Nonlinear Sliding Mode Control Research Articles

Investigating Suitable Combinations of Dynamic Models and Control Techniques for Offline Reinforcement Learning Based Navigation: Application of Universal Omni-Wheeled Robots

Abstract Omnidirectional locomotion provides wheeled mobile robots (WMR) with better maneuverability and flexibility, which enhances their energy efficiency and dexterity. Universal omni-wheels are one of the best categories of wheels that can be used to develop a WMR (Amarasiri et al., 2022, “Robust Dynamic Modeling and Trajectory Tracking Controller of a Universal Omni-Wheeled Mobile Robot,” ASME Letters Dyn. Sys. Control., 2(4), p. 040902. 10.1115/1.4055690). We study dynamic modeling and controllers for mobile robots to train in a reinforcement learning (RL)-based navigation algorithm. RL tasks require copious amounts of learning iteration episodes, which makes training very time consuming. The choice of dynamic model and controller has a significant impact on training time. In this paper, we compare a traditional Kane’s equations model to a non-holonomic canonical momenta model (Barhorst, 2019, “Generalized Momenta in Constrained Non-Holonomic Systems—Another Perspective on the Canonical Equations of Motion,” Int. J. Non-Linear Mech., 113, pp. 128–145.). We implemented four controllers: proportional integral derivative, linear quadratic regulator with integral action, pole placement, and a full nonlinear sliding mode controller. We summarize the pros and cons of each of the modeling techniques, and control laws implemented. The outcomes of our analysis will improve RL training time for path generation in unstructured environments.

Research on trajectory tracking control of ocean unmanned aerial vehicles based on disturbance observer and nonlinear sliding mode

This paper aims to solve the problem of real time tracking of unmanned aerial vehicle (UAV) with external disturbances, model uncertainty, and multiple control parameter tuning during wave glider (WG) navigation. Firstly, the dynamic model of UAV and WG is instituted; Secondly, an Expanded State Observer (ADOB) is proposed to estimate the total perturbations in real time, including model uncertainties and external wind perturbations; Moreover, the ADOB is integrated with a nonlinear integral sliding mode control to generate a nonlinear sliding mode controller (ASMC) with a compound disturbance observer for the trajectory tracking control strategy; Finally, the bandwidth parameterization theory is used to tune the parameters of the ASMC controller. Simulation and experimental results show that the UAV trajectory tracking landing control scheme proposed in this paper can effectively solve the real-time tracking problem of the UAV during WG navigation.

Sliding mode coordinated control of hybrid electric vehicle via finite-time control technique

During the transient mode switching process of the hybrid electric vehicle (HEV) from motor driving mode to hybrid driving mode, dynamic coordinated control of different components is essential to improve the vehicle comfort and dynamic performance. The key to highly quality mode switching control includes fast and stable speed and/or displacement tracking of the engine and motor. The transient mode switching stages of the HEV is divided in this paper. On this basis, by combing the nonlinear sliding mode control and the finite-time stability theory, the global fast integral terminal sliding mode controller (GFITSMC) is designed for the transition stages involving clutch slip. The GFITSMC consists of the global fast integral terminal sliding mode surface (GFITSMS) and the non-smooth reaching law (NSRL). In order to improve the controller convergence and anti-disturbance performance, the proposed controller is synthesized from the perspective of finite-time stability. It is proved that, with proper NSRL and GFITSMS parameters, the speed and displacement tracking error of the motor and engine can reach the sliding mode surface and further converge to zero in a finite time. Simulation and hardware-in-the-loop (HIL) tests are performed to validate the effectiveness of the proposed control method. Research results demonstrate that the proposed strategy not only achieves faster transient mode switching by improving the state trajectory tracking performance, but also reduces the longitudinal jerk caused by the transient mode switching significantly.

