Fixed-time Disturbance Observer Research Articles

Distributed fixed‐time sliding mode formation control for unmanned aerial‐ground vehicle (UAV‐UGV) heterogeneous system

AbstractThis study proposes a distributed fixed‐time sliding mode formation control (FTSMFC) method to address formation control problem for unmanned aerial‐ground vehicle (UAV‐UGV) heterogeneous system under the directed topology and subject to external disturbances. First, a distributed fixed‐time state observer (FTSO) is introduced to provide state estimation of the leader UAV, which overcomes the limitation of partial information availability among followers. Then, a novel fixed‐time disturbance observer (FTDO) is presented to enhance the system's anti‐disturbance ability by estimating and compensating external disturbances within a fixed time. Furthermore, by integrating sliding mode techniques and the information from the FTSO and FTDO, a distributed FTSMFC is developed to enforce the system to achieve predefined formation configuration within a fixed time independent of initial states of the system. Finally, a simulation comparison with the other controllers is carried out to show the validity and superiority of the proposed formation control law.

Observer-Based Fixed-Time Consensus Tracking for a Class of Nonlinear Multi-Agent Systems

In this paper, the problem of fixed-time consensus tracking for a class of nonlinear multi-agent systems (MASs) with uncertainties and external disturbances is addressed. To solve this problem, a new fixed-time consensus tracking protocol with disturbance rejection abilities is proposed that consists of a fixed-time distributed observer (FTDO), a fixed-time disturbance observer (FDO), and a nonsmooth backstepping controller with lumped disturbance compensation (NBCDC). The fixed-time stabilities are analyzed correspondingly. Firstly, an FTDO is designed to estimate a leader’s output by using the topology of communication networks for each follower. Second, an FDO is developed to observe the lumped disturbances composed of model uncertainties and external disturbances. Finally, an NBCDC is proposed for improving the closed-loop performance. The simulation results show that the proposed method is effective.

Fixed-Time Backstepping Sliding-Mode Control for Interleaved Boost Converter in DC Microgrids

Interleaved boost converters (IBCs) are commonly used as interface converters for DC microgrids (MGs) due to their high efficiency and low output ripple. However, the MGs system can easily become unstable due to the negative impedance characteristics of constant power load (CPL) and rapid power fluctuations. This paper proposes a fixed-time backstepping sliding-mode controller (FTBSMC) aimed at stabilizing the MGs system and achieving fixed-time tracking of the DC bus voltage. Firstly, the fixed-time disturbance observer (FxTDO) estimates the load disturbance at a fixed time, which improves the fast disturbance resistance of the system. Then, based on the dis-turbance estimation, the FTBSMC is designed, which combines the fast dynamic response of the sliding-mode control with the global stability of the backstepping control, avoiding the singularity problem of the conventional sliding-mode control. In addition, a first-order nonlinear filter is employed to avoid the direct differentiation of conventional backstepping control and at the same time to ensure global fixed-time stability. The fixed-time convergence of the proposed FTBSMC is rigorously demonstrated by using Lyapunov stability analysis. Finally, the FTBSMC proposed is verified by simulation and experiment in terms of faster dynamic response and stronger robustness.

A fast fixed-time backstepping control method for systems with mismatched disturbances

In this paper, a fast fixed-time backstepping control approach is developed for systems with mismatched disturbances. A novel fast fixed-time disturbance observer (FFTDO), which is convergent within fixed time regardless of initial conditions, is designed to efficiently estimate and compensate the disturbances. On the basis of FFTDO, a novel fast fixed-time backstepping control scheme is proposed, which can guarantee fast fixed-time convergence and high steady-state precision. In addition, a novel fixed-time filter is used to circumvent the problem of “explosion and complexity,” and to ensure overall fixed-time convergence. The fixed-time stability of the closed-loop system under the proposed controller is proved by the Lyapunov stability theory. The simulation results are carried out to confirm the feasibility and superiority of the proposed control strategy.

Fixed-time fractional-order sliding mode controller with disturbance observer for U-tube steam generator

Water level control of a U-tube steam generator plays a critical and challenging role in ensuring safe and reliable operation for a pressurized-water reactor-type nuclear power plant, as both excessively high and low water level in the U-tube steam generator would affect the normal operation of the nuclear power plant and even lead to unplanned shutdown events. This work presents a fixed-time fractional-order sliding mode water level controller coupled with a fixed-time disturbance observer, aiming to further improve the water level control performance under full operating conditions, considering uncertainties and actuator saturation. The proposed scheme is formulatedbased on the popular Irving water level model with uncertainties and the pre-existing actual water level control framework, while at the same time incorporating the benefits of the state-of-the-art anti-windup techniques, disturbance observer-based feedforward compensation techniques, fractional-order calculus, sliding mode control techniques, and fixed-time stability theorem, such that the transient water level response and steady-state control accuracy can be further enhanced even in the presence of uncertainties and actuator saturation phenomenon. It is theoretically proved that under the proposed scheme, both the estimation error of the uncertainties and the water level control error can be driven to zero within a fixed time regardless of their initial values by Lyapunov’s theorem. Meanwhile, simulation studies, involving the comparisons with a real-world adopted water level controller and a pre-existing integer-order sliding mode water level controller coupled with an uncertainty estimator, reveal the feasibility and superiority of the proposed approach.

