Backstepping Research Articles

Application of Fuzzy Adaptive Impedance Control Based on Backstepping Method for PAM Elbow Exoskeleton in Rehabilitation

In this study, a fuzzy adaptive impedance control method integrating the backstepping control for the PAM elbow exoskeleton was developed to facilitate robot-assisted rehabilitation tasks. The proposed method uses fuzzy logic to adjust impedance parameters, thereby optimizing user adaptability and reducing interactive torque, which are major limitations of traditional impedance control methods. Furthermore, a repetitive learning algorithm and an adaptive control strategy were incorporated to improve the performance of position accuracy, addressing the time-varying uncertainties and nonlinear disturbances inherent in the exoskeleton. The stability of the proposed controller was tested, and then corresponding simulations and an elbow flexion and extension rehabilitation experiment were performed. The results showed that, with the proposed method, the root mean square of the tracking error was 0.032 rad (i.e., 21.95% less than that of the PID method), and the steady-state interactive torque was 1.917 N·m (i.e., 46.49% less than that of the traditional impedance control). These values exceeded those of the existing methods and supported the potential application of the proposed method for other soft actuators and robots.

Fuzzy backstepping controller for agricultural tractor-trailer vehicles path tracking control with experimental validation

Unmanned driving technology for agricultural vehicles is pivotal in advancing modern agriculture towards precision, intelligence, and sustainability. Among agricultural machinery, autonomous driving technology for agricultural tractor-trailer vehicles (ATTVs) has garnered significant attention in recent years. ATTVs comprise large implements connected to tractors through hitch points and are extensively utilized in agricultural production. The primary objective of current research focus on autonomous driving technology for tractor-trailers is to enable the tractor to follow a reference path while adhering to constraints imposed by the trailer, which may not always align with agronomic requirements. To address the challenge of path tracking for ATTVs, this paper proposes a fuzzy back-stepping path tracking controller based on the kinematic model of ATTVs. Initially, the path tracking kinematic error model was established with the trailer as the positioning center in the Frenet coordinate system using the velocity decomposition method. Then, the path tracking controller was designed using the back-stepping algorithm to calculate the target front wheel steering angle of the tractor. The gain coefficient was adaptively adjusted through a fuzzy algorithm. Co-simulation and experiments were conducted using MATLAB/Simulink/CarSim and a physical platform, respectively. Simulation results indicated that the proposed controller reduced the trailer's online time by 36.33%. When following a curved path, the trailer's tracking error was significantly lower than that of the Stanley controller designed for a single tractor. In actual experiments, while tracking a U-turn path, the proposed controller reduced the average absolute value of the trailer's path tracking lateral error by 65.27% and the maximum lateral error by 87.54%. The mean absolute error (MAE) values for lateral error and heading error were 0.010 and 0.016, respectively, while the integral of absolute error (IAE) values were 1.989 and 2.916, respectively. The proposed fuzzy back-stepping path tracking controller effectively addresses the practical challenges of ATTV path tracking. By prioritizing the path tracking performance of the trailer, the quality and efficiency of ATTVs during field operations are enhanced. The significant reduction in tracking errors and online time demonstrates the effectiveness of the proposed controller in improving the accuracy and efficiency of ATTVs.

Trajectory Planning With A* Algorithm and Tracking With Multiple Controllers

ABSTRACTThis article consists of mathematical modelling of differential drive mobile robot (DDMR), path planning and tracking application via multiple controller usage. Robot kinematic and dynamic models were constructed and simulated in virtual 2D map environment. A* algorithm was applied to the 2D map problem to acquire optimal pathfinding, efficiency and flexibility in trajectory planning stage. After the reference trajectory is obtained by algorithm, the robot needs to be guided using control strategy that manages the speed control of electric motors. At the first part of the control problem, kinematic based backstepping control (KBBC) were used to increase the efficiency of the control system. After that Sliding Mode Control (SMC) and Proportional‐Integral‐Derivative (PID) control strategies were applied to reduce tracking errors between reference and actual coordinate values and heading angle value. To test the robustness and efficiency of control combinations, two different simulation systems were designed using Matlab‐Simulink Software. First system was designed for the non‐disturbance condition, while the second system included disturbance torque and an additional mass applied condition. Test results showcasing the performance of the controllers are presented in the concluding section, through trajectory tracking and error comparison graphs.

