring good flexibility and safety, has been widely used in rehabilitation and bionic robots. However, the complex hysteretic nonlinearities and uncertainties of the PAM cause great difficulties and challenges to the accurate modeling and controller design, especially when confronted with unknown external disturbances in applications. This paper proposes a robust control strategy with disturbance compensation for the hysteresis compensation and trajectory tracking of PAMs. Considering the high hysteretic nonlinearity of the PAM, a modified Prandtl-Ishlinskii model is used as a feedforward hysteresis compensator. For the linearized system, adaptive set-membership filtering (ASMF) is used to estimate the nonlinear terms and external disturbances of the overall system. A sliding mode controller (SMC) with disturbance compensation is designed and cascaded to the feedforward hysteresis compensator in series. The stability of the closed-loop system is theoretically proved. The proposed method guarantees that the tracking error of the PAM system is bounded. Finally, the effectiveness and robustness of the proposed controller are verified via a series of experiments on an in-house built testbench for PAMs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —With the increasing demand on human-robot interaction, the safety and compliance of robots have become one key requirement. PAM is a compliant actuator, exhibiting good flexibility, safety, and clean energy. PAM is widely used in rehabilitation robots, whereas its strong hysteresis nonlinearity and sensitivity to external disturbances affect its motion accuracy. This paper proposes an ASMF-based discrete SMC, which uses an inverse hysteresis model to compensate for the strong hysteresis of the PAM and uses ASMF to estimate the lumped disturbance of the system. Compared with the other filters, ASMF is unique in that its estimation error is bounded, which is very useful in the stability proof of the overall system. The effectiveness of the proposed controller is experimentally verified. Experimental results show that PAM’s hysteresis can be efficiently compensated, and the influence of external disturbances can be attenuated by the proposed controller, resulting in improved motion accuracy and robustness. In future work, efforts will be directed towards the modeling and control of PAMs in multi-DOF robots.

Research on optimization of supply chain inventory system under contingency conditions

A solution combining state observer (SOB) with Discrete Sliding Mode Control (DSMC) is presented to solve the problem of inventory shortage or backlog in upstream and downstream enterprises of the supply chain caused by contingency conditions. Firstly, based on the specific sales mode of the supply chain system and the logical relationship of inventory parameters, the corresponding dynamic model of the inventory system is established under reasonable assumptions, and relevant parameters are introduced to represent the impact of contingencies, and the dynamic model of inventory system under contingencies is established with the bullwhip effect. Then, the discrete sliding mode control (SOB-DSMC) based on the state observer is designed to compensate for the impact of emergencies on the supply chain inventory system adaptively while ensuring the stability of the system. Finally, based on market research and reasonable assumptions, simulation experiments are carried out. The simulation results show that the designed control system can better cope with emergencies in different situations, and can significantly improve the supply chain within 5 days after emergencies occur. The inventory situation of upstream and downstream enterprises in the system has reduced the maximum inventory fluctuations of manufacturers, distributors, and retailers by 77.13%, 60.67%, and 44.61% respectively, and fully restored to normal operation within 20 days, effectively solving the inventory backlog of upstream and downstream enterprises in the supply chain and out-of-stock issues. It can be seen that the SOB-DSMC method can guide the upstream enterprises in the supply chain to formulate reasonable production, shipping, and purchasing strategies, and provide theoretical reference and coping methods for the supply chain system to smoothly survive emergencies.

Discrete control for state of charge balance in DC microgrids considering the disturbance of photovoltaics

This study examines State of Charge (SoC) balancing control in DC microgrids subject to photovoltaic (PV) fluctuations, aiming to optimize power distribution in energy storage systems influenced by PV disturbances. The proposed approach enhances both the lifespan of storage systems and microgrid stability. To mitigate voltage variation due to PV perturbation, the paper introduces an adjustment in droop control offset. Additionally, it presents a novel discrete Sliding Mode Controller (SMC) characterized by reduced parameter sensitivity, thus enhancing control responsiveness. A SoC balancing control strategy employing sliding mode control is developed to equalize SoC levels across Battery Energy Storage Systems during both charge and discharge cycles. The stability of this strategy is substantiated through the construction of a Lyapunov function. Simulations conducted in a distributed DC microgrid environment using Simulink/SimPower Systems demonstrate the efficacy of the discrete SMC and the SoC balancing algorithm, achieving uniform SoC in energy storage nodes during operation, with improved robustness against PV perturbations.

