Backstepping Control System Research Articles

Dynamic uncertainty propagation analysis framework for nonlinear control problem based on manifold learning and optimal polynomial method and its application on active suspension system

A novel uncertainty propagation method based on manifold learning and optimal polynomial model is proposed to quantify and analyze the dynamic uncertainties of the nonlinear feedback control system. To deal with the multiple objectives and constraints of the nonlinear control problem, a barrier Lyapunov-function-based nonlinear filtered backstepping controller is developed and applied to active suspension system to obtain superior ride comfort performance under limited structural constraints. Considering the errors in the production, manufacturing, and assembly, the probability density function is employed to quantify the structural parameter uncertainties in the nonlinear control system. Moreover, to reveal the dynamic propagation mechanism of uncertainties in the system with nonlinearity, the manifold learning method is proposed to reduce the dimensionality of the dynamic system to avoid the complexity of uncertainty propagation. Simultaneously, data-driven optimal polynomial model is utilized to accurately approximate the internal mechanism of nonlinear filtered backstepping control system. Based on that, the response uncertainties of the nonlinear control system are accurately and quickly quantified through dynamic moment information and uncertain fluctuation space. Finally, an active suspension system with nonlinearities and uncertainties is developed to verify the effectiveness of the controller with improved ride comfort and better handling safety and the superiority of the framework in terms of efficiency and accuracy of the dynamic uncertainty propagation analysis for nonlinear control problem.

Robust neuro-adaptive command-filtered back-stepping fault-tolerant control of satellite using composite learning

This study proposes an adaptive neural command-filtered backstepping control system for precise and fast attitude control of a satellite considering different uncertain dynamics. Mission success crucially depends on robust attitude control resilient to model uncertainties, unmodeled dynamics, external disturbances, and actuator faults. The proposed approach synergistically combines a neural network for handling model uncertainties, unmodeled dynamics, and actuator faults, with a disturbance observer for compensating external disturbances and neural network estimation errors. The command-filtered backstepping technique avoids the explosion of complexity inherent to traditional backstepping, while integrating integral action into the design results in the elimination of the steady-state tracking error. Besides, a composite learning method optimizes the update laws for the neural network and disturbance observer weights, enhancing control performance. Despite the presence of uncertainties, the closed-loop system stability is guaranteed by the Lyapunov stability theorem. Simulation results demonstrate the proposed controller’s ability to handle severe actuator faults, unmodeled dynamics, and measurement noise without requiring explicit fault detection and isolation schemes.

Safe Robust Adaptive Motion Control for Underactuated Marine Robots.

This article presents an innovative approach to the design of a safe adaptive backstepping control system. Tailored specifically for underactuated marine robots, the system utilizes simple sensors for enhanced practicality and efficiency. Given their operation in diverse oceanic environments fraught with various sources of uncertainties, ensuring the system's safe and robust behavior holds paramount importance in the control literature. To address this concern, this paper introduces a control strategy designed to ensure robustness at both the kinematic and dynamic levels. By emphasizing the compensation for the system uncertainties, the design integrates a straightforward fuzzy system structure. To further ensure the system's safety, a funnel surface is defined, followed by the design of a suitable nonlinear sliding surface as a function of the funnel and tracking error. Using Lyapunov theory, the study formally establishes the Semi-globally Practically Finite-time Stability of the closed-loop system, validated through simulations conducted on underactuated marine robots.

Self-Stabilizing Control Strategy of Stabilized Platform for Rotary Steerable Drilling System Based on Adaptive Backstepping Control

To enhance the robustness of the toolface angle control in a fully rotary steerable drilling tool, a backstepping control law and a drilling fluid flow adaptive law are devised based on the dynamic model of the stable platform. The Lyapunov function is constructed, and it is proven that the adaptive backstepping control system of the stabilized platform is stable. Furthermore, in order to address problems such as the friction dead zone and excessive rotational kinetic energy in the stabilized platform system, which could cause toolface angle oscillations and the rapid rotation of the stabilized platform, we additionally propose an online estimation method for the balancing torque and velocity-angle control switching strategy. By combining the backstepping control law, drilling fluid flow adaptive law, and velocity-angle control switching strategy, a self-stabilizing control strategy for the stabilized platform is established. In comparison with the PID control method, the simulation results show the superiority of the proposed scheme under complex disturbances from a downhole environment. And the drilling simulation experiment results indicate that the proposed control method has a good anti-interference capability under various conditions, including drilling fluid flow rate, inclination angle, and drill collar rotational speed. Therefore, the proposed control method can improve the robustness of the stabilized platform control system.

