Robust spacecraft attitude tracking control with integral terminal sliding mode surface considering input saturation

This article investigates the attitude tracking control problem of a rigid spacecraft under the modeling inaccuracy, environmental disturbance, and input magnitude and rate saturations. A robust controller is proposed based on several nonlinear control methods, including the integral terminal sliding mode control, adaptive control, backstepping control, auxiliary system, and nonlinear observer methods. Within the control framework, a new integral terminal sliding mode surface (ITSMS) is first designed which integrates the fast nonsingular terminal sliding mode surface (FNTSMS) with a first-order filter to achieve the finite time stability without the input singularity problem. And adaptive laws are employed to compensate for the modeling inaccuracy and environmental disturbance with no prior knowledge. To satisfy the input magnitude and rate saturation constraints, a dynamic model in the form of a first-order filter is built up to restrict the dynamics of the actuators, which is then associated with the auxiliary system. Meanwhile, a nonlinear observer is used to avoid calculating the derivative of the expected virtual control signal. Semi-globally uniformly ultimate bounded stability is proved for the closed-loop system, and the tracking errors can converge to small regions around the expected equilibrium in finite time. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed controller.

This brief examines the problem of attitude tracking control with prescribed performance guarantees for a spacecraft subjected to actuator faults and input saturation. To pursue this, the open-loop tracking error dynamics with certain designer-specified performance constraints is first transformed into an equivalent “state-constrained” one, via an error transformation; furthermore, the resulting dynamics is augmented with a dynamic system, which is tactfully constructed to ensure that the control input satisfies the magnitude limits. Subsequently, a robust fault-tolerant controller is developed by using a low-pass filter and an auxiliary system in conjunction with adaptive backstepping design. It is shown that the control algorithm developed not only achieves the stable attitude tracking with prescribed behavioral metrics but also guarantees the boundedness of all the closed-loop signals. Finally, simulation results are given to evaluate the efficacy of the proposed scheme.

Neural network approximation-based backstepping sliding mode control for spacecraft with input saturation and dynamics uncertainty

The control performance of quadrotor unmanned aerial vehicles (UAVs) in complex environments can be affected by external disturbances and other factors. In this paper, an adaptive neural network backstepping controller based on the barrier Lyapunov function (BLF) is designed for a quadrotor UAV with internal uncertainties, input–output constraints and external disturbances. Radial basis function neural networks are used to approximate the uncertainties in the dynamic model of the UAV, while the minimum parameter learning method is combined to accelerate the adjustment speed of neural network weights. A robust term is designed to balance the total system disturbance and improve the anti-interference performance. The BLF is used to handle the output constraint so that the constrained parameters cannot break the predefined constraints. An auxiliary system is introduced to solve input saturation and avoid the dependence of tracking error on the input amplitude in the method of approximating input saturation using the smoothing function. The stability of the control system is demonstrated by the Lyapunov method. The simulation results show that the proposed method has high tracking accuracy compared with the backstepping dynamic surface control method, and the input and output are in the predefined range.

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

Discrete-time adaptive predictive sliding mode trajectory tracking control for dynamic positioning ship with input magnitude and rate saturations

ABSTRACTThe control performance of a permanent magnet synchronous motor (PMSM) is significantly deteriorated when faced with unknown disturbances, such as model uncertainties, parameter variations, and external interferences. This paper proposes a model‐free fast integral terminal sliding mode control (MFITSMC) approach based on an extended super‐twisting sliding mode disturbance observer (ESTSMDO), referred to as the ESTSMDO‐based MFITSMC approach. First, a unique ultra‐local model (NULM) of the PMSM is developed that accounts for unknown disturbances. Then, the MFITSMC is formulated by integrating a fast integral terminal sliding mode surface with a switching control law. The speed loop controller is designed using the MFITSMC. The ESTSMDO is meant to precisely estimate unknown disturbances and subsequently input them into the MFITSMC controller. The ESTSMDO‐based MFITSMC approach mitigates chattering and improves the system's robustness to unanticipated disturbances. Finally, the simulation and experimental validation demonstrate that the dynamic response of the PMSM system is markedly enhanced, and the chattering associated with SMC is effectively reduced.