Disturbance observer based fixed-time tracking control for unmanned aerial helicopters

In this paper, a fixed-time tracking control scheme based on the fixed-time disturbance observer is proposed for a 6-DOF unmanned aerial helicopter (UAH) with flight path constraints and composite disturbances. The composite disturbances are composed of external disturbances and system uncertainties. By using the hyperbolic tangent function, an improved disturbance observer is developed to estimate composite disturbances. Furthermore, a fixed-time back-stepping control method is employed for the position and attitude loops, which enables the UAH to track the expected path within the flight path constraints. Simulation results are given to demonstrate the effectiveness and advantages of the proposed scheme.

Distributed fixed-time output consensus for disturbed second-order multiagent systems with dead-zone input

This article investigates the fixed-time output consensus (FTOC) problem for second-order multiagent systems (MASs) with mismatched disturbance and dead-zone input under directed interaction topology. Firstly, a fixed-time disturbance observer is constructed for each agent to estimate the mismatched disturbance. Secondly, a new distributed control scheme based on the fixed-time stability theory and adding a power integrator approach is proposed, which solves the FTOC problem of the MASs. In addition, an explicit representation of the upper bound of settling time is also provided. Finally, two simulation examples demonstrate the feasibility and superiority of the devised control strategy.

Fixed-time disturbance observer-based funnel control for controllable excitation linear synchronous motor with state constraints

This paper proposes a fixed-time disturbance observer-based funnel control method for a controllable excitation linear synchronous motor (CELSM) with state constraints and disturbances. This approach simultaneously resolves the issues of prescribed tracking performance and state constraints, taking into account disturbances. We employ a fixed-time disturbance observer (DO) to estimate both matched and mismatched disturbances. Additionally, we design a modified funnel variable to confine the tracking error within a prescribed region and the singularity problem is avoided. An integral barrier Lyapunov function (iBLF) is utilized to directly tackle state constraints. Furthermore, we employ a fixed-time differentiator (FTD) to address the “explosion of complexity” issue in backstepping control. Theoretical analysis demonstrates that the tracking error asymptotically converges to the origin within a prescribed region while satisfying state constraints. Finally, simulation results demonstrate the efficacy of the proposed method.

Dynamic Modeling and Observer-Based Fixed-Time Backstepping Control for a Hypersonic Morphing Waverider

This paper proposes a fixed-time backstepping control method based on a disturbance observer for a hypersonic morphing waverider (HMW). Firstly, considering the disturbance of attitude channels, a dynamic model of a variable-span-wing HMW considering additional forces and moments is established, and an aerodynamic model of the aircraft is constructed using the polynomial fitting method. Secondly, the fixed-time stability theory and backstepping control method are combined to design an HMW fixed-time attitude controller. Based on the fixed-time convergence theory, a fixed-time disturbance observer is designed to achieve an accurate online estimation of disturbance and to compensate for the control law. In order to solve the problem of the “explosion of terms”, a nonlinear first-order filter is used instead of a traditional linear first-order filter to obtain the differential signal, ensuring the overall fixed-time stability of the system. The fixed-time stability of the closed-loop system is strictly proven via Lyapunov analysis. The simulation results show that the proposed method has good adaptability under different initial conditions, morphing speeds, and asymmetric morphing rates of the HMW.

Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following

As a flexible, autonomous and intelligent motion platform, underactuated surface vessels (USVs) are expected to be an ideal means of transport in dangerous and complex marine environments. The success and efficiency of maritime missions performed by USVs depend on their ability to accurately follow paths and remain robust against wind and wave disturbances. To this end, this paper focuses on accurate and robust path following control for USVs under wave disturbances. Model predictive control with a quasi-infinite horizon is proposed which converts the objective function from an infinite horizon to an approximate finite horizon, providing the convergence performance in long prediction horizons and reducing the computation load explicitly. To enhance robustness against disturbances, a fixed-time disturbance observer is applied to estimate the time-varying and bounded disturbances. The estimated value is provided to the controller input to form a robust control framework with disturbance feedforward compensation and predictive control feedback correction, which is substantially different from existing works. The convergence and optimality of the proposed algorithm are presented mathematically. Finally, we demonstrate the advantages of the algorithm in both theory and simulation.