Discrete sliding mode control based on a new fractional order power reaching law

This paper presents a robust controller design for a discrete linear system, dealing with internal and external disturbances. The main focus is to reduce chattering, minimize undesirable oscillations, and enhance robustness against disturbances using a new discrete sliding mode control. The novel approach involves replacing the classical Gao’s reaching law with a fractional order reaching law based on the Grunwald–Letnikov definition, leading to advantages like a simplified algorithm and improved performance against disturbances. The performances of the suggested method are evaluated through two simulation examples.

Disturbance-observer-based discrete-time sliding mode predictive control for overhead cranes with matched and unmatched disturbances

In actual working environments, underactuated overhead cranes are susceptible to the adverse effects of the mechanical friction, uncertain parameters, and other disturbances. In particular, if the payload is disturbed (i.e. the unmatched disturbance), unpredictable swings would occur. Therefore, a discrete time sliding mode predictive control for overhead cranes based on a disturbance observer is proposed. Specifically, to eliminate uncertain disturbances, we propose a disturbance observer to estimate and compensate the disturbance to the input channel. Then, a new discrete sliding mode control law is obtained by adding the disturbance error estimator to the discrete sliding mode surface. In order to reduce the chattering inherent in the sliding mode, we integrate the discrete sliding mode law into the model predictive control, and use the rolling optimization and feedback correction of the predictive control, and finally output the optimal control law to act on the system. This control method can not only further improve the control accuracy, but also has sufficient robustness. Simulation and robustness experiments under various conditions verify the effectiveness of the proposed controller.

High-Performance Flux Tracking Controller for Reluctance Actuator

To meet the ever-increasing demand for next-generation lithography machines, the actuator plays an important role in the achievement of high acceleration of the wafer stage. However, the voice coil motor, which is widely used in high-precision positioning systems, is reaching its physical limits. To tackle this problem, a novel way to design the actuator using the magnetoresistance effect is argued due to the high force densities. However, the strong nonlinearity limits its application in the nan-positioning system. In particular, the hysteresis is coupled with eddy effects and displacement, which lead to a rate-dependent and displacement-dependent hysteresis effect in the reluctance actuator. In this paper, a Hammerstein structure is used to model the rate-dependent reluctance actuator. At the same time, the displacement-dependent of the model is regarded as the interference with the system. Additionally, a control strategy combining inverse model compensation and the disturbance observer-based discrete sliding mode control was proposed, which can effectively suppress the hysteresis effect. It is worthy pointing out that the nonlinear system is transformed into a linear system with inversion bias and disturbance by the inverse model compensation. What is more, the sliding mode controller based on the disturbance observer is designed to deal with the unmodeled dynamics, displacement disturbances, and model identification errors in linear systems. Thus, the tracking performance and robustness to external disturbances of the system are improved. The simulation results show that it is superior to the PI controller combined with an inverse compensator and even to the discrete sliding mode controller connected with inverse compensator, confirming the effectiveness of the novel control method in alleviating hysteresis.

Robust discrete sliding mode controller design for a single-phase onboard integrated electric vehicle charger with disturbance estimation

A new sliding mode controller (SMC) design is proposed for a single-phase current source rectifier (CSR) integrated into onboard electric vehicle (EV) chargers. The controller's design aims to reduce the impact of varying grid impedance on the CSR's performance by using a disturbance estimator. The proposed method utilizes the Lagrange extrapolation technique for disturbance estimation, which accurately estimates disturbances caused by changes in the grid impedance. The precise state-space equation provided by the disturbance estimator is essential for designing the SMC, which can effectively handle mismatched disturbances. To mitigate the impact of the capacitor inductance filter's resonance frequency, a virtual parallel resistance with the capacitor is used, reducing the resonance amplitude. The proposed controller also controls the power factor to ensure the capacitor voltage and grid current are in phase. Simulation and experimental results demonstrate that the proposed method achieves stability and meets the harmonic content limitations of the IEC61000–3–2 standard. The total harmonic distortion (THD) is also kept below 5% despite changes in the grid impedance, demonstrating the effectiveness of the proposed method in handling varying grid conditions.