Natural logarithm sliding mode control for vibration control application

This paper presents the control synthesis of a nonlinear sliding mode control, known as the “ natural logarithm sliding mode control” (lnSMC), for a general n-th order system. The lnSMC offers a simple and straightforward design approach because it only requires tuning two design parameters. The first parameter has a physical meaning corresponding to the bounds of the state variables, which can be easily determined without a trial-and-error process. The second parameter is related to the controller’s feedback gains, which ensure that the system dynamics converged to the sliding surface. Lyapunov stability theory is used to analyze the closed-loop system and finite-time convergence stability. As a case study, the natural logarithm sliding mode controller is designed to suppress the vibration in a simple spring-mass system and an active suspension system. The simulation study shows that the proposed controllers have significant vibration suppression performance. Furthermore, the simulation study indicates that the sliding mode controller designed by using the natural logarithm sliding manifold outperforms the standard linear sliding manifold counterpart. In addition, due to the nature of the nonlinear switching function that creates boundary states, lnSMC has a huge potential to be applied in a wider area of vibration control.

Speed Stability and Anti-Disturbance Performance Improvement of an Interior Permanent Magnet Synchronous Motor for Electric Vehicles

To enhance the speed stability and anti-interference performance of the interior permanent magnet synchronous motor (IPMSM) in electric vehicles, a composite control strategy, incorporating sliding mode control (SMC) and extended state observer (ESO), was implemented to regulate the IPMSM’s speed. Firstly, three simulation analysis models of the IPMSM were established based on its electrical parameters. The current-loop regulator was a PI regulator, while the speed-loop regulators consisted of a basic SMC regulator, a linear SMC–ESO regulator, and a nonlinear SMC–ESO regulator. The simulation analysis results demonstrated that all three speed-loop regulators effectively ensured the speed stability of the IPMSM. However, the nonlinear SMC–ESO regulator exhibited superior performance in terms of enhancing the IPMSM’s resistance to disturbances. Secondly, a hardware testing platform was constructed to validate the simulation analysis findings. The hardware testing results, when compared to the simulation analysis results, revealed the need for optimization of the PI regulator’s control parameters to maintain the speed stability of the IPMSM. Moreover, contrary to the simulation analysis results, the hardware testing results indicated minimal difference in the anti-disturbance performance of the IPMSM between the linear SMC–ESO regulator and the nonlinear SMC–ESO regulator. Finally, the differences between the simulation analysis results and the hardware testing results are thoroughly discussed and analyzed, providing valuable insights for the practical implementation of IPMSM in electric vehicle drive systems.

A Lyapunov-based model predictive control strategy with a disturbances compensation mechanism for dual-arm manipulators

This paper proposes a Lyapunov-based nonlinear model predictive control (LMPC) - based on adaptive Lyapunov to solve existing problems in nonlinear dual-arm systems such as system constraints and unknown external disturbances. In practice, the constraints tend to adversely affect the system’s performance and stability. The nonlinear model predictive control NMPC is considered a promising candidate for handling system constraints while enhancing the robustness of the system. However, the rigour of the modeling procedure has a significant influence on the execution of the NMPC, system convergence cannot be assured in the face of modeling uncertainty. To solve this problem, the proposed controller takes into account external disturbances and unidentified parameters by using an adaptive mechanism constructed via the Radial Basis Function Neural Network (RBFNN). Furthermore, the dominant problem of the NMPC algorithm is the system stability which is considered by the Lyapunov theory backbones by a nonlinear Sliding Mode Control (SMC). The numerical simulations are carried out based on a pseudo-physical model to show the efficiency of the proposed control method.

