Fixed-time control for upper-limb exoskeleton with bounded disturbances

The coaxial tilt-rotor (CTR) unmanned aerial vehicle (UAV) is a distinctive multirotor aircraft which incorporates two coaxial tilt-rotor (CTR) modules and a rear rotor, enabling it to execute diverse maneuvers and achieve high-speed forward flight. In this work, according to the specific configuration of the CTRUAV, a cascaded fixed-time (FT) control strategy and a nonlinear state-varying mixer are proposed to improve the CTRUAV's stability, transient performance, and robustness. The FT convergent property of the designed control strategy is validated and discussed by simulations. Finally, real-time experiments are implemented on a self-built CTRUAV experimental platform. The simulations and experimental results with different controllers demonstrate the effectiveness and superiority of the designed control method.

A virtual synchronous machine (VSM) is a converter which, compared to other types of converters, has more friendly interactions with the power grid because it is able to simulate the external characteristics of a synchronous machine, which can provide virtual inertia and damping. When the grid voltage is unbalanced, there will be negative sequence current and power oscillations. There will also be double-frequency ripples on the DC bus, which affect the normal operation of the DC power source or load. In order to solve these problems, a comprehensive control strategy is proposed in this paper. The principle of a VSM operated as a current source converter, also called VISMA, is used in the design. A complex coefficient filter is applied to separate the positive and negative sequence components of the grid voltage. By analyzing the reasons of power oscillations under unbalanced voltage, the electrical simulation part of the VSM is improved to achieve several objectives: to suppress negative sequence current and DC voltage ripples. Additionally, the rated voltage in the reactive control part is adaptively adjusted to stabilize the system. The validity of the proposed control strategy is verified by simulation and experiment.

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.

Event-triggered attitude control for hypersonic morphing vehicles using fixed-time control technique

This paper proposes a novel command-filtered backstepping control method integrated with nonlinear disturbance observers (NDO-CFBS) to improve early-stage rehabilitation training for patients with lower-limb dysfunction across multiple postures, including sitting, lying, and standing. A backstepping control strategy is first developed for the human–robot system, considering the characteristics of passive rehabilitation training. Nonlinear disturbance observers (NDOs) are designed to compensate for model uncertainties and external disturbances. A command filter is then introduced to efficiently compute the derivatives of the virtual control variables within the backstepping framework, leading to the formulation of the NDO-CFBS method. Finally, simulation results of trajectory tracking performance are presented for the multi-posture lower limb rehabilitation robot, demonstrating the effectiveness of the proposed control strategy.

In this article, the singularity-free adaptive fuzzy fixed-time control problem is studied for an uncertain n-link robotic system with the position tracking error constraint. The controlled robotic system can be described as a multiple-input-multiple-output system.To implement the user-defined performance, an improved error conversion mechanism based on performance functions is presented such that the converted error is limited to an interval greater than zero, and an appropriate barrier Lyapunov function (BLF) is constructed to avoid the breach of position tracking error constraint. The fuzzy approximator is utilized to estimate the unknown functions. The significance and challenges of this article are to establish a new error conversion mechanism and design corresponding BLF that can be integrated into fixed-time control design to present a singularity-free adaptive fuzzy fixed-time control scheme. Benefits of the proposed adaptive fixed-time controller in comparison to the current approaches are that it cannot cause the singularity issue appearing in backstepping-based fixed-time control design and ensures quick transient response. Combining with Lyapunov stability theory, the boundedness of the closed-loop signals is ensured, and the position tracking error can be constrained in the user-defined performance boundaries. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Hệ thống chống bó cứng phanh (ABS) là một hệ thống an toàn giúp bánh xe không bị khoá cứng trong quá trình phanh khẩn cấp, đảm bảo người lái có thể kiểm soát được phương tiện và tối ưu quãng đường phanh. Vì vậy, nghiên cứu và thử nghiệm về một bộ điều khiển phi tuyến mạnh mẽ có thể áp dụng được cho hệ thống này là rất quan trọng và cần thiết. Nghiên cứu này sẽ đề xuất một chiến lược điều khiển thời gian xác định (FTC), đưa sai lệch độ trượt hội tụ trong một khoảng thời gian xác định được tính toán từ trước. Nghiên cứu cũng đề xuất một bộ ước lượng độ trượt đặt tối ưu kết hợp với bộ điều khiển để nâng cao sự bền vững của hệ thống khi xe đi trên các điều kiện đường khác nhau. Bộ điều khiển trượt toàn cục (GSMC) được đưa ra để so sánh với bộ điều khiển đề xuất. Kết quả mô phỏng trên phần mềm CarSim kết hợp MATLAB/Simulink đã chứng minh được tính khả thi của hệ thống.

