Inertia Matrix Uncertainty Research Articles

Adaptive Sliding Mode Attitude Tracking Control for Rigid Spacecraft Considering the Unwinding Problem

Based on the unwinding problem caused by the dual valued property of the quaternion description method, this paper designs an anti-unwinding sliding mode adaptive attitude tracking control with external disturbances and inertia matrix uncertainty. The sliding mode surface used in this paper contains two equilibrium points and adopts an indirect method, which greatly reduces the computational complexity. The stability and anti-unwinding performance have been proven. The simulation results have verified the effectiveness of the control method and we have compared it with the general linear sliding mode. The results show that the control method proposed in this paper is more stable, has higher convergence accuracy and has anti-unwinding performance.

Output Feedback Control for Spacecraft Attitude System with Practical Predefined-Time Stability Based on Anti-Windup Compensator

This paper investigates the problem of output feedback attitude control for rigid spacecraft subject to inertia matrix uncertainty, space disturbance, and input saturation. Firstly, a model transformation is adopted to convert an attitude system with immeasurable angular velocity into a new system. All states of the new converted system are measurable and available for feedback; however, the system contains mismatched uncertainty resulting from the coordinate transformation. Then, an adaptive nonsingular back-stepping control with practical predefined-time convergence is designed. To resolve the problem of input saturation, an anti-windup compensator is developed. It is analytically proved that the spacecraft attitude and angular velocity are practical predefined-time stable, such that the convergence time is a given tunable constant. The simulation results reveal that the proposed control framework provides rapid attitude maneuver and actuator saturation elimination.

Tan-Type BLF-Based Attitude Tracking Control Design for Rigid Spacecraft with Arbitrary Disturbances

This study deals with the problem of disturbances in observer-based attitude tracking control for spacecraft in the presence of inertia-matrix uncertainty and arbitrary disturbance. Following the backstepping control, a tan-type barrier Lyapunov function (BLF)-based attitude tracking control method with prescribed settling time and performance is systematically developed. The proposed control framework possesses three advantages over the existing attitude controllers. Firstly, the singularity problem associated with the use of fractional power in fixed-time control is effectively resolved without employing any command filter or piece-wise continuous function. Secondly, inspired by the concept of the tan-type BLF approach, any desired performance for the attitude tracking error is satisfied. Lastly, the total disturbance, including the system’s uncertainty, external disturbances, and time-derivative of the virtual control, is precisely reconstructed during a predefined time, even if the initial estimation error tends to infinity. Moreover, this time is determined as a tunable gain in the observer. The numerical simulations confirm the superior performance of the proposed control strategy in comparison with the existing pertinent works.

Disturbance observer-based constrained attitude control for flexible spacecraft

This paper investigates the difficult issue of fixed-time constrained attitude control for a flexible spacecraft under the influence of the system uncertainties, environmental disturbance and abrupt actuator faults. The contributions of the proposed control framework are twofold. Firstly, an observer is presented to precisely reconstruct the uncertain dynamics within a fixed time regardless of the initial estimation error while the settling time is given as a specific parameter. Secondly, using a combination of prescribed performance control (PPC) and barrier Lyapunov function (BLF) approaches, a simple structure constrained attitude control for flexible spacecraft is proposed while desired performance specifications for both quaternion and rotation velocity are indirectly achieved by constraining the sliding manifold. A distinctive feature of the suggested control framework is that the settling time of the closed-loop system is finite and explicitly expressed as two tunable gains even when abrupt actuators faults happen. Numerical simulations substantiate the ability of the offered control to effectively accomplish favorable attitude maneuver under the negative effect of the inertia matrix uncertainty, external disturbances, flexible structures vibration and actuators faults.

Decentralized event-triggered finite-time attitude consensus control of multiple spacecraft under directed graph

This article investigates the finite-time consensus problem for the attitude system of multiple spacecraft under directed graph, where the communication bandwidth constraint, inertia matrix uncertainties and external disturbances are considered. An event-triggered communication mechanism is developed to address the problem of communication bandwidth constraint. In this event-triggered mechanism, spacecraft sends their attitude information to their neighbors only when the given event is triggered. Furthermore, an adaptive law is designed to counteract the effect of inertia matrix uncertainties and external disturbances. Then, a finite-time attitude consensus tracking control scheme is proposed based on the event-triggered communication mechanism and adaptive law. The proposed control scheme can guarantee the finite-time stability and convergence of the multiple spacecraft systems and exclude the Zeno phenomenon. Finally, simulation results validate the effectiveness of the proposed control scheme.