Distributed sliding mode control strategy for intelligent connected vehicle platoon in complex media

This study examines the performance of a nonlinear sliding mode controller in cooperative control of the intelligent connected vehicles systems. The study begins by proposing a vehicle-to-vehicle car-following model that takes into account the impacts of disturbances both external and within in the system. Subsequently, an adaptive exponential reaching sliding mode controller based on a non-singular terminal sliding mode variable is proposed. It is analyzed theoretically using Lyapunov method, differential method and difference method and the results show that using the new controller, the system can converge in finite time with enhance dynamic performance. Finally, to verify the effectiveness of the controller proposed in this study, numerical experiments in MATLAB and simulation experiments in the ROS-Gazebo environment are conducted, and the results show that the controller proposed in this study enables the intelligent vehicle system to maintain stable operation in the face of interferences. Experiment results are in accordance with theoretical analysis.

Nonlinear sliding mode control of a three-dimensional double pendulum crane based on load swing state estimation: Design and experiments

In this paper, a controlled study of a three-dimensional overhead crane system with a two-stage spherical pendulum effect is carried out, and a nonlinear sliding mode control method based on load swing state estimation is proposed. The method derives the coupling relationship between the hook and the load swing angle based on the crane dynamics model and designs a linear expansion state observer (LESO) to observe the two-stage swing angle. Then, the swing angle information is fed into a controller containing a nonlinear sliding mode surface, and some rigorous mathematical proofs for the stability of this controller are presented. Finally, the theoretical analysis is experimentally verified using a prototype crane, and the results of the study show the effectiveness and strong robustness of the proposed control method.

Robust Nonlinear Torque Control Using Steering Wheel Torque Model for Electric Power Steering System

In this paper, a robust nonlinear torque control method using the steering wheel torque (SWT) model is proposed for electric power steering (EPS) systems. We develop an EPS model using SWT as the state variable to directly control the SWT. A robust nonlinear torque control method is designed to improve the SWT control performance of EPS. The proposed method consists of an extended state observer and a nonlinear sliding mode control (SMC) method. The extended state observer is designed to estimate the lumped disturbance, which includes modeling errors and external disturbances for robustness. The SMC is designed to track the desired SWT and suppress the estimation error. The nonlinear gain is proposed for reducing the chattering in the SMC. The proposed method is designed based on the SWT model; thus, it can improve the torque control performance while remaining robust to parameter uncertainty and external disturbances. The performance of the proposed method is validated via experiments using a pinion type EPS hardware-in-the-loop simulation.

Sliding Mode Active Disturbance Rejection Control of Permanent Magnet Synchronous Motor Based on Improved Genetic Algorithm

Sliding mode control has been widely used to control permanent magnet synchronous motors (PMSM). However, the parameters of the sliding mode controller are difficult to be tuned, which makes the control performance of PMSM hard to be improved. A nonlinear sliding mode control method that integrated a nonlinear reaching law (NRLSMC) and extended state observer (ESO) is proposed in this paper, whose parameters are tuned by an improved genetic algorithm (IGA). The control performance of the nonlinear reaching law in the nonlinear sliding mode controller is analyzed, whose stability is verified based on the Lyapunov theorem. An extended state observer is integrated into the above controller to further improve the anti-interference capability, and compensate for the observed external disturbance of the system into the speed controller in sliding mode. The optimal parameters of the above sliding mode control are tuned by IGA combined with the system speed loop model. The performance of the proposed controller is numerically simulated in MATLAB/Simulink and verified in a control system rapid control prototype (RCP) experimental platform built based on dSPACE 1202. Numerical simulation and experimental results show that the proposed controller can make the PMSM control system with the advantages of no overshoot, fast response, and strong robustness.

