Backstepping Sliding Mode Control Research Articles

Adaptive backstepping sliding mode subject-cooperative control for a pediatric lower-limb exoskeleton robot

The passive-assist rehabilitation mode with a fixed desired trajectory neglects the subject’s active involvement and degrades the therapeutic performance in case of partial muscle strength. Therefore, this study proposes a novel subject-cooperative control based on a variable admittance control scheme and a robust trajectory control scheme for a pediatric lower-limb exoskeleton robot. Initially, the system description and dynamic modeling are briefly explained. Thereafter, a neural-fuzzy–based variable admittance control ( nf VAC) is designed to incorporate a realistic subject-exoskeleton interaction and consider the subject’s active participation. Finally, a robust adaptive backstepping sliding mode control with rapid reaching law is used to handle parametric uncertainties and external disturbances. A stepwise selection of Lyapunov functions is utilized to address the stability of the trajectory control. The effectiveness of the proposed adaptive backstepping sliding mode–neural-fuzzy variable admittance control (ABSM- nf VAC) scheme is compared with two contrast control schemes, namely, adaptive backstepping-fixed admittance control (AB-FAC) and adaptive terminal sliding mode-fuzzy variable admittance control (ATSM- f VAC) for the active-assist mode with the effect of sudden reflex. Based on the numerical results, the suggested cooperative controller has demonstrated favorable tracking performance, compliant interaction, and safety aspects during gait training.

Adaptive backstepping sliding mode compensation control for electro‐hydraulic load simulator with backlash links

AbstractWhen a mechanical backlash between the loading piston rod and the steering gear piston rod connection of the electro‐hydraulic load simulator (EHLS), it will lead to poor loading accuracy. To solve this problem, an adaptive backstepping sliding mode controller based on the backlash feedforward compensation and state observer is proposed. First, the mechanism of surplus force generation in the EHLS is analyzed, and a mathematical model containing position disturbance and backlash nonlinearity is established based on the analysis results. Second, a state observer is designed to estimate the system state and the parameter adaptive law is designed to estimate the system parameters. Third, the adaptive backstepping method is combined with the non‐singular terminal sliding mode control (NTSMC) strategy to deal with the position disturbance and parameter uncertainty and to enhance the system's dynamic performance. Finally, a backlash feed‐forward compensator is engineered to restrain the detrimental effects caused by the backlash nonlinearity, and the simulation experimental results show that the designed new method can realize the precise loading of the EHLS under different working conditions, and the surplus force is suppressed better at the same time.

Enhancing pressure control of low-friction pneumatic actuator with eddy current damper via valve dead-zone compensation

This article addresses the high-performance pressure control of a pneumatic actuator that incorporates an air-bearing piston and an eddy current damper (ECD). After optimizing the pneumatic actuator, achieving precise pressure control relies on maintaining an accurate and stable airflow through the control valve. A terminal sliding mode adaptive control method (TSMAC) is proposed, proficiently integrating considerations for dead zone nonlinearities in the proportional valve and the effects of unmodeled disturbances in the pneumatic actuator. Using the opening area of the proportional valve as the input to the pneumatic system greatly simplifies the control process and reduces the workload required for valve parameter calibration. The Lyapunov-based stability analysis demonstrates that excellent asymptotic output tracking can be achieved with low steady-state error simply by knowing the boundaries of the valve opening area. The control effect of the proposed control strategy is compared with an adaptive backstepping sliding mode control method based on a linearly fitted proportional valve model on an established constant pressure control test bench. Experimental results under various loads and operating conditions illustrate the effectiveness of the proposed approach.

Adaptive fuzzy-neural network effectively disturbance compensate in sliding mode control for dual arm robot

In this study, an Adaptive Backstepping Sliding Mode Controller (ABSMC) is introduced based on the Radial Basis Function (RBF) neural network and a fuzzy logic modifier. The proposed method is used to control a Dual-Arm Robot (DAR) – a nonlinear structure with unstable parameters and external disturbances. The control aims to track the motion trajectory of both arms in the flat surface coordinate within a short time, maintaining stability, and ensuring that the tracking error converges in finite time, especially when influenced by unforeseen external disturbances. The nonlinear Backstepping Sliding Mode Control (BSMC) is effective in trajectory tracking control; however, undesired phenomena may occur if there are uncertain disturbances affecting the system or model parameters change. It is proposed to use a neural network to estimate a nonlinear function to handle unknown uncertainties of the system. The neural network parameters can be adaptively adjusted to optimal values through adaptation rules derived from Lyapunov's theorem. Additionally, fuzzy logic theory is also employed to adjust the controller parameters to accommodate changes or unexpected impacts. The performance of the Fuzzy Neural Network Backstepping Sliding Mode Control (FNN-BSMC) is evaluated through simulation results using Matlab/Simulink software. Two simulation cases are conducted: the first case assumes stable model parameters without uncertain disturbances affecting the joints, while the second case considers a model with changing parameters and disturbances. Simulation results demonstrate the effective adaptability of the proposed method when the system model is affected by various types of uncertainties from the environment