Finite-time trajectory tracking control of dynamic positioning ship based on discrete-time sliding mode with decoupled sampling period

In this paper, the finite-time trajectory tracking control problem of a dynamic positioning ship with model uncertainty and time-varying environmental disturbances is investigated based on the discrete-time sliding mode with decoupled sampling period. To overcome the influence of the sampling period variation on the system’s control effect, a finite-time discrete sliding mode controller with decoupled sampling period is designed based on the new discrete-time adaptive fast power reaching law. The sampling period condition that guarantees the finite-time convergence of the system is given. A new finite-time high-order discrete disturbance observer is proposed to estimate model uncertainty and environmental disturbance, which reduces the dependence of the observer’s estimation accuracy on the sampling period. To realize the transformation from position tracking to velocity tracking in a finite time, a new finite-time discrete virtual velocity controller is designed. The proposed control strategy decouples the sampling period and enables the finite-time trajectory tracking control of the dynamic positioning ship over a wider sampling period range. The stability analysis demonstrates that all tracking errors of the closed-loop system can converge to a small domain near zero in a finite time. Two simulation examples verify the effectiveness of the proposed control method.

Discrete sliding mode control method for particle swarm optimization-based brushless DC motor of electric vehicle

Brushless DC motor (BLDCM) is a multivariable nonlinear time-varying system, which is difficult to control. The discrete sliding mode control method for BLDCM of electric vehicle on the basis of particle swarm optimization (PSO) is studied to improve the application of BLDCM in electric vehicle. The mathematical model of BLDCM of electric vehicle is established using the state formula. Based on the mathematical model of BLDCM, through the analysis of electromagnetic torque control of BLDCM, it is clear that controlling the angle between rotor flux and stator flux can accurately control the electromagnetic torque of BLDCM. The adaptive discrete sliding mode controller (SMC) is set to control the electromagnetic torque of BLDCM of electric vehicle, and the PSO algorithm is adopted to obtain the optimal parameters of the adaptive discrete SMC to realize the discrete sliding mode control of BLDCM of electric vehicle. According to experimental results, the proposed method can achieve the accurate control of torque and speed of BLDCM of electric vehicle, and increase the application of BLDCM in electric vehicle.

Discrete Multi-Objective Switching Topology Sliding Mode Control of Connected Autonomous Vehicles With Packet Loss

Information flow topology is crucial in the control of connected autonomous vehicles. It has a substantial influence on the platoon's performance, especially in scenarios with imperfect communication. To address this issue, this study provides a real-time switching topology technique for improving the platoon's performance under various types of imperfect communication situations and constant packet dropout rates. First, a discrete sliding mode controller with a double power reaching law is designed for a nonlinear heterogeneous vehicle dynamic model with packet loss. Then, Lyapunov analysis is applied to ensure the platoon's stability and string stability. Finally, a two-step switching topology framework is introduced. The first step is to design an offline Pareto optimal topology search with some predicted imperfect communication scenarios, where the platoon's tracking ability, fuel consumption, and driving comfort are optimised using a multi-objective evolutionary algorithm based on decomposition with two opposing adaptive mechanisms. In the second step, the optimal topology is switched and selected in real-time from among the previously acquired Pareto optimal topology candidates, to reduce the control cost. To validate the proposed approach, numerical simulations are conducted. According to the results, compared to a standard robust sliding mode controller, the suggested technique enhances platoon tracking ability by 97.73 percent, fuel efficiency by 9.96 percent, and driving comfort by 20.18 percent, respectively.

