Terminal Sliding Mode Observer Research Articles

Disturbance-observer-based terminal sliding mode control of the quadrotor with thrust deviation fault

This paper presents a novel approach utilizing a sliding mode controller to control a quadrotor effectively in the presence of structural faults. While previous research has extensively explored fault-tolerant control for UAVs, particularly addressing faulty actuators and sensors, there remains a significant gap in addressing control methods for quadrotors experiencing structural faults. We focus specifically on scenarios where a fault in one of the quadrotor’s rotors diverts thrust from the vertical axis, complicating traditional control methods. Our proposed method involves two key steps: firstly, identifying the fault vector using a terminal sliding mode observer, and secondly, calculating appropriate control inputs using a sliding mode method based on the estimated fault vector. Simulation results demonstrate the robustness of this approach, showing accurate control performance even in the presence of multiple faults and disturbances. The system’s reliability hinges on the convergence of the disturbance observer’s estimation error to zero within a finite time frame. In conclusion, the developed controller offers a dependable solution for safely controlling a faulty quadrotor amidst high nonlinearity and uncertainty.

High-dynamic steering control of the pump-controlled electro-hydraulic steering system for heavy vehicles with active disturbance suppression

Low-frequency response, strong nonlinearity and unknown disturbances are the main challenges faced by the engineering application of the pump-controlled electro-hydraulic steering systems (EHSSs) for heavy vehicles. To solve the above problems, an active disturbance suppression controller is proposed based on a variable rate reaching law (VRRL) and a terminal sliding mode observer (TSMO) in the framework of the sliding mode control. This controller is unique because, the VRRL introduces a nonlinear activation function, which enables smooth switching between multiple reaching rates, effectively improving the response speed and the disturbance rejection performance of the pump-controlled EHSS. Furthermore, an adaptive incomplete disturbance compensation control strategy is proposed by incorporating a TSMO to further improve the accuracy and robustness of the steering system, which employs a VRRL-based TSMO to realize accurate estimation of the lumped disturbance in finite time, and avoids controller overcompensation by selecting a preferred disturbance compensation coefficient. The stability analysis demonstrates that the proposed controller effectively suppresses the lumped disturbance and reduces the convergence domain of the steering system. A pump-controlled EHSS experimental bench is constructed, and a series of experiments are conducted with various steering frequencies and load conditions, which validate the ability of the proposed controller to achieve high-precision dynamic steering in all-terrain conditions of the pump-controlled EHSS for heavy vehicles.

Research on an Active Adjustment Mechanism Based on Non-Singular Terminal Sliding Mode and Finite-Time Disturbance Observer

With the continuous development of synchrotron radiation light sources, higher requirements have been put forward for the stability of double-crystal monochromators in synchrotron radiation facilities. This paper designs an active adjustment mechanism for a double-crystal monochromator to improve its stability. Firstly, three spatial degrees of freedom are designed based on the active adjustment mechanism of flexible leaf spring parallel coupling, and the prototype of the mechanism is fabricated. Secondly, system identification experiments are carried out and the system transfer function curve is fitted by the nonlinear least squares method. Thirdly, the controller based on non-singular terminal sliding modes and a finite-time disturbance observer was designed for stability control and disturbance compensation. Finally, the effectiveness of the controller is verified by a model-in-the-loop approach based on the performance of the real-time target machine. The results show that the non-singular terminal sliding mode + finite-time disturbance observer control strategy can reduce the RMS value of the vibration displacement of Axis-1/Axis-2/Axis-3 by 81.25%, 78.53%, and 71.82%.

Sliding mode control strategy based on disturbance observer for permanent magnet in-wheel motor

A novel sliding mode control(NSMC) strategy combined with a fast terminal sliding mode observer(FTSMO) is suggested in this paper to solve the parameter variation issue of permanent magnet in-wheel motor(PMIWM) installed in the distributed drive electrical vehicle (DDEV). First, a novel sliding mode power converging law is employed to enhance the response speed of the PMIWM controller. Second, an FTSMO is suggested to compensate for the parameter variation of the PMIWM system to strengthen the robustness of the control object. Finally, a fuzzy controller is designed to adjust the control parameters of the NSMC to optimize the control performance. Several simulations and experiments demonstrate that the proposed FTSMO-NSMC scheme can precisely compensate for parameter variation of the control object and improve control accuracy effectively.