Active fault-tolerant control of quadrotor UAVs with nonlinear observer-based sliding mode control validated through hardware in the loop experiments

Multirotor unmanned aerial vehicles (UAV) are highly prone to motor faults, which can arise from defective motors or damaged propellers. Motor faults severely change the multirotor UAV’s dynamics and therefore endanger flight safety and reliability since the controller loses its efficiency. To cope with such crucial problems, a fault-tolerant controller is proposed in this paper for full control of a quadrotor UAV with motor faults. The proposed fault-tolerant approach consists of the nonlinear observer technique and the Sliding Mode Control (SMC). The designed novel nonlinear observer predicts the effects of motor faults on quadrotor dynamics and it is augmented with an SMC to create a fault-tolerant controller. In addition, the nonlinear observer enhances the robustness of the SMC against the uncertainties and disturbances acting on the quadrotor during flight. Any actuator fault will be treated as a disturbance detected by the nonlinear observer and will be attenuated directly by the proposed SMC. The disturbance attenuation capability achieved by the nonlinear observer decreases the amount of control action expected from the SMC, which results in advanced robustness without sacrificing the nominal control performance. The performance of the proposed nonlinear observer SMC (NOSMC) is demonstrated through simulations and testbed experiments. The results show that the proposed fault-tolerant controller effectively recovers the full control of the quadrotor with motor faults up to 40% while tracking the predefined trajectory and rotation angles as desired.

Research on the Sliding Mode – PID control algorithm tuned by fuzzy method for vehicle active suspension

The road surface's roughness is the primary source of vehicle oscillations when in motion. An active suspension is employed to enhance road holding, ride comfort, and stability. This research studies a dynamics model with 5 state variables to simulate vehicle oscillations based on four excitation scenarios from the road surface. In each instance, four distinct circumstances were discovered. Besides, the complicated control solution for an active suspension was created by this research, and it is called SMPIDF (Sliding Mode – PID tuned by Fuzzy). This is an entirely innovative algorithm with several significant benefits. The system's ultimate control signal is synthesized from the signals of the linear controller PID (Proportional – Integral – Derivative) and the nonlinear controller SMC (Sliding Mode Control). The defined fuzzy rule will continually alter the controller's settings. The simulation findings indicate that the acceleration and displacement of a car body are drastically decreased when an active suspension is managed to utilize the SMPIDF algorithm. The displacement and acceleration values do not surpass twenty percent and eighty percent, respectively, when compared to a car using a standard passive suspension. In addition, the characteristic of "chattering" does not occur when the controllers are combined. The overall effectiveness of this algorithm is rather significant. This approach applies to increasingly complicated models.

Hierarchical coordinated control of multi-axle steering for heavy-duty vehicle based on tire lateral and longitudinal forces optimization

Traditional multi-axle steering vehicle often adopts linear state feedback control, which is difficult to ensure high-precision trajectory tracking under all working conditions. Moreover, due to the failure to consider the optimal distribution of tire lateral and longitudinal forces, tires are prone to problems such as uneven load rates and wear. In this paper, considering the over-redundant and nonlinear characteristics of three-axle vehicle, a hierarchical coordinated control strategy is proposed. In the upper layer, the trajectory tracking controller is designed based on the robust nonlinear sliding mode control theory. In the middle layer, based on the optimization conditions of tire load rate and dissipative energy, the lateral and longitudinal forces optimal distribution controller is constructed under the constraint of friction circle. In the lower layer, the lateral and longitudinal forces are finally converted into tire angles and torques with the tire inverse model. The results show that the hierarchical coordinated control strategy can ensure that the multi-axle vehicle can achieve high-precision trajectory tracking under all-terrain load conditions, and the load rate and wear of each tire are relatively uniform. The coordinated control strategy proposed in this paper considers the influence of nonlinear characteristic of vehicle and tire lateral and longitudinal forces distribution on steering coordination, which can provide an important theoretical basis for the further improvement of steering coordination of multi-axle vehicle.

Robust tracking control for a quadrotor subjected to disturbances using new hyperplane-based fast Terminal Sliding Mode.