Performance Enhancement of Microgrid Systems Using Backstepping Control for Grid Side Converter and MPPT Optimization

Microgrid networks represent a crucial model in the field of power transmission and distribution, integrating renewable energy sources with modern control technologies. This research focuses on enhancing the performance of a microgrid system connected to the main grid through a three-phase converter controlled using Voltage Oriented Control (VOC). The microgrid comprises a storage element and a photovoltaic (PV) generation system. To improve system efficiency and power quality, backstepping (BS) controllers are implemented and compared with traditional control methods. Three control systems are evaluated: a conventional system using Perturb and Observe (P&O) algorithm for Maximum Power Point Tracking (MPPT) and Proportional-Integral (PI) controllers for grid-side converter (GSC) control, a hybrid system with BS-modified P&O (BS-P&O) for MPPT and PI controllers for GSC, and an advanced system employing BS-P&O for MPPT and BS controllers for GSC. The research demonstrates that BS controllers exhibit superior dynamic performance, contributing to improved regulation of DC-link voltage, active and reactive powers. Additionally, they achieve lower Total Harmonic Distortion (THD) values and increase the overall efficiency of the PV system. The proposed advanced control strategy shows particular effectiveness in tracking speed, disturbance rejection, and power quality enhancement. This study underscores the potential of nonlinear control techniques in optimizing microgrid operations and facilitating the integration of renewable energy sources into the main grid.

New Lyapunov backstepping control of the mechanical power generated by an induction motor

This paper presents a new Lyapunov backstepping control law (LBC) that makes it possible to control the mechanical power generated by an induction motor (IM), while guaranteeing its robustness and stability. This induction motor is supplied by the stator variables via two converters. One, a mains converter (two-level rectifier), facilitates the control of the direct courant (DC) bus and improves the mains power factor; the other, a motor converter (two-level inverter), enables precise control and optimisation of the energy flow during motor operation. In the first part, we presented the modelling of our motor and its converters. In the second part, we presented the control structure proposed to control and optimise the mechanical energy generated by our motor (speed, torque) to achieve optimum efficiency and transfer quality. The results of the numerical simulations demonstrate the effectiveness of the new Lyapunov control system in achieving these objectives, i.e. mechanical speed outside its references and electromagnetic torque below the nominal torque.

Output feedback control for non-strict feedback nonlinear systems: an adaptive fuzzy backstepping scheme

The adaptive fuzzy tracking control design issue is considered in this paper for a class of non-strict feedback nonlinear systems subject to external disturbances. A fuzzy high-gain state observer is constructed to reconstruct the unmeasurable states of the system by leveraging the universal approximation property of fuzzy logic systems for arbitrary unknown nonlinear functions. Within the framework of backstepping control design and in conjunction with adaptive techniques, an adaptive fuzzy control approach is presented. Subsequently, to work out the inherent ‘complexity explosion’ problem of the proposed control approach, dynamic surface control technique is introduced, leading to a simplified adaptive fuzzy output feedback control scheme. Stability analysis shows that the two proposed control schemes can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, meanwhile the system tracking error can converge to a small neighborhood around the origin. Ultimately, a numerical simulation example is provided to validate the feasibility of the proposed control scheme.

Fixed-time adaptive control of quadrotor suspension system with unknown payload mass

This paper investigates the control challenges of quadrotor suspension systems with unknown payload masses. To address the unknown external disturbances, uncertainties in system models, and unknown payloads, fixed-time stable adaptive laws are developed to estimate and compensate for these unknown factors. Additionally, a novel control structure based on a nonlinear backstepping controller is proposed for the quadrotor suspension system, achieving stable control of the quadrotor and reducing the sway of the suspended payload. The fixed-time stability of the designed closed-loop system is analytically proven using Lyapunov functions, ensuring maximum stability time. Simulink simulations validate the proposed control approach, demonstrating accurate estimation of unknown masses and the effectiveness and superiority of the controller.