Robust gimbal reorientation singularity-avoidance steering strategy for regular pentagonal pyramid configuration with two control moment gyroscopes failed

The failure configuration which consists of four single-gimbal control moment gyroscopes (SGCMGs) of the widely-used regular pentagonal pyramid SGCMG system, i.e. failure 4-SGCMG configuration, is investigated in this paper. On account of the symmetry of regular pentagonal pyramid configuration, a conversion method which could transform any failure 4-SGCMG configuration to the chosen failure system is introduced. Then, the zero-momentum gimbal angle of the chosen failure system is derived and its distribution in gimbal angle space is analyzed. In order to avoid internal singularity, preferred initial gimbal angles are calculated basing on derivation of zero-momentum gimbal angles and the corresponding terminal singular surfaces are obtained through numerical simulations. Furthermore, a constraint about maneuver direction is introduced and a robust gimbal reorientation steering strategy is proposed. Finally, simulations on a non-chosen failure configuration with inertia matrix uncertainty demonstrate the effectiveness of the conversion method and robustness of the proposed steering law.

Rigid spacecraft robust adaptive attitude Stabilization Using state-dependent indirect Chebyshev pseudospectral method

In this paper, a robust control method is proposed for rigid spacecraft attitude stabilization under inertia matrix uncertainties and external disturbances. The attitude stabilization problem is firstly reformulated into an optimal control problem, then a state-dependent indirect Chebyshev pseudospectral (SDICP) method is designed to solve the resultant optimal control problem. It is proved that, by incorporating the uncertainties into the performance index and adaptively estimating the parameters, the stabilization problem can be converted into an infinite horizon optimal control problem. Based on successive state-dependent coefficient parameterization, time domain transformation and Chebyshev spectral discretization, the proposed SDICP method turns the resultant optimal control problem into a sequence of systems of linear equations, which can be efficiently solved by basic matrix operations. Simulation results also verify the effectiveness of the proposed robust adaptive attitude stabilization method.

Adaptive Fault-Tolerant Attitude-Tracking Control of Spacecraft With Quantized Control Torque

In this article, the problem of fault-tolerant attitude-tracking control of spacecraft with quantized control torque is addressed. Actuator faults/failures, an uncertain inertia matrix and unknown disturbances are considered in the attitude controller design of the spacecraft. A dynamical quantization strategy is developed to quantize the signals of the control torque, which can reduce the data transmission rate. An adaptive fault-tolerant controller based on sliding mode techniques is constructed to address the impacts of the actuator faults/failures, quantization errors, inertia matrix uncertainties and unknown disturbances. The developed control strategy with a quantizer can ensure that the entire closed-loop system is asymptotically convergent and achieves satisfactory attitude-tracking performance. Finally, simulation results are provided to show the effectiveness of the proposed method.

A fault-tolerant attitude tracking control of spacecraft using an anti-unwinding robust nonlinear disturbance observer

This paper investigates the application of an integral sliding mode control with a robust nonlinear disturbance observer to obtain an anti-unwinding spacecraft attitude tracking response with robustness against external disturbances, inertia matrix uncertainties, and actuator faults. In the controller design, external disturbances, uncertainties, and actuator faults are lumped together and estimated by the robust nonlinear disturbance observer. The proposed robust nonlinear disturbance observer guarantees the convergence of estimated lumped disturbance error to origin in finite time. The estimated disturbance is then used in the controller as a feed-forward compensator. Further, an adaptive law is also incorporated in the proposed controller to ensure additional robustness. The stability of the overall system and anti-unwinding characteristic are proved using the Lyapunov stability theory. Finally, numerical simulation analysis is performed in the presence of all the sources of lumped disturbances. It is observed that the proposed control strategy is ensuring higher accuracy, good steady-state precision, and eliminates the unwinding phenomenon.