Robust Control of Golf Swing Robot Using Backstepping Based on Fuzzy Sliding-Mode and Super-Twisting Backstepping Sliding-Mode Algorithms

This paper focuses on trajectory tracking, robustness and stabilization of a golf swing robot which has been recently developed to simulate the ultra-high-speed swing motions of a golfer. The proposed control strategies are based on the Lyapunov stability theory and include Backstepping and Sliding-Mode Control based techniques. To attenuate the chattering phenomena caused by a discontinuous switching function and improve the dynamic response of the manipulator, a fuzzy system is used in this research; a Backstepping Sliding-Mode Controller (BSMC), a Backstepping Fuzzy Sliding-Mode Controller (BFSMC) and a Super-twisting Backstepping Sliding-Mode Controller (STBSMC) are used to evaluate the proposed hybrid controller’s BFSMC performance. The Lyapunov stability theory is used to guarantee the stability of the proposed closed-loop robot technique. Numerical simulations show the effectiveness of the proposed strategy based on the fuzzy logic mechanism under different disturbances and uncertainties.

Adaptive Fuzzy Backstepping and Backstepping Sliding Mode Controllers Based on ICD Observer: A Comparative Study

Adaptive Fuzzy Backstepping and Backstepping Sliding Mode Controllers Based on ICD Observer: A Comparative Study

Performance study of smart transformer based on Backstepping-Sliding Mode Control with integral action

Performance study of smart transformer based on Backstepping-Sliding Mode Control with integral action

Backstepping sliding mode control of stabilized platform for fully rotary steerable drilling system based on nonlinear disturbance observer

AbstractTo handle the disturbances and uncertainties issue in the control of the stabilized platform toolface angle, a composite control approach based on a backstepping sliding mode control (BSMC) method with a nonlinear disturbance observer (NDO) is proposed. First, a nonlinear mathematical model of the stabilized platform is established, and the NDO is employed to observe and compensate for the external disturbance. Then, the BSMC control approach based on the nonlinear mathematical model is designed to improve the robustness of the stabilized platform control system. The asymptotic stability of the designed controller and NDO convergence are mathematically verified using the Lyapunov theory. Furthermore, to address the dead zone torque caused by mechanical friction on the stabilized platform, which could lead to instability in the toolface angle, a novel dead zone torque estimation algorithm is presented. Finally, in comparison with other advanced control methods, simulation results show the superiority and robustness of the proposed scheme under complex disturbances from the downhole environment. And drilling simulation experiment results are provided to validate the robustness and adaptivity of the proposed method.

Intelligent fuzzy back-stepping observer design based induction motor robust nonlinear sensorless control

Introduction. The control algorithm of Induction Motor (IM) is massively dependent on its parameters; so, any variation in these parameters (especially in rotor resistance) gives unavoidably error propagates. To avoid this problem, researches give more than solution, they have proposed Variable Structure Control (VSC), adaptive observers such as Model Reference Adaptive System, Extended Luenberger Observer (ELO) and the Extended Kalman Filter (EKF), these solutions reduce the estimated errors in flux and speed. As novelty in this paper, the model speed observer uses the estimated currents and voltages as state variables; we develop this one by an error feedback corrector. The Indirect Rotor Field Oriented Control (IRFOC) uses the correct observed value of speed; in our research, we improve the observer’s labour by using back-stepping Sliding Mode (SM) control. Purpose. To generate the pulse-width modulation inverter pulses which reduce the error due of parameters variations in very fast way. Methods. We develop for reach this goal an exploration of two different linear observers used for a high performance VSC IM drive that is robust against speed and load torque variations. Firstly, we present a three levels inverter chosen to supply the IM; we present its modelling and method of control, ending by an experiment platform to show its output signal. A block diagram of IRFOC was presented; we analyse with mathematic equations the deferent stages of modelling, showed clearly the decoupling theory and the sensorless technique of control. The study described two kinds of observers, ELO and EKF, to estimate IM speed and torque. By the next of that, we optimize the step response using the fuzzy logic, which helps the system to generate the PI controller gains. Both of the two observers are forward by SM current controller, the convergence of SM-ELO and SM-EKF structures is guaranteed by minimizing the error between actual and observed currents to zero. Results. Several results are given to show the effectiveness of proposed schemes.