Investigation of the performance of oil-free linear compressor with magnetic resonance spring for pulse tube cryocooler

This study proposes a new type of oil-free linear compressor with a magnetic resonance spring, which uses a magnetic resonance spring to provide restoring force and adopts gas-lubricated bearings to provide support force for the piston. The frequency characteristics of the compressor, including magnetic spring stiffness, gas spring stiffness, and resonance frequency, are studied through experiments and theoretical analysis. The magnetic spring stiffness is 31403.31 N/m of the design compressor. Hooke’s law and Fourier decomposition are employed for the gas spring stiffness measuring the compression pressure gauged. Meanwhile, the gas spring stiffness is also obtained from the amplitude-frequency characteristic of the compressor by the back stepping technique with an electric parameter frequency scan. The experimental results demonstrate that the three measurement methods have good consistency in measuring the gas spring stiffness. The equivalent gas spring stiffness measured using the three methods and theoretical model are 72600.92 N/m, 71275.84 N/m, 71967.15 N/m, and 71929.25 N/m at 3 MPa charged pressure measured respectively. In addition, the refrigeration performance of the pulse tube cryocooler driven by the compressor is tested and the lowest temperature obtained in the cold end is 46.3 K under different charge pressure. Furthermore, an optimal frequency exists that enhances the refrigeration performance of the pulse tube cryocooler, and this optimal frequency remains constant regardless of changes in the charge pressure.

Design of a Hybrid Excitation Controller for Multimachine Infinite Bus Power System

Abstract: A significant portion of contemporary power networks is still conventional power system that uses synchronous generators to produce electricity. Conventional power systems are operated under various operating situations by means of excitation systems and turbine-governor systems of synchronous generators. This paper proposes an excitation controller for synchronous generators (SGs) in a multi machine infinite bus (MMIB) power system through combining the idea of the nonlinear backstepping (BS) and partial feedback linearization methods. The model of third-order has been linearized into a second-order linearized system that is independent of the rotor angle which is unmeasurable, using the partial feedback linearization approach. In this case, the BS is applied to the partially linearized system. The idea is to find a control input that drives the system towards a desired behaviour while ensuring the transformed states converge to their target values. Lastly, simulation research is carried out on an MMIB system to analyse how the proposed control mechanism (BS-PFLC) performs in stabilizing the system under a three phase-to-ground fault conditions of power networks. To demonstrate the effectiveness of the BS-PFLC, an existing excitation controller has been used to compare the performance.

Nonlinear Backstepping Controller for Current Control of Grid-Connected Five-Level Inverter

Nonlinear Backstepping Controller for Current Control of Grid-Connected Five-Level Inverter

Adaptive fuzzy optimal output-feedback fault-tolerant control for the USV system with intermittent actuator faults

This paper presents a novel fuzzy optimal output-feedback fault-tolerant control (FTC) method for uncertain nonlinear unmanned surface vehicle (USV) systems, which are subject to intermittent actuator failures and unmeasured states. The proposed optimal controller is composed of a fuzzy feedforward fault-tolerant output-feedback controller and a fuzzy error feedback optimal controller. The fuzzy feedforward fault-tolerant output-feedback controller is designed by using the fuzzy state observer and backstepping control design technique. The fuzzy optimal feedback controller is given by adopting adaptive dynamic programming (ADP) theory. It is proven that the presented fuzzy optimal FTC scheme is able to ensure that the USV system is uniformly ultimately bounded (UUB), and the optimal control performance is achieved. The validity is confirmed by computer simulation results.

