Terminal Attractor Research Articles

Adaptive backstepping control using a novel dual-differentiator for multi-degree-of-freedom manipulator uncertain systems with unknown multi-disturbances

In this article, the adaptive sliding mode backstepping controller (ASMBC) using a novel dual-differentiator is proposed for multi-degree-of-freedom (MDOF) manipulator systems with uncertain states and multi-disturbances. The dual-differentiator comprises a tracking differentiator (TD) and a disturbance observer (DOB) based on the proposed TD. A novel tracking differentiator based on the inverse hyperbolic sine function and terminal attractor function (IHSTD) is introduced to reconstruct unknown states like velocity responses of the manipulator systems. Furthermore, the other differentiator, DOB based on aforementioned IHSTD (IHSTD-DOB), is involved in estimating the uncertain and stochastic multi-disturbances affecting the manipulator systems. Then, an ASMBC scheme, combining proposed dual-differentiator, is developed for achieving accurate tracking control of manipulator. Additionally, to handle the “explosion of term” issue in backstepping control, the designed IHSTD is also utilized to estimate the derivative of the virtual control law. The stability of the controller is rigorously analyzed using the Lyapunov method. Finally, numerical simulation results are presented to validate the effectiveness of the proposed scheme. Comparison experiments with the traditional DOB, the scheme except IHSTD, and the classical sliding mode control method are carried out by Simulink. The results illustrate that the present control method not only has an excellent tracking performance but also accurately estimates the unpredictable multi-disturbance and reconstructs the unknown states of the manipulator systems.

Design of Fractional-Order Non-Singular Terminal Sliding Mode Observer Sensorless System for Surface-Mounted Permanent Magnet Synchronous Motor

A new sensorless speed control system for a fractional-order terminal non-singular sliding mode surface-mounted permanent magnet synchronous motor is proposed. The fractional terminal non-singular sliding mode surface, which can converge in finite time, is designed by combining the fractional-order control theory with the terminal attractor concept. Then, a new control rate is proposed to reduce system buffeting. Secondly, an adaptive back electromotive force filter is designed to reduce the harmonics in the sliding mode function estimation and improve the observation accuracy. In addition, the theoretical analysis of the designed system proves that the system can converge in a finite time. Then, a fraction-order phase-locked loop with variable factors is designed to make the system more capable of tracking the rotor. Finally, a simulation and experiment platform is built, and a comparison experiment is carried out, which proves that the designed algorithm has a stronger rotor position tracking ability and a better dynamic performance of the system.

Research on Optimal Fast Terminal Sliding Mode Control of Horizontal Vibration of High-speed Elevator Car System

An optimal fast terminal sliding mode control strategy is proposed to suppress effectively the horizontal vibration of the high-speed elevator car system is caused by uncertainties such as rail unevenness, elevator load variation, and component friction and wear. Firstly, considering the elevator's composition structure and vibration characteristics, a 4-degree-of-freedom car system horizontal vibration active control model with a symmetric distribution of the control center is established. Secondly, considering the nonlinear factors of the rolling guide shoe and the external excitation, an optimal fast terminal sliding mode controller (PFTSMC) based on the sliding mode variable structure control is designed to eliminate the horizontal vibration of the car, define the nonsingular terminal sliding mode surface, and introduce the fast terminal convergence law based on the fast terminal attractor to ensure the accessibility of the sliding mode motion and reduce the jitter vibration. In addition, optimization of controller parameters using random weight particle swarm algorithm (RNW-PSO) to improve the controller's vibration suppression performance and robustness. Finally, the proposed controller can achieve more than 51.2% attenuation of horizontal vibration acceleration and displacement, showing that PFTSMC can effectively reduce the horizontal vibration of high-speed elevator car systems and improve ride comfort.

Improved active disturbance rejection speed control for autonomous driving of high-speed train based on feedforward compensation.