Velocity-free spacecraft attitude stabilization using two control torques

The attitude stabilization of an inertial-pointing underactuated rigid-body spacecraft using two torques under time-varying disturbances and inertia matrix uncertainties is examined. An observer-based time-varying output feedback control law is proposed where angular velocity measurements are not available. The stability of the combined controller–observer system is proven rigorously to show local ultimate boundedness of all states. A comprehensive numerical example is presented with sampled-data implementation of the observer-based control law to demonstrate convergence even with very large initial attitude errors.

Robust finite-time adaptive control algorithm for satellite fast attitude maneuver

A robust adaptive finite-time controller for satellite fast attitude maneuver is proposed in this paper. The finite-time sliding mode is proposed based on standard sliding mode, hence the terminal convergence rate could be largely improved, and the inherent robustness to some typical perturbations is maintained. A new method is proposed to deal with the singularity issue based on the property of Euler rotation. In order to deal with inertia matrix uncertainty, finite-time adaptive law for inertia matrix estimation variables is proposed. Considering that the variable estimation system has no direct feedback, an auxiliary state converging slower than system is designed to achieve finite-time stability. The overall global finite-time stability is proved by Lyapunov method and the performance of the controller is demonstrated by numerical simulation results.

Robust stabilization of spacecraft attitude motion under magnetic control through time‐varying integral sliding mode

SummaryMagnetic spacecraft attitude control is suitable for missions with moderate pointing and stabilization requirements. It would be especially preferable if an implemented three‐axis magnetic control law guarantees global and moreover robust stabilization. Motivated by this consideration, in this work, the integral sliding mode control method is successfully applied to the purely magnetic attitude control problem for the first time in literature. The resulting magnetic integral sliding mode control system, which is designed via Lyapunov's direct method by taking the four major environmental disturbance torques and the full inertia matrix uncertainty into account, has the expected insensitivity against environmental disturbances in the plane of continuous actuation. Along the instantaneous direction of underactuation, which continuously varies in control space as the satellite moves along the orbit, there is no counteraction to perturbations. However, as seen in the results of the high‐fidelity simulation, state trajectories are ultimately bounded in the vicinity of the reference state independently from the initial state thanks to the proven robustness of the global stability. Performance robustness of the obtained control system against disturbances and model uncertainty is evaluated to be superior through a couple of comparisons with existing control laws even though it is partial due to the intrinsic underactuation in the system.

Time efficient sliding mode controller based on Bang–Bang logic for satellite attitude control

In order to improve the convergence rate of standard sliding mode controller, time efficient controllers based on Bang–Bang logic for satellite attitude stabilization and tracking control are developed in this paper. The time efficient open-loop control algorithm Bang–Bang control is combined with closed-loop sliding mode control to improve system robustness. A two-stage structure sliding mode with a fixed angular velocity stage and a fixed deceleration stage is proposed in this paper. The sliding mode parameter is real-time updating hence the modified sliding mode could have Bang–Bang character. The system inertia matrix uncertainty and disturbance torque is discussed and the controller proposed in this paper is robust to the perturbation. The control torque constraint is also discussed and the constraint on control parameters is given. The performance of the controller is demonstrated by numerical simulation.

Adaptive sliding mode stabilization and positioning control for a multi-vectored thrust airship with input saturation considered

This article addresses a position and attitude stabilization control scheme for a class of multi-vectored airship with parameter uncertainty and input saturation considered. Airship parameters such as the inertia matrix and aerodynamic coefficients are hard to measure due to the uneven gas distribution and unforeseen shape changing. The propellers airships use often have saturation issues. These phenomena are unavoidable. To meet these challenges, we propose two adaptive sliding mode control methods. Both achieve airship position and attitude stabilization without the prior knowledge of the inertia matrix or aerodynamic coefficients. The second algorithm also takes input saturation into consideration. Simulations illustrate the effectiveness of our scheme. Compared with former works, our method achieves position, attitude, velocity and angular velocity stabilization with inertia matrix uncertainty, aerodynamic coefficient uncertainty, and input saturation.

Velocity-Free Attitude Stabilization of a Nadir-Pointing Underactuated Rigid Spacecraft

This paper examines the velocity-free attitude stabilization of an underactuated nadir-pointing rigid spacecraft in a circular orbit in the presence of time-varying disturbances. A nonlinear observer is used to estimate the angular velocity of the spacecraft to complete an output feedback control law. A sliding-mode control strategy is proposed for this stabilization problem in conjunction with a nonlinear observer. The local ultimate boundedness of the closed-loop system is rigorously proven. Numerical examples demonstrate the performance of the controller in the presence of time-varying disturbances, nonzero orbital eccentricity, inertia matrix uncertainties, and measurement noise in a sampled data implementation. In particular, even though the theoretical ultimate boundedness guarantees are local, the numerical examples demonstrate ultimate boundedness with large initial attitude errors.