Chassis Coordinated Control for Full X-by-Wire Four-Wheel-Independent-Drive Electric Vehicles

In this paper, a full X-by-wire chassis coordination control scheme is proposed by synthetically utilizing the Direct Yaw-moment Control, Active Front Steering, Anti-Slip Regulation and Active Roll Control to improve the longitudinal, yaw and roll stability. First, a vehicle state prediction module is established to predict vehicle yaw and roll stability and to generate three reference vehicle states, i.e., the desired roll angle, yaw rate and longitudinal velocity. Then, a decentralized event-triggered discrete sliding mode control scheme is developed to track these reference states by coordinating the X-by-wire subsystems based on their respective effective working areas. For yaw rate control, dynamic torque regulation factors are introduced to prevent wheel slip and lock-up based on real-time slip ratio feedback. Under longitudinal driving conditions, a robust sliding mode control and a hybrid control-based method are used under emergency acceleration or braking conditions. The hardware-in-the-loop (HIL) tests under the slalom, double lane change and fish hook tests show that the proposed chassis coordinated control scheme can comprehensively improve vehicle ride comfort, handling performance, longitudinal and lateral stability, and rollover prevention ability.

Trajectory tracking control of upper limb rehabilitation robot based on optimal discrete sliding mode control

In this paper, an optimal sliding mode control method for trajectory tracking of discrete-time systems based on linear quadratic regulator is proposed to improve the trajectory tracking control accuracy and robustness of upper limb rehabilitation robot under the condition of highly nonlinearities, external disturbances, and unmodeled dynamics. Firstly, considering the uncertainty of the mass and moment of inertia of the connecting rod arm of the upper limb rehabilitation robot and the uncertainty of external interference, the dynamic model of the upper limb rehabilitation robot is established by using the Euler Lagrange method, and the linear time-varying state equation of the rehabilitation robot system under the influence of both nonlinear and uncertain factors is derived. Secondly, directing at the chattering problem in sliding mode control, a sliding mode control method based on a new discrete time reaching law is designed to reduce the amplitude of chattering in the control input signal of the upper limb rehabilitation robot system and improve the tracking speed. Furthermore, combined with linear quadratic optimal control, the optimal discrete integral sliding mode control law (LQRSMC) is finally obtained. Meanwhile, for the sake of reducing the influence of the uncertain signal on the system, a robust control law is adopted to estimate and compensate the uncertain interference. The stability of the upper limb rehabilitation robot system is verified by the sliding mode approach condition of the discrete system. Finally, the genetic algorithm is used to further optimize the weighted value, and MATLAB/Simulink is used to simulate the state trajectory of the upper limb rehabilitation robot under various weighted values. The control strategy can not only effectively weaken the trajectory tracking oscillation problem of the upper limb rehabilitation robot, but also overcome the external disturbance and modeling uncertainty, while ensuring the robustness of the rehabilitation robot system.

Distributed resilient multi-event cooperative triggered mechanism based discrete sliding-mode control for wind-integrated power systems under denial of service attacks

In wind-integrated power systems (WIPSs), denial of service (DoS) attacks bring about time delays and packages dropout in system data transmission, it may even deteriorate system performance. In order to maintain the reliability and safety of WIPSs, under the dynamical event triggered framework, a novel distributed resilient multi-event cooperative triggered scheme is derived to decrease the occupation of network channel. Furthermore, considering the random load disturbance of WIPSs and wind speed fluctuation, the resilient triggered scheme based H∞ load frequency sliding-mode control strategy is proposed. Based on Lyapunov stability theory, the controller is obtained by solving linear matrix inequality. Compared with the traditional event triggered mechanism, the proposed distributed resilient multi-event cooperative triggered mechanism based sliding-mode controller provides stronger robustness, higher wind energy capture efficiency for WIPSs under DoS attacks. Meanwhile, the resilient triggered scheme improves the utilization efficiency of network resources. A four-area WIPSs is investigated and the numerical analysis shows the proposed strategy is feasibility and effectiveness.

Novel disturbance estimation for robust discrete sliding mode control of DC/DC buck converter with approximate reduced order model

Novel disturbance estimation for robust discrete sliding mode control of DC/DC buck converter with approximate reduced order model

Novel disturbance estimation for robust discrete sliding mode control of DC/DC buck converter with approximate reduced order model

Novel disturbance estimation for robust discrete sliding mode control of DC/DC buck converter with approximate reduced order model

Human gait tracking for rehabilitation exoskeleton: adaptive fractional order sliding mode control approach

