Convergence Of Position Tracking Errors Research Articles

Robust fault detection and adaptive fixed-time fault-tolerant control for quadrotor UAVs

This note scrutinizes an adaptive fault-tolerant control (FTC) approach tailored for unmanned aerial vehicles (UAVs), addressing the critical need for both fault accommodation and disturbance suppression. Departing from traditional reliance on robust discontinuous control strategies prone to chattering and demanding precise uncertainty bounds, our FTC method ensures fixed-time stability, guaranteeing the convergence of attitude tracking errors to zero. Central to our approach is an adaptive algorithm adept at concurrently estimating unknown actuator faults and upper bounds of lumped uncertainties. Moreover, our adaptive schemes accurately estimate the upper bound of the lumped uncertainty term, encompassing model uncertainties, external disturbances, and unmodeled dynamics, thereby eliminating the need for assuming known bounds on uncertainties. Stability analysis under the developed control law is thoroughly performed using the Lyapunov stability theory. Notably, our strategy employs an extended Kalman filter (EKF) observer for state estimation and fault detection, facilitating fault detection through an adaptive threshold technique dynamically adjusted based on real-time mean and variance of the residual signal. Through comprehensive simulation and experimental validations, our proposed methodology demonstrates significant advancements in ensuring safety and reliability in UAVs.

Fixed-Time Filtered Adaptive Parameter Estimation and Attitude Control for Quadrotor UAVs

In this article, a fixed-time filtered adaptive parameter estimation and control scheme is proposed for attitude tracking of quadrotor unmanned aerial vehicles. A nonsingular fixed-time sliding mode surface is constructed to avoid the existence of the singularity issue resulted from the differentiation of the sliding mode variable. Through designing auxiliary filtered matrices, a fixed-time parameter update law is developed to achieve the fixed-time parameter convergence. Then, an adaptive neural controller is designed to ensure the fixed-time convergence of attitude tracking errors in the presence of the model uncertainties. Instead of using any piecewise continuous functions, the possible singularity issue in the conventional fixed-time controller design can be overcome by constructing auxiliary functions, and thus the fixed time stability analysis becomes more concise. The efficiency of the presented scheme is validated through experiments on a practical Quanser quadrotor platform.

Fuzzy-Based Fixed-Time Nonsingular Tracker of Exoskeleton Robots for Disabilities Using Sliding Mode State Observer

In this article, the position tracking control of the wheelchair upper-limb exoskeleton robotic system is investigated with the aim of rehabilitation of disabled people. Hence, the fuzzy nonsingular terminal sliding mode control method by using the state observer with a fixed-time convergence rate is designed in three main parts. In the first part, the fixed-time state observer is proposed for estimation of the states of the system. Secondly, the fixed-time convergence of position tracking error of the upper-limb exoskeleton robot system is examined by using the nonsingular terminal sliding mode control approach. In the third part, with the target of the improvement of the controller performance for removal of the chattering phenomenon which diminishes the controller performance, the fuzzy control method is used. Finally, the efficiency and proficiency of the proposed control method on the upper limb exoskeleton robotic system are demonstrated via the simulation results which are provided by MATLAB/Simulink software. In this part, simulation results are obtained based on different initial conditions in two examples using various desired values. Thus, it can be demonstrated that the proposed method applied to the upper-limb exoskeleton robot system is robust under various initial conditions and desired values.

Semi-globally smooth control for VTVL reusable launch vehicle under actuator faults and attitude constraints

The present paper deals with the control problem of vertical takeoff vertical landing (VTVL) reusable launch vehicle (RLV) under actuator faults and multi-type attitude constraints (unilateral constraints, symmetric/asymmetric bilateral constraints, or without constraints). A semi-globally smooth control system is proposed based on a novel barrier function (BF) to realize the finite-time convergence of attitude tracking errors into a small neighborhood of the origin. Moreover, the attitude constraints unviolated under multiple disturbances are guaranteed. To further enhance the disturbance rejection ability, a BF-based adaptive disturbance observer (DO) is derived and incorporated into the control system, which is responsible for reconstructing the disturbance in finite time. The proposed control systems are characterized by the following four points. One is to ensure the finite-time convergence of attitude tracking errors and guarantee the non-violation of constraints without requiring any prior information regarding the Lipschitz constant and upper bound of the disturbance. The second is to provide a unified instrument for control problems with the aforementioned multi-type state constraints. The third is the smoothness property contributing to the chattering-free convergence of attitude tracking errors. The high performance and robustness concerning non-Lipschitz disturbance (such as the sudden actuator faults) are the fourth. Ultimately, the effectiveness of the proposed control systems was demonstrated by the numerical simulation results.

Distributed attitude consensus tracking control for spacecraft formation flying via adaptive nonsingular fast terminal sliding mode control

This article investigates the distributed attitude consensus tracking control for spacecraft formation flying with unknown external disturbances and model uncertainties. First, a terminal sliding mode disturbance observer (TSMDO) is constructed to estimate the generalized disturbances including external disturbances and model uncertainties. The finite-time convergence of the estimation errors using TSMDO is analyzed. Second, a variable structure control law is developed to avoid introducing initial errors of the TSMDO. Third, a novel adaptive nonsingular fast terminal sliding mode (ANFTSM) control law based on TSMDO is proposed to ensure the convergence of attitude tracking errors to zero. Based on theoretical analysis, the finite-time stability can be guaranteed by Lyapunov theory. Finally, the effectiveness of the developed control law is verified via numerical simulations.