Intelligent Backstepping Control of Permanent Magnet-Assisted Synchronous Reluctance Motor Position Servo Drive with Recurrent Wavelet Fuzzy Neural Network

An intelligent servo drive system for a permanent magnet-assisted synchronous reluctance motor (PMASynRM) that can adapt to the control requirements considering the motor’s nonlinear and time-varying natures is developed in this study. A recurrent wavelet fuzzy neural network (RWFNN) with intelligent backstepping control is proposed to achieve this. In this study, first, a maximum torque per ampere (MTPA) controlled PMASynRM servo drive is introduced. A lookup table (LUT) is created, which is based on finite element analysis (FEA) results by using ANSYS Maxwell-2D dynamic model to determine the current angle command of the MTPA. Next, a backstepping control (BSC) system is created to accurately follow the desired position in the PMASynRM servo drive system while maintaining robust control characteristics. However, designing an efficient BSC for practical applications becomes challenging due to the lack of prior uncertainty information. To overcome this challenge, this study introduces an RWFNN as an approximation for the BSC, aiming to alleviate the limitations of the traditional BSC approach. An enhanced adaptive compensator is also incorporated into the RWFNN to handle potential approximation errors effectively. In addition, to ensure the stability of the RWFNN, the Lyapunov stability method is employed to develop online learning algorithms for the RWFNN and to guarantee its asymptotic stability. The proposed intelligent backstepping control with recurrent wavelet fuzzy neural network (IBSCRWFNN) demonstrates remarkable effectiveness and robustness in controlling the PMASynRM servo drive, as evidenced by the experimental results.

Research on RBF neural network adaptive control of three-point contactless measuring device for CNC roller grinder

Abstract In order to improve the CNC roll grinder production efficiency, a novel three-point non-contact measurement device is proposed. An adaptive back-stepping control system that combines with a radial basis function neural network (RBFNN) was designed to control the measurement device working position and also to track the periodic reference movement trajectory. In the proposed control system, the RBFNN approximation and tracking ability are used to identify the unknown measuring device dynamic information. Then, the Lyapunov stability theorem is used to derive the adaptive online learning algorithm. All control algorithms are placed in the control chip based on the TMS320F28335 archive. The simulation results show that the proposed control system has a good control effect when applied to the three-point non-contact measuring device in CNC roll grinders.

Higher-order tracking properties of adaptive backstepping control systems

This paper shows that an adaptive backstepping control system with relative degree ρ has the higher-order tracking properties: the ith-order derivatives of the tracking error e(t)=y(t)−ym(t) (between the system output y(t) and its reference trajectory ym(t) whose jth-order derivatives are bounded, for j=0,1,…,ρ) converge to zero asymptotically with time t, for i=1,…,ρ−1, in addition to the commonly-seen zero-order tracking property: e(t) converges to zero. Such new higher-order tracking properties hold for various adaptive backstepping control systems with asymptotic zero convergence of e(t), indicating that the tracking capacity of such systems is more than what has been known.

Robust Backstepping Control Combined with Fractional-Order Tracking Differentiator and Fractional-Order Nonlinear Disturbance Observer for Unknown Quadrotor UAV Systems

In this paper, we studied a fractional-order robust backstepping control (BSC) combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. A fractional-order filtered error and a fractional-order tracking differentiator were utilized in a conventional BSC system to improve the positioning control performance of a highly coupled nonlinear quadrotor UAV system and bypass the differentiation issue of the virtual control and compensation of the transformation error in the conventional BSC design. A new fractional-order disturbance observer with the sine hyperbolic function was then proposed to enhance the estimation performance of the uncertain quadrotor UAV. Sequential comparative simulations were conducted, demonstrating that the proposed positioning controller and observer utilizing fractional-order calculus outperformed those of the conventional controller and observer systems.

A New Intelligent Dynamic Control Method for a Class of Stochastic Nonlinear Systems

This paper presents a new method for a comprehensive stabilization and backstepping control system design for a class of stochastic nonlinear systems. These types of systems are so abundant in practice that the control system designer must assume that random noise with a definite probability distribution affects the dynamics and observations of state variables. Stochastic control is intended to determine the time course of control variables so that the control target is achievable even with minimal cost. Since the mathematical equations of stochastic nonlinear systems are not always constant, not every model-based controller can be accurate. Therefore, in this paper, a type-3 fuzzy neural network is used to estimate the parameters of the backstepping control method. In the simulation, the proposed method is compared with the Type-1 fuzzy and RBFN methods. Results clearly show that the proposed method has a very good performance and can be used for any system in this class.