Integral Backstepping Sliding Mode Control for Maximizing the Power Production of Wind Turbines

Wind turbine control has attracted increasing attention, driven in part by evolving challenges due to the growing size and complexity of wind turbines. Addressing these challenges and maximizing wind turbine power production requires the application of advanced nonlinear control methods. Sliding Mode Control (SMC) has emerged as a promising approach in this context. Recent studies have explored the integration of an integral term with SMC, called I-SMC. This technique has been shown to result in system responses that exhibit chattering phenomena with noticeable state errors. This study aimed to address these issues through the introduction of a novel controller known as Integral Backstepping SMC (IB-SMC). This study demonstrated that IBSMC not only ensured the stability of wind turbines but also outperformed other control strategies, even in the presence of disturbances of approximately 30% of the rated electromagnetic torque. To validate the effectiveness of the proposed controller, extensive simulation tests were carried out using MATLAB /Simulink software to evaluate the controller's responsiveness to rapid changes in conditions, as well as its robustness and overall performance. A comparison was carried out between the IBSMC and previous SMCs to evaluate their ability to reduce steady-state error and chattering.

Fractional-order backstepping sliding mode control for the speed tension and screw down system of the reversible cold strip rolling mill

This paper investigates the robust control problem of the speed tension and screw down system of Reversible Cold Strip Rolling Mill (RCSRM). A finite-time observer is proposed to observe the uncertainties of the system. Based on the finite time observer, a fractional-order backstepping sliding mode controller is designed for each sub-system of the speed tension and screw down system of RCSRM. The Particle Swarm Optimization (PSO) algorithm is used to optimize the main parameters of the designed controller. By Lyapunov stability, the tracking error of the system can converge to the neighbourhood of the equilibrium point in a finite time. Finally, simulation research is carried out on the actual data of a 1422 mm RCSRM, and the effectiveness of the designed controller is verified.

A backstepping sliding mode control algorithm of electro-hydraulic position servo system of valve-controlled symmetric cylinder based on extended state observer

Electro-hydraulic position servo system of valve-controlled symmetrical cylinder (EPSSVCS) is a very important and widely used electro-hydraulic servo system, the performance of which is often affected by friction nonlinearity and external random disturbances together with unmodeled dynamic factors such as parameter uncertainty in practical work. To improve the tracking performance of the system, a backstepping sliding mode control algorithm (BSMC) based on an extended state observer was presented in this paper. Firstly, a nonlinear mathematical model of the EPSSVCS was established which takes into account the composite disturbance induced by the systematic friction nonlinearity, external disturbances and unmodeled dynamic factors. Then, an extended state observer (ESO) was designed which can effectively estimate the velocity, acceleration, and composite disturbance of the valve-controlled cylinder online. Furthermore, a kind of BSMC was presented based on the online ESO estimates and the displacement feedback signals. The control law was given and the system stability was proved. The analysis results showed that the output signal of the system can effectively track the input signal under the influence of typical external disturbances and unmodeled dynamic factors, which illustrated the effectiveness of the established nonlinear mathematical model and the stability of the designed control system. Moreover, by taking the parameters of the electro-hydraulic servo system of a certain type of CNC machine tool as a real example, the proposed algorithm (BSMC) was compared with the conventional PID control algorithm, the backstepping sliding mode control algorithm (BSC), and the adaptive robust control algorithm (ARC), and the results verified the superiority of the BSMC. This work may provide a useful reference for the research in the field of related control systems.

Tillage depth regulation system via depth measurement feedback and composite sliding mode control: A field comparison validation study