The leader-follower consensus problem of first-order multi-agent systems with nonzero leader's control input and external disturbances is studied in this paper. By designing a novel fixed-time controller to solve consensus problem. The controller can better suppress external disturbance and non-zero leader's control input. Through fixed-time control strategy, each followers can achieve consensus with the leader at the setting time, the system achieves rapid stability, and the setting time is irrelevant of the initial state of the system. Finally, the effectiveness of the proposed controller is verified by a numerical simulation example.

This paper focuses on the design of a disturbance rejection controller for a tailless aircraft based on the technique of nonlinear dynamic inversion (NDI). The tailless aircraft model mounted on a three degree-of-freedom (3-DOF) dynamic rig in the wind tunnel is modeled as a nonlinear affine system subject to mismatched disturbances. First of all, a baseline NDI attitude controller is designed for sufficient stability and good reference tracking performance of the nominal system. Then, a nonlinear disturbance observer (NDO) is supplemented to the baseline NDI controller to estimate the lumped disturbances for compensation, including unmodeled dynamics, parameter uncertainties, and external disturbances. Mathematical analysis demonstrates the convergence of the employed NDO and the resulting closed-loop system. Furthermore, an anti-windup modification is applied to the NDO for control performance preserving in the presence of actuator saturation. Subsequently, the designed control schemes are preliminarily validated and compared via simulations. The baseline NDI controller demonstrates satisfactory attitude tracking performance in the case of nominal simulation; the NDO augmented NDI controller presents significantly improved ability of disturbance rejection when compared with the baseline NDI controller in the case of robust simulation; the anti-windup modified scheme, rather than the baseline NDI controller nor the NDO augmented NDI controller, can preserve the closed-loop performance in the case of actuator saturation. Finally, the baseline NDI scheme and the NDO augmented NDI scheme are implemented and further validated in the wind tunnel flight tests, which demonstrate that the experimental results are in good agreement with that of the simulations.

Nowadays the feedback linearization and backstepping techniques are introduced as methods for linearization of a system with coordinate transformation and nonlinear designing, respectively. The feedback linearization and backstepping techniques are robust methods, however this study indicates that combining of them and adding nonlinear disturbance observer increases the system robustness. In this paper, the system linearization with backstepping process has been studied. Combining of above mentioned techniques has been used for linearization in this method. The systems have been practically exposed to disturbances and uncertainties. Nonlinear disturbance observer has a good ability to estimate disturbances and nonlinear dynamics, so it is useful method for increasing performance of control methods, reducing the effects of disturbances and system uncertainties. The presented control method with nonlinear disturbance observer improves the system robustness against different types of uncertainties, so this method is a modified technique. The proposed design process consists of two steps: First, the nonlinear disturbance observer has been designed to estimate the uncertainties and external disturbances applied to system. Second, a controller has been designed using combined feedback linearization-backstepping method that used prior estimations to decrease the effects of external disturbances and uncertainties in the control input.

In this paper, a speed–current single‐loop control strategy for permanent magnet synchronous linear motors (PMSLMs) with load variations is investigated. First, a second‐order model of the PMSLM is developed by combining the speed and q ‐axis current. Then, a speed regulation strategy consisting of a nonsingular terminal sliding mode control and second‐order nonlinear disturbance observers is designed for the developed second‐order model to improve the response and disturbance rejection performance of the PMSLM. The matched and mismatched disturbances of the second‐order model are estimated by second‐order nonlinear disturbance observers. The convergence of the studied control strategies is analyzed by the Lyapunov theory. Finally, the simulation and experimental results show the advantages of the studied control strategy in terms of response and robustness compared with the PID and SMC based on cascade structure.