Model-free predictive flux vector control for N ∗ 3-Phase PMSM drives considering parameters mismatch

This paper develops a novel model free-predictive flux vector control method (MF-PFVC) for high-performance stator flux and torque monitoring of the multi-module three-phase PMSM (N ∗ 3-Phase PMSM) drive with parameters mismatch. The proposed MF-PFVC method is based on a convenient combination of direct predictive torque control (PTC) and model free predictive control techniques. First, the voltage source inverter (VSI) vector control of N ∗ 3-Phase PMSM is determined by the three-segment stator windings structure. Then, the parameter mismatch sensitivity of the N ∗ 3-Phase PMSM drive system is analyzed based on the conventional PTC. Furthermore, a novel MF-PFVC method with multivariable unknown disturbance integral terminal sliding mode observer (SMO) is proposed for N ∗ 3-Phase PMSM drive, which can effectively enhance robustness against the parameters mismatch. Finally, compared with the conventional PTC, the simulation and experimental results of MF-PFVC method illustrated improved stator flux control performance concerning lower stator flux ripple as well as reduced torque ripple while it can eliminate the influence of parameter mismatch.

Adaptive Quick Sliding Mode Reaching Law and Disturbance Observer for Robust PMSM Control Systems

The permanent magnet synchronous motor (PMSM) has been of interest to eco-friendly industries on account of its advantages such as high performance, efficiency, and precision control. However, perturbations due to PMSM parameter uncertainty, load torque, and external disturbance interfere with the construction of PMSM precision control systems. Therefore, a robust control system is needed to avoid unnecessary system movement caused by perturbations. In this paper, sliding mode control (SMC) is adopted to implement a robust control system for the PMSM. In order to reduce the reaching time from the initial system state to the sliding surface and the chattering phenomenon that can cause the system to malfunction, the adaptive quick sliding mode reaching law based on an exponential function and power equation is proposed. Although the SMC is robust to disturbance and parameter uncertainty, unexpected disturbances can destabilize the system. To estimate the unmatched disturbance in a short time, the second-order fast terminal sliding mode observer (SFTSMO) is proposed. The results show that the motor control system based on the proposed method has a fast convergence speed to an objective value, position tracking performance, and robustness.

Improved Position Sensorless Resonant Frequency Tracking Control Method for Linear Oscillatory Machine

To improve the reliability of control system and obtain the maximum output efficiency, it is very necessary to carry out the position sensorless piston stroke control and the resonance frequency tracking control for linear oscillatory machine (LOM) at the same time. The conventional resonant frequency tracking control method based on model reference adaptive system (MRAS) has the problem of low estimation accuracy caused by inaccurate model parameters. In order to obtain more accurate resonant frequency, an improved position sensorless resonant frequency tracking control method is proposed in this article. In this method, the adjustable model is constructed based on the mechanical dynamics equation of LOM to track the system resonant frequency. A hybrid terminal sliding-mode observer (HTSMO) is designed to replace the conventional reference model, which can obtain more accurate velocity reference signal for adjustable model by introducing the current error feedback link, thereby further improving the resonant frequency tracking accuracy. Moreover, a second-order generalized integrator (SOGI) is introduced to filter the estimated velocity signal of HTSMO. The filtered velocity signal is not only used for the adjustable model to track the resonant frequency, but also used to obtain the smooth piston stroke signal for the stroke closed-loop control. Comprehensive simulation and experimental results have proved the effectiveness and the superiority of the proposed method.

Design of Lumped Disturbance Observer in Current Loop of IPMSM Based on Recursive Integral Sliding Mode Surface

To overcome the problem of current control effect being reduced by unideal factors in a motor control system, such as motor parameter variation, inverter dead time, nonlinearity of the system, etc., a sliding mode disturbance observer for an interior permanent magnet synchronous motor is proposed in this paper. The model of an interior permanent magnet synchronous motor with unideal factors is designed, and the unideal factors are unified into lumped disturbances of motor stator voltage. Then, the observer for lumped disturbance is designed. A recursive integral sliding surface is used to replace the terminal sliding surface to avoid the noise sensitivity and singularity problem of the traditional terminal sliding mode observer. The observer can estimate the lumped disturbance of the current loop without relying on the accurate system model in finite time. Moreover, the structure of the current loop does not need to be adjusted while using the observer to observe and compensate for disturbances. Experiments are carried out to verify the effectiveness of the proposed observer.

Sensorless Control Based on Discrete Fractional-order Terminal Sliding Mode Observer for High-Speed PMSM with LCL Filter

Sensorless Control Based on Discrete Fractional-order Terminal Sliding Mode Observer for High-Speed PMSM with LCL Filter

Sensorless control strategy for permanent magnet synchronous motor based on adaptive non-singular fast terminal sliding mode observer

Sensorless control strategy for permanent magnet synchronous motor based on adaptive non-singular fast terminal sliding mode observer

Sensorless control of permanent magnet synchronous motor based on fixed‐time terminal sliding mode observer

AbstractIn the sensorless control of a sliding mode observer (SMO)‐based permanent magnet synchronous motor (PMSM), a large gain is required to ensure the stability of the sliding motion. Nonetheless, this can lead to the unexpected chattering and degrade the precision of position estimation. To overcome this trouble, we have proposed a fixed‐time nonsingular terminal SMO (NTSMO). The convergence time is independent of the initial value. Firstly, a fixed‐time nonsingular terminal sliding mode surface is designed so that the current observation error fixed‐time converges to zero, and the singularity issue can be averted. Secondly, via the phase‐locked loop tactic, the rotor position and speed are calculated from the measured back electromotive force. Thirdly, a Lyapunov function‐based proof is utilized to assure the stability of the observer. Finally, the validity of this method is confirmed by simulation tests and experiment results.