Due to the complex and changeable train operation environment and the unstable and time-varying parameters, accurate modeling is limited. Therefore, a modified active disturbance rejection control algorithm based on feedforward compensation (FC-MADRC) is proposed targeting the speed control problem of trains under the circumstances of external disturbances, which reduces the dependence on the train model. Firstly, the state space equation is established based on the single-particle mathematical model of the train, and all the running resistances are regarded as disturbances. Secondly, the FC-MADRC algorithm is designed. Based on the terminal attractor function and the novel Sigmoid function, an improved tracking differentiator (ITD) is designed. An improved fal (nsfal) function with better smoothness is constructed by using the properties of the Dirac δ function, and an ameliorative nonlinear state error feedback (ANLSEF) and a modified extended state observer (IESO) are designed based on the nsfal function. Furthermore, based on the thought of PID, the integral term of error is introduced into ANLSEF for the nonlinear operation to reduce the steady-state error of train speed tracking. In order to promote the robustness and control accuracy of the system, the feedforward compensation term and disturbance compensation term are combined to perform dynamic compensation for disturbances in real time. Finally, the simulation is carried out with CRH380A train data. The results indicate that compared with conventional ADRC and 2DOF-PID, FC-MADRC has the more vital anti-disturbance ability and higher tracking accuracy. FC-MADRC has the advantages of solid anti-disturbance, fast response, and high tracking accuracy. Under the premise of external disturbance, it can still achieve accurate speed tracking under different road conditions.

Nonsingular fast terminal sliding mode control for two-stage converters of AC island photovoltaic microgrid

Taking into account almost all kinds of variations and uncertainties to which AC island photovoltaic (PV) microgrid is often subjected, this paper proposes a new nonsingular fast terminal sliding mode control (NFTSMC) strategy for two-stage converters to enhance robustness against those disturbances and improve system dynamic performance. Firstly, to effectively decrease the adverse effect on the system from intermittent solar irradiation and uncertain environmental temperature, a NFTSMC cascaded with perturb and observe (P&O) scheme is put forward for fore-stage DC/DC converter, and PV output voltage is controlled to track its reference and thus maximum power point tracking (MPPT) performance is improved. Then, to significantly decrease the adverse effect on the system from variations of load and LC filter parameters, by incorporating an extended state observer (ESO) into NFTSMC, an ESO-based NFTSMC scheme is proposed for post-stage DC/AC converter, and the load voltage is regulated to track its reference and thus system robustness is strengthened, in which ESO is designed to replace load current sensor and thus reduce hardware cost. By using global terminal attractor without discontinuous switching function, the proposed NFTSMC strategy can not only strengthen system robustness but also improve system dynamic performance. Lastly, on account of the variations of PV generation and load demand, a conventional double-loop PI scheme is put into use for bidirectional DC/DC converter and thus system power balance is ensured. Comprehensive MATLAB simulation and StarSim/Hardware experiment results show that the proposed NFTSMC strategy for two-stage converters can overcome negative effects caused by various internal and external disturbances, and thus enable island PV microgrid to operate reliably and supply high-quality AC power.

DESIGN OF A FAST ADAPTIVE NEURO-SLIDING MODE CONTROLLER FOR PIEZOELECTRIC ACTUATORS

In this paper, an adaptive controller is applied to the piezoelectric actuators, PEA, in order to handle them. Our paper deals with the design of a new adaptive neuro-fast terminal sliding mode controller. The new adaptive control law using the terminal attractor concept is used in the finite time control procedure of the non-linear model. The PEA converges to the desired trajectory in a very short time. The controller allows for obtaining good results in terms of trajectory tracking and error minimization. The adaptive scheme is used to reduce the high noise order presented in piezo materials, especially at the micro-positioning level. The results of the simulations undertaken have demonstrated the robustness of the proposed approach and make it possible not only to guarantee the high accuracy of the monitoring but also to maintain the high stability of the piezoelectric actuator.

Improved Adaptive Terminal Sliding-Mode Reaching Law for Speed Control of TPMLSM With Disturbance Observer

This paper investigates the speed regulation issue of the tubular permanent magnet linear synchronous motor (TPMLSM) control system based on sliding-mode control (SMC) and disturbance compensation technology. By introducing the terminal attractor on the basis of exponential reaching law, an improved adaptive terminal sliding-mode reaching law (IATSMRL) is proposed to ensure the state variables of the control system to reach their equilibrium points quickly and suppress the chattering effectively. Based on the IATSMRL, the sliding-mode speed controller is designed to improve the dynamic performance of the TPMLSM control system. To further compensate the lumped disturbance in the TPMLSM control system, the paper utilizes an extended sliding-mode disturbance observer (ESMDO) to obtain the estimated lumped disturbance. Then an anti-disturbance sliding-mode speed controller is designed to strengthen the disturbance rejection capability of the TPMLSM control system and further improve the dynamic performance. The stability of the controller is proved by the Lyapunov stability theory. Comprehensive simulation and experimental results have been carried out to demonstrate the superiority of the proposed method.

