Command filtered backstepping control with nonlinear disturbance observer for multi-posture lower limb rehabilitation robot

This paper deals with the tracking control problem of quadrotor unmanned aerial vehicles (QUAVs) with external disturbances. First, because the QUAV model contains two non-integrity constraints, the dynamic model of the QUAV is decomposed into two subsystems which are independently controlled, so as to reduce controller design complexity. Secondly, the nonlinear disturbance observer (DOB) technique is integrated into a backstepping control method to design the controller for the first subsystem, in which a DOB is applied to estimate the lumped uncertainty. Based on the double power reaching law and the DOB, a multivariable sliding mode control (MSMC) scheme is developed for the second subsystem. Thirdly, based on Lyapunov theory, the closed-loop system is proved to be asymptotically stable. Finally, our comparative simulation results demonstrate that the presented control scheme behaves better in terms of tracking performance than the adaptive backstepping control (ABC) approach.

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 order to improve the coordinated tracking control performance for the speed and tension system of reversible cold strip rolling mill, a backstepping control strategy is proposed based on command filter in this paper. Controller for each of the speed and tension subsystems is designed based on backstepping respectively, meanwhile the command filters are adopted to generate the virtual control inputs and their first time derivatives, which avoid the “differential explosion” phenomena during using the backstepping control, optimize the controller structures, and improve the coordinated tracking control performance of the system effectively. Theoretical analysis shows that the resulting speed and tension closed-loop system is globally asymptotically stable. Finally, simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill by using the actual data, and results show the superiority of the proposed control strategy in comparison with the decentralized overlapping control strategy.

Based on a nonlinear disturbance observer, a backstepping sliding mode robust control is proposed for a wire-driven parallel robot (WDPR) system used in the wind tunnel test to dominate the motion of the end effector. The control method combines both the merits of backstepping control and sliding mode robust control. The WDPR is subject to different types of disturbances, and these disturbances will affect the motion precision of the end effector. To overcome these problems, a nonlinear disturbance observer (NDO) is designed to reject such disturbances. In this study, the design method of the nonlinear disturbance observer does not require the reliable dynamic model of the WDPR. Moreover, the design method can be used not only in the WDPR but also in other parallel robots. Then, a backstepping design method is adopted and a sliding mode term is introduced to construct a desired controller, and the disturbances are compensated in the controller to reduce the switching gain and guarantee the robustness. For the sake of verifying the stabilization of the closed-loop system, the Lyapunov function is constructed to analyze the stabilization of the system. Finally, the feasibility and validity of the proposed control scheme are proved through both simulation and experimental results.

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.

Adaptive disturbance observer-based event-triggered fuzzy control for nonlinear system

In this paper, considering the simultaneous influence of multi-source disturbances, system modeling uncertainties and input–output constraints, an adaptive robust attitude tracking control scheme is proposed for near space vehicles (NSVs) which is expressed as a stochastic nonlinear system. A multi-dimensional Taylor polynomial network (MTPN) is utilized to handle the system uncertainties, and the nonlinear disturbance observer (NDO) based on MTPN is designed to estimate the external disturbances. Furthermore, by constructing the auxiliary system to tackle the input saturation and introducing the Tan-type barrier Lyapunov function (TBLF) to solve the output constraint, the constrained control strategy can be obtained. Combining with backstepping control (BC) technique and stochastic control method, an adaptive robust stochastic control scheme is developed based on NDO, MTPN, and auxiliary system, and the closed-loop system stability in the sense of probability is analyzed based on stochastic Lyapunov stability theory. Finally, numerical simulations further demonstrate the feasibility of the proposed tracking control scheme.

A sliding mode control algorithm based on nonlinear disturbance observer (NDO) is proposed for integrated guidance and control (IGC) system in this paper. Firstly, the IGC model is established as a linear system with mismatched uncertainties. Secondly, a NDO with finite time convergence is used to estimate the disturbances and their derivatives. Thirdly, an integral sliding mode surface is designed to obtain the rudder deflection command directly instead of the back-stepping control (BC) algorithm used in conventional IGC system, which achieves the real sense of IGC, and the stability of the system is proved strictly by Lyapunov stability theory. Finally, the superiority of the IGC method based on NDO is verified by simulation.

To solve the control problem for a class of uncertain pure feedback nonlinear systems subjected to external disturbances and multiple constraints, an adaptive robust control methodology is proposed based on a disturbance observer. To handle unknown nonlinearity and external unknown disturbances, a nonlinear disturbance observer is constructed based on a radial basis function neural network, which uses a Butterworth low-pass filter to remove the algebraic loop problem. Then, to guarantee that the system can stably track the desired trajectory under the state constraints, input saturation, and prescribed tracking performance constraints, we developed a novel barrier Lyapunov function and a backstepping controller that combines an auxiliary bounded function, a Nussbaum function, and a first-order sliding-mode differentiator. Subsequently, the stability of the closed-loop system is rigorously proved by Lyapunov analysis. Finally, simulations are conducted to demonstrate the effectiveness of the proposed approach.

Auxiliary-system-based composite adaptive optimal backstepping control for uncertain nonlinear guidance systems with input constraints

To enhance the power output performance of high-power electrolytic plating equipment and improve the dynamic response capability and disturbance rejection ability of the DC-DC converter—a core component in electrolytic plating systems—this study proposes a predictive control strategy for phase-shifted full-bridge converters based on an improved nonlinear disturbance observer. The implementation framework comprises three key technical components: Firstly, a model predictive control (MPC)-based inner-loop controller architecture is constructed to optimize the dynamic response characteristics of the current inner-loop system. Subsequently, an enhanced nonlinear disturbance observer is designed to accurately estimate parameter variations in converter electronic components and external disturbances. Finally, a feedforward compensation module is developed to mitigate the inherent duty cycle loss phenomenon in phase-shifted full-bridge converters. Simulation results demonstrate that the proposed control strategy significantly improves system dynamic performance, achieving a 25% reduction in settling time compared with conventional methods while maintaining robust disturbance rejection capabilities under ±10% voltage fluctuations. This integrated approach effectively addresses the conflicting requirements between dynamic response speed and anti-interference performance in high-power electrochemical process control systems.

Adaptive sliding mode control based nonlinear disturbance observer for active suspension with pneumatic spring

Multi-cable parallel suspension system (MCPSS) is designed to lift a heavy object with rapid development of deep resources exploitation. An adaptive fuzzy backstepping control strategy combining with nonlinear disturbance observer is studied to synthetically control the posture for the underactuated MCPSS with tension constraint in this article. Firstly, a theoretical modelling of the MCPSS with boundary constraints is derived by the extended Hamilton’s Principle. Secondly, the parameter uncertainties and time-varying disturbances are compensated by the fuzzy system and nonlinear disturbance observer, respectively. Thirdly, an adaptive fuzzy backstepping feedback controller based on the reference model is proposed to suppress vibration and control posture of the suspension platform. Finally, an Automatic Dynamic Analysis of Mechanical Systems (ADAMS) simulation and a numerical calculation are used to illustrate the theoretical model and the proposed control performance.

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.

Nonlinear disturbance observer based robust backstepping control for a flexible air-breathing hypersonic vehicle