The existing methodologies employed for the quantification and regulation of tractor’s tillage depth present considerable shortcomings, primarily characterized by their low accuracy and poor disturbance rejection proficiency in complex agricultural terrains. In this study, we present a sophisticated feedback control strategy designed to mitigate these challenges. Our innovative approach hinges on calculating tillage depth from the alignment of the tractor’s hydraulic lifting arm, achieved by employing a mechanical angle sensor. This sensor adeptly gages the angle of the lifting arm, aligning it with the tillage angle of the pull rod and the implement’s angle, resulting in a robust relational model correlating the lifting arm angle with the tillage depth. This pioneering method amalgamates the accuracy inherent in the static model, derived from the tillage angle-based depth measurement, with the dynamic stability afforded by the mechanical ascertainment of the lifting arm angle. In conjunction, we introduce a Hybrid Extended State Observer-Based Backstepping Sliding Mode Controller (HESO-BacksteppingSMC). The HESO is instrumental in estimating unmeasured state variables and lumped disturbances, utilizing the system’s output feedback signal. Our control frame component capitalizes on the fast power-reaching law to yield a continuously smooth control signal, effectively eradicating the conventional chattering phenomenon inherent in controllers and amplifying its functional applicability. Theoretical evaluations affirm the uniformly and ultimately bounded stability of the errors associated with our proposed observer and controller, underscoring their robustness. The superior performance of our proposed tillage depth measurement and control methodology has been corroborated through a series of comprehensive simulation and field plowing trials, attesting to its precision and reliability in complex agricultural settings.

Robust high‐gain observer‐based sliding mode controller for pitch and yaw position control of an AUV

AbstractThis article addresses a trajectory tracking control problem concerning an autonomous underwater vehicle's pitch and yaw channel dynamics in the presence of model uncertainties, underwater disturbances, and input saturation. Three different observers are introduced to estimate unknown state variables: a Luenberger‐type cubic observer, a sliding mode observer, and a high‐gain observer (HGO). Initially, a backstepping controller is employed to tackle the tracking problem, extending it to incorporate backstepping sliding mode control (SMC). The mentioned observers are utilized in both aspects of the controller design. Our proposed control law assesses trajectory tracking performance by introducing virtual control inputs, with the sliding surface designed to guide the current state variables toward approximating the virtual state variables. By combining backstepping and SMC, ensure that the state variables of the closed‐loop system converge to the desired state using the HGO. A rigorous analysis is incorporated to validate the robust performance of our proposed control law under conditions of model uncertainties and underwater disturbances. Furthermore, the control law is extended for anti‐windup compensation, mitigating adverse effects on stern and rudder plane saturation levels. Lyapunov stability theory is adopted to establish the stability of the closed‐loop system. Our simulation results convincingly demonstrate the effectiveness of the HGO‐based backstepping SMC law compared to alternative control approaches.

Backstepping Sliding Mode Control Algorithm for Unmanned Aerial Vehicles Based on Fractional-Order Theory

Aiming at the problems of slow convergence speed and low tracking accuracy in attitude control and position tracking of quadrotor unmanned aerial vehicles (UAVs). This paper combines the fractional-order calculus theory with the backstepping sliding mode control algorithm, using the backstepping control to compensate for the nonlinearity of the system and the fractional-order theory to eliminate the jitter brought about by the sliding mode control, and proposes a new fractional-order backstepping sliding mode control strategy for the trajectory tracking control of the quadrotor UAV. The proposed fractional-order sliding mode surface increases the control flexibility and improves the robustness and anti-interference ability of the system to some extent. The stability analysis of the system is carried out using the Lyapunov stability theory, and the results prove the stability of the proposed controller. Finally, the effectiveness and feasibility of the proposed method are verified by comparing it with the traditional backstepping sliding mode controller. The simulation results show that the fractional-order reverse-step sliding mode control algorithm proposed in this paper is significantly better than other control algorithms in terms of convergence speed and also has a certain degree of superiority in terms of error elimination.

Fault-tolerant attitude control of the satellite in the presence of simultaneous actuator and sensor faults

In this paper, a robust attitude control algorithm is developed based on backstepping sliding mode control for a satellite using reaction wheels and thrusters that can perform its mission despite faulty actuators. In this method, the actuator dynamics have been considered to design the controller and the asymptotic stability of the proposed algorithm has been proven based on the Lyapunov theory. The designed controller can converge the attitude of the system into the desired path in the presence of faulty actuators. Then a fault-tolerant attitude estimation system is designed based on federated unscented Kalman filters that can be effectively employed to detect and isolate sensor faults. Finally, the performance of the designed attitude estimation and controller is investigated by simulation in the presence of both actuator and sensor faults.