A New Fast Control Strategy of Terminal Sliding Mode with Nonlinear Extended State Observer for Voltage Source Inverter.

To overcome the sensitivity of voltage source inverters (VSIs) to parameter perturbations and their susceptibility to load variations, a fast terminal sliding mode control (FTSMC) method is proposed as the core and combined with an improved nonlinear extended state observer (NLESO) to resist aggregate system perturbations. Firstly, a mathematical model of the dynamics of a single-phase voltage type inverter is constructed using a state-space averaging approach. Secondly, an NLESO is designed to estimate the lumped uncertainty using the saturation properties of hyperbolic tangent functions. Finally, a sliding mode control method with a fast terminal attractor is proposed to improve the dynamic tracking of the system. It is shown that the NLESO guarantees convergence of the estimation error and effectively preserves the initial derivative peak. The FTSMC enables the output voltage with high tracking accuracy and low total harmonic distortion and enhances the anti-disturbance ability.

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

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

On a Finitely Activated Terminal RNN Approach to Time-Variant Problem Solving.

This article concerns with terminal recurrent neural network (RNN) models for time-variant computing, featuring finite-valued activation functions (AFs), and finite-time convergence of error variables. Terminal RNNs stand for specific models that admit terminal attractors, and the dynamics of each neuron retains finite-time convergence. The might-existing imperfection in solving time-variant problems, through theoretically examining the asymptotically convergent RNNs, is pointed out for which the finite-time-convergent models are most desirable. The existing AFs are summarized, and it is found that there is a lack of the AFs that take only finite values. A finitely valued terminal RNN, among others, is taken into account, which involves only basic algebraic operations and taking roots. The proposed terminal RNN model is used to solve the time-variant problems undertaken, including the time-variant quadratic programming and motion planning of redundant manipulators. The numerical results are presented to demonstrate effectiveness of the proposed neural network, by which the convergence rate is comparable with that of the existing power-rate RNN.

Trajectory Tracking of UAVs Using Sigmoid Tracking Differentiator and Variable Gain Finite-Time Extended State Observer

The problem of quadrotor attitude and position control is considered in the presence of generally lumped disturbances: external disturbances and model uncertainty. The improved active disturbance rejection controller (ADRC) for quadrotor trajectory tracking is proposed for compensating the lumped disturbances. Firstly, the improved sigmoid tracking differentiator (ISTD), combining improved Sigmoid function and sliding mode terminal attractor is proposed, which can accelerate the global convergence rate and effectively reduce the chattering. Secondly, a novel variable gain finite-time extended state observer (VGFESO) approach is proposed to effectively estimate the lumped disturbances, while the observation errors are convergent to zero in finite time. Then, a super-twisting sliding model controller (STWSMC) is utilized for tracking control of the desired position and attitude. Finally, the convergence of VGFESO and the closed-loop stability of the control system are proved. The results show that the convergence time of the proposed control scheme is the shortest, and the integral absolute error of improved ADRC is reduced from 2.64 to 0.91. The anti-disturbance capability of the proposed controller is fully illustrated when compared with ADRC and robust adaptive nonsingular fast terminal sliding-mode controller (RANFTSMC).

Study on influence of switching frequency on sliding mode control performance of permanent magnet synchronous motor

Aiming at the deficiencies of the speed loop PI control algorithm of permanent magnet synchronous motor (PMSM) in variable working conditions, a new fast reaching law sliding mode control algorithm based on double-power is proposed. Firstly, a new sliding mode reaching law is proposed, and the reaching law includes system state variables and the power function of the terminal attractors. It can reach the sliding mode surface at a faster speed, reduce chattering and improve system performance. Secondly, the reachability and existence of the new reaching law are proved by the Lyapunov function, and a new reaching law sliding mode controller (NRLSMC) is designed. Then, the theoretical analysis of the switching frequency of the system is carried out, and the effects of different switching frequencies on the performance of sliding mode control (SMC) of PMSM are explored. Simulation and experimental results demonstrate that the proposed NRLSMC can effectively attenuate the disadvantages of large overshoot and long transition time under variable working conditions compared with ordinary sliding mode controller (OSMC) and PI controller. Moreover, the relative optimal switching frequency that improves the above performance is obtained, and the existence of the optimal sampling period for stable convergence of the system is proved.