Predefined time convergence guaranteed performance control for uncertain systems based on reinforcement learning

The prescribed performance control method (PPCM) is commonly employed to ensure the guaranteed performance control of non-linear systems. However, traditional approaches suffer from certain drawbacks, such as the dependence of parameter settings for the performance constraint function on the initial tracking error value and the inability to specify the convergence time of tracking error according to engineering requirements. This paper focuses on designing a fault tolerant control strategy with prescribed convergence time and prescribed transient performance for uncertain systems, considering parameter perturbance, actuator faults, and unknown initial states. Firstly, we introduce an error conversion function that transforms the tracking error with any initial value into a new error variable starting from zero. This resolves the issue of depending on the initial value of tracking error in setting parameters for the performance constraint function in prescribed performance control methods. Subsequently, we derive a novel Lyapunov stability criterion for predefined time (PDT) convergence and design a fault-tolerant control strategy using backstepping control method while ensuring prescribed convergence time and prescribed performance. In this approach, we propose a new online reinforcement learning intelligent algorithm to estimate compound interference caused by actuator faults, control saturation constraint increment, system parameter perturbation, and external interference. The theoretical proof establishes predefined time convergence of the closed-loop system. Finally, numerical simulations are conducted on industrial robots with actuator faults to validate the effectiveness of our designed control strategy.

Enhanced Operation Mode Design and Motion Control of a Dual-Redundancy Electro-Hydrostatic Actuator

In dual-redundancy electro-hydrostatic actuators (EHAs), the dual pumps are mainly designed for safety, where the cylinder is controlled mainly by one pump while the other one is standby for redundancy. However, such a strategy is basically like a single-pump-controlled system, and the flow from the pump may be inaccurate when the cylinder moves slowly, which will affect the motion control performance. A new dual-redundancy EHA is designed, and a series of corresponding operation modes are developed, enabling differential operation of the dual pumps. With the proposed operation modes, the inevitable flow inaccuracy problem of the single pump can be addressed through the coordination control of the dual pumps. In order to achieve better motion tracking performance, a model-based backstepping controller is synthesized, where the nonlinearities and uncertainties of the EHA are handled by model compensation and robust feedback design. Comparative simulations with existing control methods for EHAs are conducted and better motion tracking precision is achieved, especially during low-speed motion.

Adaptive NN Force Loading Control of Electro-Hydraulic Load Simulator

To address the issues of derivative explosion in traditional backstepping control and the strong nonlinearity of hydraulic systems, this paper develops an adaptive neural network control method tailored for electro-hydraulic load simulators. Neural networks are employed to handle external disturbances, modeling uncertainties, and the derivatives of virtual control inputs. First, the precise state-space equations of the system are derived. Next, the approximation property of neural networks is used to design an adaptive backstepping controller, and the symmetric barrier Lyapunov function is used to prove the boundedness of the controller and control parameters. Finally, experiments are conducted to verify the effectiveness and reliability of the control algorithm. The results demonstrate that the proposed control algorithm exhibits excellent tracking performance and effectively reduces control errors.

Trajectory tracking control of autonomous vehicles based on event‐triggered model predictive control

AbstractThis paper presents a lateral control scheme based on event‐triggered model predictive control for trajectory tracking of autonomous vehicles. Firstly, the augmentation system is constructed based on the known road curvature information, and the model predictive controller is utilized to obtain the optimal control sequence. Then, an event‐triggered mechanism is introduced to improve the real‐time performance of the control system. The strategy targets to reduce the computational complexity and solving frequency of the optimization problem. In addition, a contraction constraint is structured using the backstepping control strategy to ensure the stability of the control system. Finally, experiments are conducted through the CarSim/Simulink joint simulation platform, and compared with the traditional model predictive control, the method proposed in this paper has better tracking accuracy and improves the real‐time performance of the control system.

Distributed Adaptive Multi‐Lane Fusion Control for 2‐D Plane Vehicle Platoon With Distance Constraints and Angle Sensor Faults

ABSTRACTThis article investigates the distributed adaptive multi‐lane fusion control for two‐dimensional (2‐D) plane vehicle platoons with variable distance constraints, input hysteresis, and angle sensor faults. Variable distance constraints occur within a limited time interval (VDCOLT), which limits vehicle spacing within a variable range during preset time intervals while keeping the vehicle spacing unconstrained at other times. Combined with a transformed error function, a new shifting function is introduced to convert the constrained spacing error variables into the unconstrained variables while keeping the unconstrained variable unchanged. Designing the position controller ensures that the distance satisfies VDCOLT and reduces the adverse effects caused by unknown signs of input hysteresis by using a Nussbaum function. Moreover, a new angle controller based on the hyperbolic tangent function is designed to solve the problem of angle sensor faults. Furthermore, the stability of the vehicle platoon is achieved through the backstepping control and sliding‐mode control methods. Finally, a numerical simulation is provided to verify the proposed techniques.