To improve the rehabilitation training effect of hemiplegic patients, in this paper, a discrete adaptive fractional order fast terminal sliding mode control approach is proposed for the lower limb exoskeleton system to implement high-precision human gait tracking tasks. Firstly, a discrete dynamic model is established based on the Lagrange system discretization criterion for the lower limb exoskeleton robot. Then, in order to design a discrete adaptive fractional order fast terminal sliding mode controller, the Grünwald–Letnikov fractional order operator is introduced to combine with fast terminal attractor to construct a fractional order fast terminal sliding surface. An adaptive parameter adjustment strategy is proposed for the reaching law of sliding mode control, which drives the sliding mode to the stable region dynamically. Moreover, the stability of the control system is proved in the sense of Lyapunov, and the guidelines for selecting the control parameters are given. Finally, the simulations are tested on the MATLAB-Opensim co-simulation platform. Compared with the conventional discrete sliding mode control and discrete fast terminal sliding mode control, the results verify the superiority of the proposed method in improving lower limb rehabilitation training.

Data-Driven Model-Free Adaptive Sliding Mode Control Based on FFDL for Electric Multiple Units

The electric multiple units (EMUs) have become a very convenient and powerful means of transportation in our daily life. Safe and punctual trajectory tracking control is the key to improve the performance of the EMUs system, but it is difficult to realize due to the influence of environmental uncertainty, coupling and nonlinearity. In this paper, a model-free adaptive sliding mode control (MFASMC) method is proposed for the EMUs. This method can solve the dependence of the model-based control method on the train model and eliminate the influence of external disturbances on the robust performance of the system. In this method, the running process of the EMUs is equivalent to a full format dynamic linearization (FFDL) data model, and a model-free adaptive controller (MFAC) is designed based on the data model. Then, to reduce the influence of measurement disturbance and improve the robustness of the system, a discrete sliding mode control (SMC) algorithm is introduced. Furthermore, to prevent the control input from being too large, the parameter estimation error is introduced as an additional correction term of the algorithm. In the end, the simulation experiment is carried out with CRH380A EMUs as the object. Compared with the traditional MFAC and the traditional SMC, the speed tracking effect of each power unit of the MFASMC algorithm is more effective, the change of control force is stable, the acceleration meets the requirements of driving, and has a strong inhibitory effect on external disturbances.

Genetic algorithm tuned adaptive discrete-time sliding mode controller for grid-connected inverter with an LCL filter

The development of a two-stage cascaded control strategy for a single-phase grid-connected inverter with an LCL filter based on inverter-side current is proposed. The main objective of the proposed controller is to minimize both the grid current tracking error and the current total harmonic distortion and to overcome the system resonance introduced because of the third-order LCL filter. In the first part, a feed-forward controller calculates the reference values for the system states at the steady-state operation with no external disturbance. In contrast, an adaptive discrete-time sliding mode controller is used for disturbance rejection caused by parameter uncertainties in the second stage. The proposed control approach also considers the nonlinear behavior of the pulsed nature of the inverter’s hard switching pulse width modulation modulator. The grid-side current is taken as in-phase to the grid voltage for the inverter-side reference values calculation. Numerical simulation and experimental tests were performed to validate the proposed control strategy’s faster dynamic response under external disturbances and parametric uncertainties. An improvement of approximately 18% in THD was recorded against the variation of grid-side impedance ranging from 50%–150% over the conventional discrete sliding mode control These results demonstrate the robustness and effectiveness of the proposed controller to integrate the solar photovoltaic energy sources seamlessly.

Model Predictive Control – Sliding Mode Control of a pH system

This paper studies the feasibility of using discrete sliding mode controller (SMC) to achieve offset-free control of nonlinear processes in the presence of disturbances. The performance of the SMC is compared to a multiple model predictive controller (MMPC) studying the ability of set-point tracking using the pH system as a case study. The results presented from the comparison show that SMC can perform offset-free control of a pH system, with the major drawback being slow response as well as oscillation at some pH values. Finally, a design of a combination between MMPC and SMC (MMPC-SMC) is proposed, with MMPC carrying out basic control response while the SMC fulfils the role of eliminating the offset. However, the inaccurate reading in the MATLAB simulation model does not generate the expected results on the pH control. Therefore, the modification on the MATLAB models is required to achieve the improved control system on the offset-free behaviour for the set-point tracking.