This paper presents a finite-time approach for tracking control of a quadrotor system subjected to external disturbances and model uncertainties. The proposed approach offers a preassigned performance guarantee. Firstly, integral terminal sliding manifolds and nonsingular terminal sliding manifolds are considered to produce the new hyperplane sliding variables for both position and attitude of a quadrotor. The designed hyperplane sliding variables guaranteed a finite-time convergence. The objective is to develop a finite-time control scheme for a disturbed quadrotor to follow a predefined trajectory based on a nonlinear sliding mode controller. The main contribution of this paper is to design a hyperplane-based nonlinear sliding mode control strategy for a quadrotor subjected to disturbances. A concept of robust controllers for a quadrotor is presented based on Lyapunov theory, which proves finite-time stability of the proposed control technique. Numerical simulations with two different scenarios verify the accuracy of the proposed hyperplane-based sliding mode control approach. The simulations study also included a comparison with another nonlinear controller. Results demonstrated overperformance of the proposed control strategy.

Sliding mode control for pulsed load power supply converters in DC shipboard microgrids

Pulsed power load (PPL) is a special load type in shipboard microgrids (SMGs), which consists of the generation module, energy storage system, and various types of loads. Having a reliable power supply to shipboard loads is a challenge as the SMG operates in islanded mode in most cases. Particularly, the PPLs require high transient power transfer with fast dynamics and strong robustness. Conventional solution to supply for the PPL is based on proportional-integral (PI) control, which can be used by linearizing the system around the equilibrium operation point. However, for a pulsed power supply (PPS) system, the load demand drastically changes in a short time, usually in millisecond level, making the operating point changes when the pulsed power is triggered or terminated. To supply the PPL with fast dynamics and robustness, an improved PPS control method is presented in this paper. By adopting a nonlinear sliding mode control (SMC) method, fast voltage regulation and robust pulse power tracking can be achieved. In the PPS, the PPL power demand is divided into two terms: one is the average power that is supplied by the SMG and the other is the fast pulsed power that is supplied by the storage capacitor. The size and cost of the storage capacitor are reduced as it is intentionally driven to a deep discharge. The PPS system configuration and coordination principle, SMC controllers, and sizing of passive elements in the PPS are analyzed in detail. The effectiveness of the presented PPS is verified by simulation results.

Robust nonlinear control of regenerative fuel cell, supercapacitor, battery and wind based direct current microgrid

Due to their simple structure and tremendous energy efficiency, direct current (DC) microgrids are becoming popular. The recent transition in power generation and consumption is based on the integration of renewable energy sources using DC microgrids. To facilitate this integration, a multi-source DC microgrid structure with five different sources including hybrid photoelectrochemical and photovoltaic (HPEV) cell, fuel cell, supercapacitor, battery and wind is presented in this paper. All the sources are linked to the DC bus via DC–DC power converters. Maximum power points for HPEV and wind have been obtained using artificial neural network. Nonlinear sliding mode controller, integral sliding mode controller, double integral sliding mode controller and super-twisting sliding mode controller have been presented for the output voltage regulation of the power sources. Global asymptotic stability of the framework has been verified using Lyapunov stability analysis. For load-generation balance, energy management system based on fuzzy logic has been devised. The proposed nonlinear controllers have been simulated and compared using MATLAB/Simulink®. Real-time hardware in the loop (HIL) experiment has been performed on the C2000 Delfino Microcontroller F28379D Launchpad for the validation of the proposed nonlinear controllers framework and compared with simulation results to validate the performance of the designed system.

Robust Motion Planning in Robot-Assisted Surgery for Nonlinear Incision Trajectory