Model-free fast integral terminal sliding-mode control method based on improved fast terminal sliding-mode observer for PMSM with unknown disturbances

This paper presents a novel model-free fast integral terminal sliding-mode control (MFFITSMC) method based on an improved fast terminal sliding-mode observer (IFTSMO) for permanent magnet synchronous motor (PMSM) drive system, which can effectively eliminate the impact caused by unknown disturbances, such as parameter perturbations and external disturbances. The PMSM mathematical model with unknown disturbances is first established, and the ultra-local model (ULM) of the PMSM speed loop is constructed. Next, the model-free fast integral terminal sliding-mode controller is designed in the speed loop based on the ULM. Then, the IFTSMO is designed to precisely estimate the unknown term of the ULM, and the estimated unknown term is fed back to the MFFITSMC controller to perform compensation for unknown disturbances in real time. Finally, compared with the proportional–integral (PI) control method and the conventional model-free sliding-mode control (MFSMC) method, the results of simulations and experiments demonstrate that the presented MFFITSMC method reduces the dependence on the precise model and achieves the purpose of anti-disturbance control of the PMSM drive system.

Containment Control of Autonomous Underwater Vehicles With Stochastic Environment Disturbances

This article is concerned with a containment control issue for autonomous underwater vehicles (AUVs), subject to unavailable velocity signals in cyber side and stochastic environment disturbances in physical side. We first divide the environmental disturbances into deterministic and stochastic parts. Based on this, a terminal sliding mode observer is developed to estimate the velocities of AUVs in finite time. With the estimated velocities, a distributed containment controller is designed for each AUV to follow a convex hull spanned by trajectories of the leader AUVs. For the developed velocity observer, a double power reaching law is employed to reduce the chattering and improve the convergence rate. Besides that, an adaptive strategy is incorporated into the containment controller, such that the steady-state errors caused by stochastic environment disturbances can be compensated. Stability conditions for the velocity observer and containment controller are also provided. Finally, we conduct the simulation and experimental studies to verify the effectiveness.

Terminal sliding mode observer based dynamic surface quasi‐synchronization control of multiple electro‐hydraulic systems under compositive outputs constraint

AbstractThis paper focuses on the high accuracy synchronous control issue of multiple electro‐hydraulic systems (MEHS). For the parametric uncertainty and external load disturbance of electro‐hydraulic systems (EHS), a type of terminal sliding mode observer (TSMO) is introduced for MEHS in this paper, which able to estimate the parametric uncertainty and external load disturbance in finite time. Then, based on the proposed fast uncertainty estimation strategy, a synchronous controller is designed for MEHS, in which both dynamic surface design and barrier Lyapunov function (BLF) method has been adopted to realize a better tracking performance of MEHS. The feasibility and effectiveness of proposed algorithms in this paper are verified by simulation. Then, a series of comparative experimental results are provided to illustrate the advantages of both disturbance estimation capacity of TSMO and synchronous tracking control performance of proposed control strategy for MEHS.

Intelligent sliding mode fault-tolerant control of aviation propulsion motor system based on adaptive chaotic gray wolf optimization

In order to solve the problem of motor fault caused by extreme low temperature and vibration in the high altitude of aviation propulsion motor, using the intelligent sliding mode fault-tolerant control, a speed controller based on variable exponential power reaching law and an extended sliding mode disturbance observer is designed; furthermore, the parameters are optimized by the adaptive chaotic gray wolf optimization algorithm. In addition, a second-order nonsingular terminal sliding mode observer and a frequency adaptive complex coefficient filter are designed. First, variable exponential power reaching law is helpful to eliminate the speed tracking error and buffeting for the speed controller, the external disturbance can be estimated and compensated using the extended sliding mode disturbance observer, and adaptive chaotic gray wolf optimization algorithm can enhance the accuracy of parameters. Second, for the sake of making the aviation propulsion motor run smoothly in the case of speed sensor fault, second-order nonsingular terminal sliding mode observer is designed to estimate the speed and position of aviation propulsion motor, and adaptive complex coefficient filter is designed to improve the estimation accuracy. Finally, based on MATLAB/Simulink simulation and STM32 motor series experiments, the effectiveness of the proposed observer and controller algorithm is verified.