Experimental Investigation of an Adaptive Fuzzy-Neural Fast Terminal Synergetic Controller for Buck DC/DC Converters

This study proposes a way of designing a reliable voltage controller for buck DC/DC converter in which the terminal attractor approach is combined with an enhanced reaching law-based Fast Terminal Synergetic Controller (FTSC). The proposed scheme will overcome the chattering phenomena constraint of existing Sliding Mode Controllers (SMCs) and the issue related to the indefinite time convergence of traditional Synergetic Controllers (SCs). In this approach, the FTSC algorithm will ensure the proper tracking of the voltage while the enhanced reaching law will guarantee finite-time convergence. A Fuzzy Neural Network (FNN) structure is exploited here to approximate the unknown converter nonlinear dynamics due to changes in the input voltage and loads. The Fuzzy Neural Network (FNN) weights are adjusted according to the adaptive law in real-time to respond to changes in system uncertainties, enhancing the increasing the system’s robustness. The applicability of the proposed controller, i.e., the Adaptive Fuzzy-Neural Fast Terminal Synergetic Controller (AFN-FTSC), is evaluated through comprehensive analyses in real-time platforms, along with rigorous comparative studies with an existing FTSC. A dSPACE ds1103 platform is used for the implementation of the proposed scheme. All results confirm fast reference tracking capability with low overshoots and robustness against disturbances while comparing with the FTSC.

Backstepping sliding mode fault-tolerant control for the wind turbine system with disturbance observer

To guarantee the safe and stable operation of wind farms, this article establishes a backstepping sliding mode fault-tolerant controller for the wind turbine system to surmount uncertain problems, including actuator gain–bias faults, system modeling errors, and external stochastic disturbances. The nonlinear disturbance observer is employed for the stochastic disturbances, which can online estimate and compensate the external disturbance term. In addition, the backstepping control strategy is introduced to reduce the complexity of fault-tolerant controller design. Subsequently, combining the backstepping control algorithm and nonlinear disturbance observer, a disturbance observer-based backstepping sliding mode fault-tolerant control approach is applied for the wind turbine system. Thereinto, the terminal attractor is employed, which is mainly utilized to improve the convergence rate of the sliding surface and reduce the chattering phenomenon. The stability of the wind power closed-loop control system is rigorously verified via Lyapunov stability theory, which can obtain satisfactory control performance. Finally, numerical simulation results demonstrate that the proposed control approach can guarantee that the system state quickly reaches stability within 6–8 s, and the steady-state adjustment time is greatly reduced to 50%–62% when compared with the proportional–integral–derivative control and sliding mode control.

Research on NFTSMC Speed Control of Improved Terminal Attractor of Permanent Magnet Synchronous Motor Based on SM-MRAS

Research on NFTSMC Speed Control of Improved Terminal Attractor of Permanent Magnet Synchronous Motor Based on SM-MRAS

Robust Adaptive Fuzzy Control of Nonlinear Systems

In this paper, an adaptive Fuzzy Fast Terminal Synergetic Controller (FFSC) for a certain class of SISO unknown nonlinear dynamic systems is proposed, that uses the concept of terminal attractor design, adaptive fuzzy synergetic control scheme, and Lyapunov synthesis approach. In contrast to the existing adaptive fuzzy synergetic control design, where the fuzzy systems are used to approximate the unknown system functions while the synergetic control guarantees robustness and achieves the asymptotic stability of the closed-loop system, in our technique both the continuous synergetic control law and the fuzzy approximator are derived to ensure finite-time convergence. Lyapunov conditions for finite-time stability and accuracy proofs in mathematics are presented to prove that the proposed adaptive scheme can achieve finite-time stable tracking of reference input and guarantee of the bonded system signals. Simulation results illustrate the design procedures and demonstrate the performance of the proposed controller.