Adaptive dynamic programming base on MMC device of a flexible high-altitude long endurance aircraft

Flexible high-altitude long endurance (HALE) aircraft face challenges such as the delay effect caused by aeroelasticity and low efficiency during high-altitude cruising. This paper addresses a new active control scheme that replaces traditional aerodynamic control surfaces with longitudinal and lateral moving masses and adopts an observer-based adaptive dynamic programming (ADP) control strategy, aiming to solve the attitude control of HALE aircraft with flexible wings. Firstly, considering the account of unsteady aerodynamics, attitude angular velocity, and moving masses, complete dynamic model is established for a flexible aircraft, in order to more accurately describe the state of the HALE aircraft. This model includes two moving masses to replace traditional ailerons and elevators. It is difficult to design attitude control strategies considering the delay effects and unknown dynamic disturbances of HALE aircraft. To this end, the actor-critic structure of the ADP approach is designed to achieve the near-optimal control strategy of the system, which eliminates the need for prior knowledge of model parameters. A fixed time disturbance observer (FTDO) is proposed to estimate the future tracking error information and unknown disturbances to improve the control performance of the attitude. Finally, the stability of the system is proved via the Lyapunov technique and a comprehensive simulation of HALE aircraft is provided. The simulation results show that the proposed control algorithm can enable the aircraft attitude angles to quickly response and maintain stability under gust wind. Compared with a single ADP control strategy, this paper's algorithm has advantages in response speed and error.

Integral barrier Lyapunov function-based fixed-time integrated guidance and control with asymmetric field-of-view angle constraints

The missile integrated guidance and control (IGC) problem with seeker’s asymmetric field-of-view (FOV) angle constraints is addressed. In the introduced model, the fin deflections controller is used to drive the body line-of-sight angle rate, which avoids the solving and tracking of aerodynamic angles in traditional IGC method. A novel fixed-time convergence virtual input based on the integral barrier Lyapunov function is designed to ensure the asymmetric FOV angle constraints are never violated. The virtual input is tracked by a new proposed pre-defined fixed time controller with adjustable initial convergence speed. The lumped uncertainty including aerodynamic coefficient and target maneuvering is coped by the fixed-time disturbance observer. It is proved that the closed-loop system states are converged to the bounded region in a fixed-time and the asymmetric FOV angle constraints are satisfied. The 6-degree of freedom flight simulations and comparisons verified the advantages of the proposed algorithm.

Fixed-time coordination control for 6-DOF attitude-orbit coupled spacecraft formation flying

This paper presents a distributed fixed-time control protocol for 6-DOF(degree-of-freedom) attitude-orbit coupled spacecraft formation flying with external disturbances. Firstly, the 6-DOF attitude-orbit coupled dynamics is established. The communication topology between the spacecraft in the formation is described by a directed graph. Secondly, a fixed-time disturbance observer (FxTDO) is designed to ensure that the estimation errors of the unknown external disturbances can converge to zero in fixed time. Thirdly, based on non-singular fixed-time terminal sliding mode (NFFTSM) surface, the fixed-time coordination control protocol is proposed combined with the fixed-time disturbance observer, which can guarantee that each spacecraft can track their desirable positions and attitudes in fixed time. The stability of the closed-loop system is proved through Lyapunuov method. Finally, simulation results for a formation with one virtual leader and five followers demonstrate the effectiveness of the proposed control scheme.

Fixed-time trajectory tracking control of a quadrotor UAV under time-varying wind disturbances: theory and experimental validation

This paper adopts a fixed-time method to study the trajectory tracking issue of a quadrotor unmanned aerial vehicle (UAV) under time-varying wind disturbances. Firstly, in order to address the impact of time-varying wind disturbances on UAV, a fixed-time disturbance observer is constructed to accurately estimate wind disturbances. Secondly, to improve control accuracy and convergence rate, a robust fixed-time controller is designed for the position and attitude system by combining the sliding mode control theory with fixed-time techniques. Furthermore, it is rigorously analyzed that the tracking error of the observer and controller can converge to zero via Lyapunov criterion, and the convergence time is independent of the initial state. Finally, the effectiveness and robustness of the designed control strategy are verified by numerical simulations and actual flight experiments, providing an effective connection between control theory and practical applications.

Fixed-time anti-disturbance constraint fuzzy synchronization control for PMSM based four-wheel-independent-drive EVs

A fixed-time anti-disturbance constraint fuzzy synchronization control method is proposed, for the sake of solving the problem of fast recovery of synchronization between in-wheel permanent magnet synchronous motors (PMSMs) in four-wheel-independent drive electric vehicles. The system model of in-wheel PMSM is presented in the beginning, and fuzzy logic systems are used for approximating the uncertainty parts of the PMSM model. Based on the PMSM model, a fixed-time disturbance-observer is designed to account for fast estimation of fluctuating load torque. Then, the neighborhood synchronization error is constructed based on a directed-graph, and a performance function is designed to guarantee the neighborhood synchronization error evolves strictly within the prescribed bound. Besides, the fixed-time bound of all signals is proved. Finally, the hardware-in-the-loop platform is built, and the electronic differential and the nonlinear vehicle model are employed to validate the advanced performance of the design control method.