SABO optimization algorithm-based backstepping controller for DSIG within a wind turbine system

SABO optimization algorithm-based backstepping controller for DSIG within a wind turbine system

Sparse Online Gaussian Process Adaptive Control of Unmanned Aerial Vehicle with Slung Payload

In the past decade, Unmanned Aerial Vehicles (UAVs) have garnered significant attention across diverse applications, including surveillance, cargo shipping, and agricultural spraying. Despite their widespread deployment, concerns about maintaining stability and safety, particularly when carrying payloads, persist. The development of such UAV platforms necessitates the implementation of robust control mechanisms to ensure stable and precise maneuvering capabilities. Numerous UAV operations require the integration of payloads, which introduces substantial stability challenges. Notably, operations involving unstable payloads such as liquid or slung payloads pose a considerable challenge in this regard, falling into the category of mismatched uncertain systems. This study focuses on establishing stability for slung payload-carrying systems. Our approach involves a combination of various algorithms: the incremental backstepping control algorithm (IBKS), integrator backstepping (IBS), Proportional–Integral–Derivative (PID), and the Sparse Online Gaussian Process (SOGP), a machine learning technique that identifies and mitigates disturbances. With a comparison of linear and nonlinear methodologies through different scenarios, an investigation for an effective solution has been performed. Implementation of the machine learning component, employing SOGP, effectively detects and counteracts disturbances. Insights are discussed within the remit of rejecting liquid sloshing disturbance.

Virtual Generator to Replace Backup Diesel GenSets Using Backstepping Controlled NPC Multilevel Converter in Islanded Microgrids with Renewable Energy Sources

This work presents an islanded microgrid energy system that uses backstepping control applied to neutral point clamped (NPC) multilevel converters coupled with batteries to behave as virtual generators, able to absorb surplus renewable energy, therefore increasing the penetration of renewable energy sources. Additionally, on a charged battery the virtual generator allows turning-off the backup diesel generator set (GenSet). Aside from improving energy efficiency, the battery-connected multilevel converter aims to regulate frequency, improves power quality, and keeps the microgrid operational in the event of a GenSet failure. The backstepping controlled NPC multilevel converter emulates a virtual generator injecting power to perform as the primary and secondary microgrid frequency controller. Additionally, AC voltage control is implemented, which enables running the islanded microgrid only with multilevel converters, supplied by the battery while integrating solar and wind energy sources. Energy demand and renewable energy forecasts are used to manage the battery state-of-charge. Simulation results, obtained from switched and phasor models show that energy storage and the backstepping frequency control enables the compensation of power fluctuations from renewable energy sources. Furthermore, in the event of the main GenSet failure, the controlled virtual generator keeps the microgrid running for a few minutes, until another GenSet is ready to supply the microgrid. Therefore, the microgrid integration of the battery-connected multilevel converter results in a significant boost in energy efficiency by allowing the disconnection of the backup GenSet.

Observer-Based Fixed-Time Consensus Tracking for a Class of Nonlinear Multi-Agent Systems

In this paper, the problem of fixed-time consensus tracking for a class of nonlinear multi-agent systems (MASs) with uncertainties and external disturbances is addressed. To solve this problem, a new fixed-time consensus tracking protocol with disturbance rejection abilities is proposed that consists of a fixed-time distributed observer (FTDO), a fixed-time disturbance observer (FDO), and a nonsmooth backstepping controller with lumped disturbance compensation (NBCDC). The fixed-time stabilities are analyzed correspondingly. Firstly, an FTDO is designed to estimate a leader’s output by using the topology of communication networks for each follower. Second, an FDO is developed to observe the lumped disturbances composed of model uncertainties and external disturbances. Finally, an NBCDC is proposed for improving the closed-loop performance. The simulation results show that the proposed method is effective.