This paper investigates the optimization control of clamping force in electronic-mechanical braking (EMB) systems, which are characterized by significant nonlinearities. To address the impact of factors such as gaps, wear, friction, and disturbances on the clamping force output accuracy within the brake actuator, an improved sliding mode control strategy (ISMC) embedded with a nonlinear disturbance observer (NDO) is proposed. The control strategy targets the clamping force and comprehensively accounts for the nonlinear aspects of the EMB system by modeling them as composite disturbances. A cascaded NDO is used to predict and compensate for the total disturbances in real-time, thereby improving control precision. Furthermore, the sliding mode control rate is enhanced by replacing the traditional switching function with a saturation function to mitigate chattering effects. Simulation and experimental results demonstrate that the proposed EMB controller can rapidly and accurately align the output clamping force with the target value, without compromising system stability. It significantly suppresses chattering, adapts to road surfaces with varying friction coefficients, and improves response speed by 44.2%, while reducing overshoot by an average of 79.67% across various braking conditions. Additionally, the controller is capable of rapidly and accurately adjusting the target value in response to sudden wheel load changes, ensuring stability and reliability during the braking process and reducing the vehicle’s braking distance by an average of 7.61%. In long-duration braking tests, the disturbance compensation mechanism allows the controller to estimate and compensate for output errors in real-time, minimizing the risk of performance degradation due to prolonged braking. In conclusion, the EMB controller designed in this study significantly enhances the braking system’s response speed, stability, and safety under dynamic and complex conditions.

This paper presents an improved fixed-time control strategy for path tracking of autonomous gun-launched coaxial-rotor micro aerial vehicles (MAVs) operating under unknown aerodynamic forces. The proposed algorithm combines a filtered fixed-time hierarchical backstepping (FTHB) method with a fixed-time disturbance observer (FDO). Using a coordinate transformation, the complex dynamics of the MAV are decoupled into fully actuated and underactuated subsystems. The novelty of this work lies in two key contributions: (1) the design of a fixed-time hierarchical backstepping controller for the nominal system, ensuring fixed-time stability, with fixed-time filters employed to estimate virtual control inputs and thereby reduce the complexity of the backstepping design, and (2) the integration of fixed-time observers to estimate unknown disturbances in fixed time, effectively addressing the challenges posed by aerodynamic uncertainties affecting the entire system. The effectiveness of this control strategy is rigorously demonstrated through fixed-time stability analyses. A comprehensive comparative assessment, covering both qualitative and quantitative evaluations, is carried out through extensive simulations comparing the proposed controller with a fixed-time controller, a finite-time controller, and a disturbance observer-based controller. This evaluation clearly underscores the robustness and superior performance of the proposed control strategy.

Dynamic uncertainties and unknown disturbances will degrade the tracking performance of robots. When using a disturber observer-based controller, the key to effectively compensate for these uncertainties is to measure or estimate as accurately as possible any disturbance. To relax restrictions on the design of the current nonlinear disturbance observer for the robot, a universal nonlinear disturbance observer is proposed for higher estimation performance. The stability of the proposed universal nonlinear disturbance observer is theoretically analyzed and the boundaries of estimation error are proven according to the vector differential equation. Finally, the proposed universal nonlinear disturbance observer is evaluated via simulation by comparison to the nonlinear disturbance observer. The result shows a faster estimation speed and a higher estimation accuracy of the universal nonlinear disturbance observer.

For the speed and tension system of the reversible cold strip rolling mill, a dynamic surface backstepping recursive sliding mode control (DSBRSMC) strategy is proposed based on the immersion and invariance (I&I) adaptive method and the nonlinear disturbance observer (NDO). First, a relatively complete mathematical model for the speed and tension system of the reversible cold strip rolling mill driven by alternating current (AC) asynchronous motors is established. Next, the I&I adaptive method is adopted to estimate the system perturbation parameters, and the NDO is developed to observe the system uncertainty. Again, controllers for the speed and tension system are presented by combining the backstepping control, the dynamic surface control, and the recursive sliding mode control together. Theoretical analysis shows that the closed-loop system is stable in the Lyapunov sense. Finally, simulation research is conducted by using the actual data, and results show the validity of the proposed control strategy.