Trajectory control and vibration suppression of rigid‐flexible parallel robot based on singular perturbation method

AbstractTo accurately, stably, and efficiently control the complex rigid‐flexible coupled robot, this paper takes Delta robot as the study object and decomposes it into slow subsystem and fast subsystem in different timescales by using singular perturbation principle, which the slow subsystem representing the rigid motion and the fast subsystem representing flexible vibration. In addition, the backstepping control system is designed for the slow subsystem, and the dynamic surface control system based on K‐observer is designed for the fast subsystem, and the overall control scheme is proposed by combining the backstepping control system and the dynamic surface control system, and the stability of the proposed overall control scheme is proven. Finally, the proposed control scheme is compared with proportional derivative control and trajectory control with workspace lattices, and the related experimental results are analyzed in details.

Backstepping Control of Switched Reluctance Motor with Artificial Neural Network based Flux Estimator

The paper presents a new approach to design a nonlinear controller for switched reluctance motors (SRMs) based on backstepping technique and artificial neuron network (ANN) in flux estimator. Backstepping controller with an ANN flux estimator will be applied for controlling SRMs which have a nonlinear drive model. The ANN flux estimator was trained off-line using backpropagation algorithm. The stability of the closed control loop was analyzed and proved accroding to the Lyapunov stability standard. The numerical simulation results confirmed the accuracy of the estimator and the quality of the backstepping control system.

Retraction Note to: Integral Backstepping Control of LPMSM Drive System Using Revised Recurrent Fuzzy NN and Mended Particle Swarm Optimization

A linear permanent magnet synchronous motor (LPMSM) drive system is keeping in many nonlinear effects such as the external load force, the flux saturation, the cogging force, the column friction and Stribeck force, and the parameters variations. Due to the uncertainty effects the existing linear controllers can not achieve better control performances for the LPMSM drive system. To raise robustness under occurrence of uncertainty, the integral backstepping control system with hitting function is proposed for controlling the LPMSM drive system in accordance with the Lyapunov function. To improve larger chattering phenomenon under uncertainties effects, the integral backstepping control system with revised recurrent fuzzy neural network (RRFNN) and mended particle swarm optimization (MPSO) is proposed to operate the LPMSM drive system to raise robustness of system. The RRFNN is used to estimate the value of the external lumped force uncertainty. Moreover, the error compensation control with the error compensation mechanism is proposed to compensate the minimum reconstructed error of the error estimation law. Besides, four variable learning rates in the weights of the RRFNN are regulated by virtue of MPSO with segment regulation to speed-up parameter’s convergence. Finally, comparative performances through some tentative upshots are verified that the integral backstepping control system by virtue of RRFNN with MPSO has better control performances than those of the proposed methods for the LPMSM drive system.

Grey Wolf and Weighted Whale Algorithm Optimized IT2 Fuzzy Sliding Mode Backstepping Control with Fractional-Order Command Filter for a Nonlinear Dynamic System

In this study, a fractional-order sliding mode backstepping control method was proposed, which involved the use of a fractional-order command filter, an interval type-2 fuzzy logic system approximation method, and a grey wolf and weighted whale optimization algorithm for multi-input multi-output nonlinear dynamic systems. For designing the stabilizing controls of the backstepping control, a novel fractional-order sliding mode surface was suggested. Further, the transformed errors that occurred during the recursive design steps were easily compensated by the controllers constructed using a new fractional-order command filter. Thus, the differentiation issue of the virtual control in the conventional backstepping control design could be bypassed with a simpler controller structure. Subsequently, the unknown plant dynamics were approximated by an interval type-2 fuzzy logic system. The uncertainties, such as the approximation error and the external disturbance, were compensated by the fractional-order sliding mode control that was added in the backstepping controller. Furthermore, the controller parameters and the fuzzy logic system were optimized via a grey wolf and weighted whale optimization algorithm to obtain a faster tuning process and an improved control performance. Simulation results demonstrated that the fractional-order sliding mode backstepping control scheme provides enhanced control performance over the conventional backstepping control system. Thus, in this paper, a fractional-order sliding mode surface and fractional-order backstepping control are studied, which provide more rapid convergence and enhanced robustness. Furthermore, a hybrid grey wolf and weighted whale optimization algorithm are proposed to provide an improved learning performance than those of conventional grey wolf optimization and weighted whale optimization methods.