Robust fixed-time flight controller for a dual-system convertible UAV in the cruise mode

This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle (UAV) in the presence of parameter uncertainties, unmodeled uncertainties and wind disturbances. First, a fixed-time disturbance observer (FXDO) based on the bi-limit homogeneity theory is designed to estimate the lumped disturbance of the convertible UAV model. Then, a fixed-time integral sliding mode control (FXISMC) is combined with the FXDO to achieve strong robustness and chattering reduction. Bi-limit homogeneity theory and Lyapunov theory are applied to provide detailed proof of the fixed-time stability. Finally, numerical simulation experimental results verify the robustness of the proposed algorithm to model parameter uncertainties and wind disturbances. In addition, the proposed algorithm is deployed in a open-source UAV autopilot and its effectiveness is further demonstrated by hardware-in-the-loop experimental results.

Disturbance observer based fixed-time control of stochastic systems

In this paper, the novel fixed-time anti-disturbance control scheme is proposed for a class of stochastic systems subjected to multiple disturbances and faults, and the disturbances consist of derivative-bounded disturbances and multiply noise. Based on the pole placement method, the fixed-time disturbance observer (Fixed-time DO) is devised to estimate derivative-bounded disturbances and an adaptive law is employed to approach the time-varying fault. Then a composite fixed-time controller is constructed to make the system converge to equilibrium position within a pre-specified time. At the same time, simulation examples illustrate that the proposed controller is effective and the convergence time is not related to the initial states of the system.

Distributed Event-Triggered Control for Manipulator with Fixed-Time Disturbance Observer

This article studies an event-triggered fixed-time trajectory tracking control problem of an n-joint manipulator system. Firstly, a fixed-time disturbance observer is proposed to reconstruct the total disturbance composed of external disturbances and model uncertainties, using the estimation as feedforward compensation to enhance the system robustness. Subsequently, based on the backstepping framework, a fixed-time controller with an event-triggering mechanism is designed for the manipulator to ensure the convergence of tracking errors to zero within a fixed time. Additionally, two event-triggering conditions are devised to reduce the transmission time of control input and the computation time of control output. Simultaneously, Zeno behavior is excluded through theoretical proof, validating the fixed-time stability of the closed-loop system. Finally, simulation verification is conducted on a two-joint manipulator, with results confirming the effectiveness of the control strategy.

Fixed-Time Trajectory Tracking Control of Fully Actuated Unmanned Surface Vessels with Error Constraints

This paper proposes a fixed-time prescribed performance control technique to address the challenge of precise trajectory tracking control for unmanned surface vessels (USVs) in the presence of external time-varying disturbances and input saturation. To begin with, a fixed-time disturbance observer is created to handle the time-varying external interference. The observer can accurately estimate and compensate for the disturbance in a fixed time, which effectively improves the robustness of the system. Furthermore, to guarantee both the transient and steady-state response of the system, we employed a specific control technology that ensures the trajectory tracking error remains within a preset bounded range. Then, combined with the fixed-time disturbance observer, the command filter, the prescribed performance control technology, and the fixed-time stability theory, a fixed-time trajectory tracking control law is designed to make the trajectory tracking error of the system converge in a fixed time. Finally, an experiment was designed to validate the suggested control scheme. The results show that under the same conditions, compared with the nonlinear controller and the finite-time controller, the absolute error tracking index of this paper is the lowest, which means that the presented control scheme has higher accuracy.

Trajectory Tracking Control of Remotely Operated Vehicles via a Fast-Sliding Mode Controller with a Fixed-Time Disturbance Observer

Time-varying nonlinear external disturbances, as well as uncertainties in model and hydrodynamic parameters, make remotely operated vehicles (ROVs) trajectory tracking control complex and difficult. To solve this problem, this paper proposes a fast sliding mode controller with a fixed-time disturbance observer (FSMC-FDO), which consists of a sliding mode controller based on a fast reaching law and a novel fixed-time disturbance observer. The FSMC can solve the contradiction between system response time and chatter amplitude in sliding mode control. The FDO can compensate for time-varying external disturbances. The Lyapunov theory is used to prove the stability of the entire control scheme. Simulation results show that FSMC-FDO exhibits a good trajectory tracking performance with a better robustness than the conventional sliding mode control (CSMC) on the basis of exponential reaching law (ERL), while significantly reducing chatter.