This study investigated associations of attitude tracking control of an underactuated spacecraft with consideration of saturation and perturbations. A nonsingular attitude tracking control was proposed which did not need limiting initial conditions of the quaternions. The controller was analyzed based on Lyapunov criteria and LaSalle’s invariance theorem in the large-angle maneuver. In order to control, the complete kinematic and dynamic model of the underactuated spacecraft was reconstructed. According to simulation results, our controller has excellent robustness against the hard saturation, external disturbances, time-varying inertia uncertainties, and internal disturbances of actuators. As result, we found that the attitude controller was asymptotically stable under the soft saturation and the perturbations so that quaternions and angular velocity converged to the desired path within the 80 s. Also, it was still asymptotic stable under the hard saturation whose level is equal to 0.035 Nm, 3.5% of the soft saturation level. In this case, errors of quaternions and angular velocity were converged to the origin within the 150 s. Finally, the closed-loop system was verified by Adams-MATLAB co-simulation. The maximum verification errors for quaternions were less than 19%, while the maximum verification errors for angular velocity were less than 13.5%.

Finite-time output feedback attitude control for rigid spacecraft under control input saturation

For the spacecraft attitude system with external disturbance and system uncertainty in the task of non-cooperative target damping by electromagnetic eddy current, combining with the prescribed performance control theory, an adaptive sliding mode controller based on disturbance observer is designed in this paper. And this controller is designed to ensure the expected dynamic and steady-state responses of spacecraft attitude tracking control. A new finite time convergence performance function is designed, which doesn’t need the exact initial error value. Aiming at the problem of control singularity caused by the increase of disturbance during steady-state of the new system after error transformation, we design an adaptive sliding mode controller based on disturbance observer, in which the observation gain matrix is related to the performance function. The effectiveness and robustness of the proposed control law is verified by simulation.

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

Safety control using barrier certificates for multiagent systems with input saturation and formation constraints

A dual-loop fault-tolerant control scheme is investigated for UAV attitude control systems subject to actuator faults, input saturation, and external disturbances in this paper. In the outer loop of attitude angles, a nonlinear dynamic inversion controller is developed as baseline controller for fast response and is augmented by a neural network disturbance observer to enhance the adaptability and robustness. Considering input saturation, actuator faults, and external disturbances in the inner loop of attitude angle velocities, the unbalanced input saturation is first converted into a time-varying system with unknown parameters and disturbances using a nonlinear function approximation method. An L1 adaptive fault-tolerant controller is then introduced to compensate for the effects of lumped uncertainties including system uncertainties, actuator faults, external disturbances, and approximation errors, and the stability and performance boundaries are verified by Lyapunov theorem and L1 reference system. Some simulation examples are carried out to demonstrate its effectiveness.

A multi‐motor coordinated tracking control strategy based on a disturbance sliding‐mode observer and an anti‐saturation non‐singular fast‐terminal sliding mode is proposed to address the issues of slow convergence and controller output saturation in multi‐motor coordinated control systems. Firstly, a mathematical model of a multi‐motor traction system considering uncertain parameter perturbations, external disturbances, and dead zones was established. Secondly, a disturbance sliding‐mode observer was designed based on the mathematical model to eliminate motor disturbances and estimate the torque. The observer's forward compensation was added to design a total‐consensus‐based fast non‐singular terminal sliding‐mode controller. Then, a fast anti‐saturation auxiliary system with fast finite‐time convergence was constructed. Finally, a comparative experiment was conducted with traditional anti‐saturation sliding‐mode control to demonstrate that the proposed method had faster convergence, stronger disturbance rejection, and better tracking performance in the presence of multi‐motor parameter perturbations, unknown disturbances, and input saturation.

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.