Performance improvement of modern variable-velocity wind turbines technology based on the doubly-fed induction generator (DFIG)

In the latest decades, Green energies received significant support from the international community and became the key solution for the global environmental issues caused by the increasing consumption of fossil fuels. One of the cleanest sources of renewable energy that allow producing green energy is wind power which is developing with a fast rate and becoming mature and more economically competitive due to the advanced techniques for extraction. Today, the modern wind power systems technology is based on the variable-velocity Doubly Fed Induction Generators (DFIGs). To improve the operation, the production and the stability of the modern variable-velocity wind turbines technology, the current paper proposes an adaptive backstepping control structure for a wind power system based on the doubly-fed Induction generator (DFIG) in power grid-connected mode. This adaptive nonlinear control structure is proposed to cope with nonlinearity and effects of the parameter uncertainties and variations in the DFIG wind power system under study, whose main purpose is the power extract optimization from variable-velocity DFIG wind turbine while enhancing the stability of the whole system. Design of the adaptive nonlinear backstepping control system as rotational velocity and rotor current regulators have been implemented based on the wind power system dynamic model with unknown parameters. The system’s unknown parameters are dynamically estimated through the parameters adaptive update laws formulated during the design process, and these estimation laws together with the control actions for the DFIG-wind turbine are derived in such a way that the stability of the whole system according to the Lyapunov stability theory is ensured. Numerical simulation tests were conducted to evaluate the robustness and effectiveness of the proposed adaptive control structure. The obtained results show clearly that the proposed method has advanced robustness to cope with the system parameter variations and uncertainties.

Adaptive neural network and nonlinear electrohydraulic active suspension control system

In this article, an adaptive neural network control system is proposed for a quarter car electrohydraulic active suspension system coping with dynamic nonlinearities and uncertainties. The proposed control system is primarily designed to stabilize a sprung mass position of the quarter car electrohydraulic active suspension. Linear controllers such as the proportional–integral–differential controller have limited control performances. The limited control performances are caused by dynamic phenomena such as nonlinearity, parametric uncertainties, and stiff external disturbances. To overcome these dynamic phenomena, we propose a combined adaptive radial basis function neural network with a backstepping control system for a quarter car active suspension system. This setup can handle the unmatched model uncertainty of the system, while the adaptive neural network can take care of its unknown smoothing functions. In general, radial basis function neural network can represent a complicated function, and therefore, semi-strict-feedback dynamic systems are considered to simplify the adaptive neural network control design. Simulation results are indicated to illustrate adaptive neural network control effectiveness.

Permanent-Magnet SLM Drive System Using AMRRSPNNB Control System with DGWO

Because permanent-magnet synchronous linear motors (SLM) still exhibit nonlinear friction, ending effects and time-varying dynamic uncertainties, better control performances cannot be achieved by using common linear controllers. We propose a backstepping approach with three adaptive laws and a beating function to control the motion of permanent-magnet SLM drive systems that enhance the robustness of the system. In order to reduce greater vibration in situations with uncertainty actions in the aforementioned control systems, we propose an adaptive modified recurrent Rogers–Szego polynomials neural network backstepping (AMRRSPNNB) control system with three adaptive laws and reimbursed controller with decorated gray wolf optimization (DGWO), in order to handle external bunched force uncertainty, including nonlinear friction, ending effects and time-varying dynamic uncertainties, as well as to reimburse the minimal rebuild error of the reckoned law. In accordance with the Lyapunov stability, online parameter training method of the modified recurrent Rogers–Szego polynomials neural network (MRRSPNN) can be derived by utilizing an adaptive law. Furthermore, to help reduce error and better obtain learning fulfillment, the DGWO algorithm was used to change the two learning rates in the weights of the MRRSPNN. Finally, the usefulness of the proposed control system is validated by tested results.

Fractional-order command filtered backstepping sliding mode control with fractional-order nonlinear disturbance observer for nonlinear systems

This study developed a fractional-order command filter-based backstepping control (BSC) combined with a fractional-order sliding mode surface and a fractional-order nonlinear disturbance observer. The fractional-order based command filter was introduced to obtain a much faster convergence time than the previous command filter and resolve an explosion of complexity of BSC. Next, the fractional-order sliding mode surface was combined directly with the recursive controller-design process of the BSC system to enforce robustness to a disturbance compared to the conventional BSC system. Finally, the fractional-order nonlinear disturbance observer was considered to obtain fast and improved disturbance estimation performance over the conventional integer-order based one. The proposed fractional-order BSC control system showed more straightforward controller structure and improved performance than the conventional integer-order based BSC system. This was proven by a comparative simulation of a nonlinear dynamic system.