Artificial Intelligence of Things-Based Optimal Finite-Time Terminal Attractor and Its Application to Maximum Power Point Tracking of Photovoltaic Arrays in Smart Cities

The combination of artificial intelligence of things (AIoT) and photovoltaic power generation can save energy and reduce carbon emissions and further promote the development of smart cities. In order to obtain the maximum power output from photovoltaic (PV) arrays, we can use optimal maximum power point tracking (MPPT) technique with AIoT sensing to improve system efficiency. The optimal MPPT technique is the finite-time terminal attractor (FTTA) based on the gradient particle swarm optimization (GPSO), which can be applied to track the maximum power of a PV array system. The FTTA not only provides fast finite-time convergence but also attenuates steady-state errors, making it ideal for nonlinear system applications. The GPSO is used to search the control parameters of the FTTA, which is able to find the global best solution. This avoids unmodeled dynamic behavior of the system excited by the quiver, which slows down the control convergence and prematurely traps the system into a local optimum. The MATLAB computer software is used to simulate the proposed PV maximum power point tracking system. The results show that more accurate and better tracking control of the PV array can be produced under partial shading conditions and then improve the steady-state and transient performance.

Optimal guidance for lunar soft landing with dynamic low-resolution image sequences

To relieve the burden of obtaining high-precision lunar surface information during lunar soft landing, a new guidance algorithm based on dynamic low-resolution image sequences is proposed. The integrated procedure of dynamic descent stage considering obstacle-avoiding requirement without the hover measurement is designed, which enables the spacecraft to optimize the final landing site by rolling in orbit. A small number of points are used to obtain the variance, slope and roughness of the field of vision subarea, and the shortest distance spiral search algorithm is used to determine the safest landing point. In order to reduce unnecessary control, an acceptance domain algorithm of alternative landing sites is designed to judge whether or not to accept the change of landing sites in dynamic low-precision image sequences. Assuming that the control acceleration is adjustable, the non-singular fast terminal sliding mode (NFTSM) controller based on terminal attractor is adopted and improved, and the stability of the closed-loop system is also proved. The validity, reliability and effectiveness of the proposed guidance algorithm are verified by numerical simulation on the case with disturbance and large sample data. The results demonstrate that the image information required for stable lunar soft landing is far less than that of the traditional methods, which can greatly reduce the burden of the onboard computer.

Learning-Based Control for Deployment of Tethered Space Robot via Sliding Mode and Zero-Sum Game

The underactuated dynamics with input saturation due to limited tension is the greatest challenge of stabilizing the deployment of tethered space robot (TSR), and existing sliding mode methods rely on the assumptions of inherently bounded control command and vanishing state-dependent disturbance. This paper proposes a nearly optimal control law based on variable construct control and neural network technique, which can get rid of the assumptions. The new reduced-order system with synchronization states can be established by the nearly optimal reaching law based on the zero-sum game strategy, which is approximately solved by the actor-disturbance-critic neural network. Meanwhile, the terminal attractor is synthesized into the sliding surface to enhance fast convergence. A numerical simulation was conducted to verify the proposed analyses, and this study’s results show that the method works effectively to ensure a fast response of the underactuated dynamics under limited input and disturbance.

Fractional-order deployment control of space tethered satellite via adaptive super-twisting sliding mode

This paper proposes a novel adaptive super-twisting sliding mode control scheme with the fractional-order terminal attractor, realizing a fast and stable deployment of space tethered satellite (STS). The considered STS system takes both in-plane and out-of-plane motions into account, whose nonlinear dynamics and open-loop error dynamics are derived. The proposed scheme investigates a super-twisting sliding mode controller with the fractional-order terminal attractor, and an adaptive law based on the RBF neural network (RBFNN) estimator. Significantly, the former accelerates the convergence speed of system states and smooths the control effect. The latter handles the adverse effect of system uncertainty and external disturbance, receiving a more stable deployment performance. According to the presented Lyapunov-based approach, the adaptive gains of the proposed controller are derived to adjust the control effect adaptively under the practical situation, and the finite convergence time is estimated to verify the finite-time stability. Finally, simulation results on the tether deployment of STS are provided to validate the effectiveness and superiority of the proposed controller.