Adaptive fractional backstepping intelligent controller for maximum power extraction of a wind turbine system

Controlling wind power plants is a challenging issue, however. This is due to its highly nonlinear dynamics, unknown disturbances, parameter uncertainties, and quick variations in the wind speed profiles. So robust controllers are needed to overcome these challenges. This paper suggests two novel control approaches for doubly fed induction generator-based wind turbines. Its key objective is to regulate the generator speed and rotor currents. A radial basis function (RBF) neural network disturbance observer based fractional order backstepping sliding mode control (SMC) is presented to control the rotor currents. This RBF neural network-based disturbance observer estimates unknown disturbances. Also, a new adaptive fractional order terminal SMC is suggested for the control of the generator speed. This robust chattering-free controller that does not require any information about the bound of uncertainties fractional calculus is adopted in the SMC design to eliminate undesired chattering phenomena. The controller parameters are optimally tuned utilizing the ant colony optimization algorithm. The proposed approach was validated using a simulation study entailing various conditions. Its performance was also compared to that of the conventional backstepping and conventional backstepping sliding mode controller. The simulations results verified the approach's ability to maximize power extraction from the wind and properly regulate the rotor currents. The proposed method has about 20% less tracking error than the other two methods, which means 20% higher efficiency.

Coordinated Control of Quadrotor Suspension Systems Based on Consistency Theory

This paper designs a cooperative control method for the multi-quadrotor suspension system based on consistency theory and realizes the cooperative formation trajectory tracking control of the multi-quadrotor suspension system by designing a consistent formation cooperative algorithm of virtual piloting and a nonlinear controller. First, a new quadrotor suspension system model is established based on the traditional quadrotor model using the Newton–Euler method. This model can accurately reflect the influence of the load on the quadrotor while obtaining the swing of the load. Then, the vertical and horizontal positions are designed separately based on the quadrotor motion characteristics, and the formation algorithm based on the virtual pilot consistency theory ensures that the final convergence of each position is consistent. An integral backstepping controller and an integral backstepping sliding mode controller are designed for quadrotor position, attitude, and load swing control to achieve accurate and fast quadrotor trajectory tracking control while reducing load swing. The stability of all the controllers is demonstrated using Lyapunov functions. Finally, a multi-quadrotor suspension system formation cooperative simulation experiment is designed to verify the designed control method.

Adaptive Neural Network-Based Sliding Mode Backstepping Control for Near-Space Morphing Vehicle

In order to obtain good flight performance in the near-space morphing vehicle (NMV) cruise phase, this paper proposes an adaptive sliding mode backstepping control scheme based on a neural network, aiming at the reduction of elevator control efficiency and issues of uncertainties. Firstly, this paper analyzes the aerodynamic parameters of NMV in the states of winglet stretching and retracting during the cruise phase. Based on the above, the flight efficiency of NMV can be improved by retracting winglets in the level flight mode and stretching winglets in the altitude climbing mode. Secondly, an enhanced triple power reaching law (ETPRL) is proposed to ensure that the sliding mode control system can converge quickly and reduce chattering. Then, the sliding mode control based on ETPRL and backstepping control are combined to ensure the stability of the system, and adaptive control laws are developed to estimate and compensate for uncertainties. In addition, in face of the problem of reduced elevator control efficiency, the adaptive neural network is used to estimate and compensate for interference on the control channel to improve tracking accuracy and robustness of NMV. Finally, three sets of simulations verified the effectiveness of the proposed method.

Nonlinear dynamics and chaos control of circular dielectric energy generator

The current study focuses on the nonlinear dynamics of the dielectric elastomer generator (DEG). To begin with, we will go through DEG’s operating principles, parameters, materials, and deformation modes. On this basis, the dynamical modeling for the nonlinear behavior of the DEG system is described, and the second-order nonlinear ordinary differential equation representing radially symmetric motion is derived using Hamilton’s variational principle. A static applied electric field allows the DEG system to attain two equilibrium states: thick and thin. The effects of the stiffening phenomenon on the dynamics of the DEG system are investigated. The system converges to a stable equilibrium point under constant loads, and the convergence position and velocity are closely related to both the initial states. Subjected to periodic loads, certain phenomena such as quasiperiodicity and chaos are detected, and the chaotic phenomena are explored using the bifurcation diagram and 0-1 chaos test. Furthermore, parametric studies are carried out using numerical analyses to demonstrate the influence of load amplitude and external frequency on the dynamics of the DEG system. Once the DEG enters the chaotic regime, the chaotic zone is transformed into a stable manifold using established chaos control techniques such as system parameter change and parametric perturbation. However, because these techniques require changes in system design, we proposed a chaos control by using a non-linear controller, specifically, adaptive integral backstepping sliding mode control (AIBSMC) as one demonstrative candidate. The controller also enables the DEG system to follow motion along a predefined trajectory. The current work may be expected to substantially impact the future design and performance of energy harvesters.