Linear permanent magnet synchronous motor drive system using AAENNB Control system with error compensation controller and CPSO

Due to nonlinear friction and uncertainty effects of linear permanent magnet synchronous motor (LPMSM), the existing linear controllers cannot achieve good control performance. In order to increase the robustness of system under some uncertainties disturbances, the proposed adaptive amended Elman neural network backstepping (AAENNB) control system with error compensation controller is adopted for controlling the LPMSM drive system. Firstly, the field-oriented control (FOC) is applied to formulate the dynamic equation of the LPMSM drive system. Secondly, a backstepping approach is proposed for controlling the motion of LPMSM drive system. The proposed backstepping control system and the mover position of the LPMSM drive system possess good transient control performance under the uncertainties action for the tracking of periodic references. Because of the LPMSM with nonlinear and time-varying dynamic characteristics, an adaptive amended Elman neural network uncertainty observer (AAENNUO) with the adaptive law is proposed to estimate the required lumped uncertainty. Moreover, the error compensation controller with the error estimation law is proposed to compensate the minimum reconstructed error according to Lyapunov stability theorem. Furthermore, to improve convergent speed and to obtain better learning performance, the varied learning rate of the weight in the AENN is regulated by use of the corrected particle swarm optimization (CPSO) algorithm with segment regulation mechanics, that is, the innovativeness for using the CPSO algorithm. At last, the usefulness of the proposed control system is confirmed by experimental results.

RETRACTED: Integral backstepping control with RRFNN and MPSO of LPMSM drive system

A linear permanent magnet synchronous motor drive system is existed in many nonlinear effects such as the external load force, the flux saturation, the cogging force, the column friction and Stribeck force, and the parameters variations. Due to the uncertainty effects, the linear permanent magnet synchronous motor drive system is hard to achieve the good control performance by using linear controller. To raise robustness under occurrence of uncertainty, the integral backstepping control system with hitting function is first proposed for controlling the linear permanent magnet synchronous motor drive system. The used integrator can ameliorate the system’s robustness under the parameters uncertainties and external force disturbances. To reduce vibration of control strength, the integral backstepping control system by means of the revised recurrent fuzzy neural network with mended particle swarm optimization is next proposed to operate the linear permanent magnet synchronous motor drive system to raise robustness of system. Furthermore, four variable learning rates in the weights of the revised recurrent fuzzy neural network are adopted by using mended particle swarm optimization to speed up parameter’s convergence. Finally, comparative performances through some experimental upshots are verified that the integral backstepping control system by means of revised recurrent fuzzy neural network with mended particle swarm optimization has better control performances than those of the proposed methods for the linear permanent magnet synchronous motor drive system.

Smart backstepping control using revised recurrent fuzzy neural network and revised ant colony optimization for linear permanent magnet synchronous motor drive system

Because of the uncertainty’s action in a linear permanent magnet synchronous motor drive system such as the external load force, the cogging force, the column friction force and the Stribeck effect force and the parameters variations, it is difficult to reach specific control performances by using the existing linear controller. To raise robustness under occurrence of parameters uncertainties and external force disturbances, the smart backstepping control system with three adaptive laws is proposed for controlling the linear permanent magnet synchronous motor drive system. In accordance with the Lyapunov function, three adaptive laws are derived to ameliorate the system’s robustness. Furthermore, the smart backstepping control system using revised recurrent fuzzy neural network and revised ant colony optimization with the compensated controller is proposed to improve the control performance. The revised recurrent fuzzy neural network acts as the estimator of the uncertainty’s disturbances. In addition, the compensated controller with error estimation law is proposed to compensate the minimum rebuilt error. Moreover, two learning rates of the weights in the revised recurrent fuzzy neural network are derived according to the discrete-type Lyapunov stability to assure convergence of the output tracking error and are adopted by using the revised ant colony optimization to speed-up parameter’s convergence. Finally, some comparative performances are verified through some tentative upshots that the smart backstepping control system by virtue of revised recurrent fuzzy neural network and revised ant colony optimization with the compensated controller results in better control performances for the linear permanent magnet synchronous motor drive system.