Event-triggered finite-time consensus control of leader–follower multi-agent systems with unknown velocities

We proposed an event-triggered finite-time consensus (FTC) control scheme for second-order leader–follower nonlinear multi-agent systems (MASs) with unknowable velocities and external disturbances. Because of the immeasurable problem of system velocities, a terminal sliding mode observer (TSMO) which forces velocity errors to converge to zero in a finite time is introduced. Then, construct a distributed event-triggered control law by backstepping method, so that each follower can update the control law independently based on its state error threshold. It is demonstrated that the control scheme can achieve FTC stability and simultaneously ensure the global robustness of the system via the Lyapunov stability analysis. Meantime, the control scheme reduces frequent updates of the control law. Furthermore, there exists a positive lower bound for the inter event time sequence so that the Zeno phenomenon is rejected. In conclusion, the validity of the consensus control protocol is verified by the numerical simulations.

Finite-time fault detection and reconstruction of permanent magnet synchronous generation wind turbine via sliding mode observer

In this study, a method for fault detection of a permanent magnet synchronous generator (PMSG) wind turbine is proposed. The dynamic model of the wind energy conversion system is simulated and the system’s fault is diagnosed using a proposed terminal sliding mode observer (TSMO). The nonlinear state-space equations of the closed-loop wind turbine are derived, which include a robust adaptive controller that is implemented for maximum power capture and a PI controller that is designed for pitch angle control. Then, utilising a new approach, a TSMO is designed for estimating the states and faults in a finite time. The stability and convergence of the states and fault estimation error are investigated via the Lyapunov stability theory. A PMSG wind turbine is simulated and using TSMO the states are estimated and a blade imbalance fault (BIF) fault is detected. The state and fault estimation errors converge to zero in a finite time.

Adaptive neural network projection analytical fault-tolerant control of underwater salvage robot with event trigger.

To solve the problem of control failure caused by system failure of deep-water salvage equipment under severe sea conditions, an event-triggered fault-tolerant control method (PEFC) based on proportional logarithmic projection analysis is proposed innovatively. First, taking the claw-type underwater salvage robot as the research object, amore universal thruster fault model was established to describe the fault state of equipment failure, interruption, stuck, and poor contact. Second, the controller was designed by the proportional logarithmic projection analytical method. The system input signal was amplified and projected as a virtual input, which replaces the original input to isolate and learn the fault factor online by the analytical algorithm. The terminal sliding mode observer was used to compensate for the external disturbance of the system, and the adaptive neural network was used to fit the dynamic uncertainty of the system. The system input was introduced into the event-triggered mechanism to reduce the output regulation frequency of the fault thruster. Finally, the simulation results showed that the method adopted in this study reduced the power output by 28.95% and the update frequency of power output by 75% compared with the traditional adaptive overdrive fault-tolerant control (AOFC) method and realized accurate pose tracking under external disturbance and system dynamic uncertain disturbance. It has been proven that the algorithm used in this research can still reasonably allocate power to reduce the load of a fault thruster and complete the tracking task under fault conditions.

Improved Position Sensorless Piston Stroke Control Method for Linear Oscillatory Machine via an Hybrid Terminal Sliding-Mode Observer

Since the piston stroke of linear oscillation machine (LOM) is very important for the safe and reliable operation of the system, it is necessary to effectively control the piston stroke. Besides, considering that the use of position sensor will reduce the system reliability, so the accurate position sensorless method is needed to obtain the stroke signals. In this article, a hybrid terminal sliding-mode observer is designed by combing a second-order nonsingular terminal sliding mode (SNTSM) and a high-order sliding-mode (HOSM) to estimate the back-electromotive force signals of the LOM. The SNTSM surface is selected to ensure that the system state variables can converge in a finite time and the HOSM control law is designed by introducing a variable exponential reaching law, which can strengthen the stability of the observer and greatly reduce the sliding chattering. Since the piston stroke is calculated by integrating the estimated piston velocity, the pure integral saturation will occur due to the presence of dc components in the measured current and voltage. In order to cope with this problem, one self-adaptive band-pass filter is introduced to replace the pure integrator, which can obtain smooth stroke signals with almost no amplitude and phase offset. Moreover, the current amplitude controller is designed to improve the control accuracy and response speed. Finally, comprehensive simulation and experimental results are provided to verify the effectiveness and the superiority of the proposed method.

Output feedback sliding mode control based on non-singular terminal sliding mode observer

In this article, the finite-time output feedback sliding mode control problem is investigated for a class of continuous-time linear systems with unmeasurable states. First, a novel terminal sliding mode observer is established to estimate the unmeasured system states. Second, a novel integral sliding surface is introduced with tunable parameters. Then, an output feedback sliding mode controller with power terms is constructed to drive the given system to the origin in a finite time. A switching from the terminal sliding mode to a usual sliding manifold is taken to avoid singularity problem. Finally, two application-oriented examples are offered to verify the effectiveness of the proposed algorithm.