Single-parameter-learning-based finite-time tracking control of underactuated MSVs under input saturation

This paper investigates the adaptive finite-time (FT) tracking control problem of underactuated marine surface vehicles (MSVs) subject to parameter uncertainties and external disturbances under input saturation. The input saturation nonlinearity is approximated employing Gaussian error function. Definition of hand position is extended to transform the original motion mathematical model of underactuated MSVs into the standard integral cascade form. The compounded uncertain vector synthesizing the uncertain parameters and unknown external disturbances is transformed into a linear parameterized form with a single parameter. Then, by employing the adaptive vector-backstepping design framework, a novel adaptive FT tracking control law is designed, and the estimation of the single unknown parameter is provided by an adaptive law online. Theoretical analysis shows that under the proposed tracking control scheme, FT convergence of position tracking errors of underactuated MSVs into a small set around the origin is ensured, while all signals in the closed-loop tracking control system are bounded. Simulation and comparison verify the effectiveness of the proposed novel adaptive tracking control scheme.

Adaptive integral backstepping controller for linear induction motors

Linear induction motors offer the possibility to perform a direct linear motion without the nead of mechanical rotary to linear motion transformers. The main problem when controlling this kind of motors is the existence of indesirable behaviours such as end effect and parameter variations, which makes obtaining a precise plant model very complicated. This paper proposes an adaptive backstepping control technique with integral action based on lyapunov stability approach, which can guarantee the convergence of position tracking error to zero despite of parameter uncertainties and external load disturbance. Parameter adaptation laws are designed to estimate mover mass, viscous friction coefficient and load disturbance, which are assumed to be unknown constant parameters; as a result the compensation of their negative effect on control design system. The performance of the proposed control design was tested through simulation. The numerical validation results have shown good performance compared to the conventional backstepping controller and proved the robustness of the proposed controller against parameter variations and load disturbance.

Anti-Unwinding Attitude Control with Fixed-Time Convergence for a Flexible Spacecraft

This paper investigates the fixed-time attitude tracking control problem for flexible spacecraft with unknown bounded disturbances. First, with the knowledge of norm upper bounds of external disturbances and the coupling effect of flexible modes, a novel robust fixed-time controller is designed to deal with this problem. Second, the controller is further enhanced by an adaptive law to avoid the knowledge of norm upper bounds of external disturbances and coupling effect of flexible modes. This control law guarantees the convergence of attitude tracking errors in fixed time where the settling time is bounded by a constant independent of initial conditions. Moreover, the proposed controllers can prevent the unwinding phenomenon. Simulation results are presented to demonstrate the performance of the proposed control scheme.

Fixed-time control for spacecraft attitude tracking based on quaternion

In this paper, the attitude tracking control problem is investigated for a rigid spacecraft. Robust finite time controllers based on the quaternion and Lagrange-like model are proposed to solve this problem with model uncertainties and external perturbations. The controllers guarantee the convergence of attitude tracking errors in fixed time, where the settling time can be set in advance, and this merit is different from all the existing controllers for spacecraft attitude tracking problem.The controllers are derived using the Lyapunov theory, so the stability of the closed-loop system is guaranteed. Moreover, the modified controllers are provided to alleviate the chattering phenomenon and eliminate the singular problem. Finally, simulation results are given to demonstrate the efficiency of the proposed methods.

Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking

This paper studies finite-time attitude tracking control problem of a rigid spacecraft system with external disturbances and inertia uncertainties. Firstly, a new finite-time attitude tracking control law is designed using nonsingular terminal sliding mode concepts. In the absence and presence of external disturbances and inertia uncertainties, this controller can drive the attitude and angular velocity tracking errors to reach zero in finite time. Secondly, a finite-time disturbance observer is introduced to estimate the disturbance, and a composite controller is developed which consists of a feedback control based on nonsingular terminal sliding mode method and compensation term based on finite-time disturbance observer. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system is ensured by the Lyapunov approach. Numerical simulations on attitude control of spacecraft are also given to demonstrate the performance of the proposed controllers.

Sliding mode tracking control of an underactuated surface vessel

This study concerns the robust tracking control problem for an underactuated surface vessel with parameter uncertainties. In recent work by McNinch and collegeaues, a sliding mode control (SMC) law is presented and experimentally implemented for trajectory tracking of an underactuated autonomous surface vessel. The authors believe, however, their theory formulation involves essential flaws. Motivated by the obtained result by McNinch and collegeaues, a new revised SMC law is proposed under the same assumptions. The control law is similarly developed by introducing a first-order sliding surface in terms of surge tracking errors and a second-order surface in terms of lateral motion tracking errors; however, the desired surge and sway velocities are presented as a new form to guarantee the convergence of position tracking errors. Simulation results are provided to validate their method.

Quaternion-based finite time control for spacecraft attitude tracking

This paper investigates the spacecraft attitude tracking control problem. Two robust sliding mode controllers based on the quaternion and Lagrange-like model are proposed to solve this problem both in the absence of model uncertainties and external disturbances as well as in the presence of these. The controllers can guarantee the convergence of attitude tracking errors in finite time rather than in the asymptotic sense, where time tends to infinity. By constructing a particular Lyapunov function, the convergences of the proposed controllers for the closed-loop systems are proven theoretically. To alleviate the chattering phenomenon while at the same time guaranteeing the finite convergence during the process of attitude tracking, a new function is introduced into the controller. Numerical simulations are finally provided to illustrate the performance of the proposed controllers.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time sliding mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode control with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a second control law is also designed by combining the second order sliding mode control and an adaptive backstepping technique.This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lyapunov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.