In the era of digital OTs (operating theatres), the developments in robot-assisted surgery (RAS) can greatly benefit the medical field. RAS is a method of technological advancement that uses robotic articulations to assist in complicated surgeries. Its implementation improves the ability of the specialized doctor to perform surgery to a great extent. The paper addresses the dynamics and control of the highly non-linear 3DOF surgical robot manipulator in the event of external disturbances and uncertainties. The integration of non-linear robust SMC (sliding mode control) with a smoothing mechanism, a FOPID (fractional-order proportional integral derivative) controller, and a fuzzy controller provides a high degree of robustness and minimal chatter. The addition of fuzzy logic to the controller, named intelligent fuzzy-SFOSMC (smoothing fractional order sliding mode controller) improves the system’s performance by ruling out the disturbances and uncertainties. The prototype model is developed in a laboratory and its outcomes are validated on OP5600, a real-time digital simulator. Simulation and experimental results of the proposed fuzzy-SFOSMC are compared with conventional controllers, which illustrates the efficacy and superiority of the proposed controller’s performance during the typical surgical situations. The proposed fuzzy-SFOSMC outperforms conventional controllers by providing greater precision and robustness to time-varying nonlinear multi-incision trajectories.

Intelligent Fractional Order Sliding Mode Based Control for Surgical Robot Manipulator

In the era of digital OT (Operating Theatre), the developments in Robot-Assisted Surgery (RAS) can greatly benefit the medical field. RAS is a method of technological advancement that uses surgical robots to assist complicated surgeries. Its implementation improves the ability of the specialised doctors to perform surgery to a great extent. This paper addresses the dynamics and control of the highly non-linear 3DOF surgical robot manipulator in the occurrence of external disturbances and uncertainties. The integration of non-linear robust SMC (Sliding Mode Control) with smoothing mechanism, FOPID (Fractional-Order Proportional Integral Derivative) controller and fuzzy controller provides a high degree of robustness and minimal chatter. The addition of type-2 fuzzy logic to the controller, named intelligent T2F-SFOSMC (Type-2 Fuzzy-Smoothing Fractional Order Sliding Mode Controller), improves the system’s performance by ruling out the disturbances and uncertainties. The prototype model is developed in a laboratory and its outcomes are validated on OP5600: a real-time digital simulator. The simulation results and experimental results of the proposed T2F-SFOSMC are compared with conventional controllers, which illustrates the efficacy and superiority of the proposed controller’s performance during the typical situation of surgery. The proposed T2F-SFOSMC outperforms conventional controllers by providing greater precision, stability and robustness to time-varying nonlinear multi-incision trajectory.

Design a new control algorithm AFSP (Adaptive Fuzzy – Sliding Mode – Proportional – Integral) for automotive suspension system

When a vehicle is driving, the most significant source of oscillations is the irregularities in the surface of the road. An active suspension is utilized to enhance the vehicle’s stability and ride comfort. In this work, the dynamic model with multi variables is considered to simulate vehicle oscillations based on four excitation cases from the road surface. In addition, this research also established the AFSP complex control solution for an active suspension system. This is a completely novel algorithm with many outstanding advantages. The final control signal of the system is synthesized from the signals of the linear controller PI (Proportional – Integral) and the nonlinear controller SMC (Sliding Mode Control). The controller’s parameters will change continuously depending on the established fuzzy rule. According to simulation outcomes, the vehicle body displacement and acceleration dramatically declined when the AFSP algorithm directed an active suspension. The values of acceleration and displacement do not exceed 80% and 20%, compared to the scenario in which the vehicle just utilized the typical passive suspension system. Besides, a phenomenon of “chattering” also does not appear when combining the controllers. Overall, the efficiency of this algorithm is high. This algorithm can be applied to more complex models.

An Adaptive Sliding Mode Control for Multi-Span Nonlinear Web Material Linkage Systems

This study presents an adaptive controller for multi-span nonlinear web material linkage systems with the characteristic of a variable moment of inertia and operating radius of rolls. Sliding mode control is used to control web tensions as well as velocities of the system due to its robustness against modeling imprecision. In addition, an adaptive law combined with sliding mode control is proposed to estimate the moment of inertia. As a result, the adaptive sliding mode control structure takes advantage of nonlinear sliding mode control and adaptation algorithm to deal with parameter changes. To verify the controller, the stability of the whole system is proved based on Lyapunov’s stability theory. The simulation results illustrate reliable performance by comparing several nonlinear controllers.