Robust finite time control algorithm for satellite attitude control

Finite time controllers robust to inertia matrix uncertainty for satellite attitude stabilization control and attitude tracking control are developed in this paper. A three-stage finite sliding mode is constructed to improve system convergence rate. The singularity issue is solved by using the property of Euler Axis when it's paralleled to angular velocity. Based on this finite time sliding mode, finite time controller is developed to ensure the system state could reach the sliding mode in finite time. System inertia matrix uncertainty and disturbance torque is considered in this paper. The control torque constraint is also considered to ensure the norm of control torque does not exceed system upper bound. Finite time stability of the controller is proved and the controller performance is demonstrated by simulation results.

Anti-unwinding constrained attitude control for flexible spacecraft with actuator saturation

In this paper, two novel anti-unwinding constrained attitude controllers for flexible spacecraft are designed based on inverse optimal approach and unit quaternion representation of attitude subjected to inertia matrix uncertainty and external disturbance. One accounts for actuator amplitude constraint and the other considers actuator amplitude and rate constraints at length. A new saturation compensator is designed and embedded into the controllers to eliminate the effect of actuator saturation. The proposed controllers can avoid the issue of attitude slewing unwinding due to the double values of unit quaternions. The stability of the resulting closed-loop systems by the proposed controllers is guaranteed by Lyapunov-based approach. Simulation results are presented to assess the performance of the proposed methods.

Continuous time-varying sliding mode based attitude control for reentry vehicle

The attitude control for reentry vehicle is responsible for the robust operation to avoid the major deterioration from parametric uncertainties and external disturbances. Targeting these practical issues, both the cases with and without a priori knowledge of upper bound on the lumped uncertainty (i.e. the joint effect caused by external disturbance and inertia matrix uncertainty) are addressed, and correspondingly two continuous time-varying sliding mode based attitude controller design strategies are proposed to achieve the robust tracking of the attitude commands while alleviating the control chattering. Firstly, to deal with the case where the upper bound on the second derivative of the lumped uncertainty is known in advance, a nonlinear disturbance observer based continuous time-varying sliding mode control algorithm is developed so that the asymptotic stability of the closed system is guaranteed. Furthermore, in order to address the more practical case that the upper bound on the lumped uncertainty is unavailable, a continuous adaptive time-varying sliding mode control algorithm is derived with the related switching gains adjusted on-line, by which the trajectories of the closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, the proposed strategies are applied to the attitude control of X-33 RLV in the reentry phase to illustrate the effectiveness of the theoretical results.

Switching Gain Reduction in Adaptive Sliding Mode Control for Rigid Spacecraft Attitude Maneuvers

This paper investigates the overadaptation problem in current adaptive sliding mode control (ASMC) for rigid spacecraft attitude maneuvers. The inertia matrix uncertainty and external disturbance are taken into account, and an adaptive scheme is employed for the switching gain calculation. A detailed analysis of existing ASMC design reveals the fact that the switching gain would be overestimated if the ASMC algorithm is developed in the framework of conventional sliding mode control (SMC), owing to the unrelated adaptation caused by initial tracking error. The global sliding mode concept of integral sliding mode control (ISMC) is exploited to solve such a problem. The advantages of the proposed strategy are twofold. First, a much smaller switching gain is generated as compared to conventional ASMC. Second, the resulting small switching gain would not slow down the system response. The advantages of the proposed strategy are verified by both theoretical analysis and simulation results.

Disturbance observer-based adaptive integral sliding mode control for rigid spacecraft attitude maneuvers

This article considers the attitude tracking problem of a rigid spacecraft involving inertia matrix uncertainty and external disturbance. The adaptive sliding mode control is utilized for the attitude controller design. The major concern is reducing the switching gain generated by current adaptive sliding mode control, thereby alleviating the chattering problem. By eliminating the influence of initial tracking error from the switching gain adaptation, an adaptive integral sliding mode control scheme is first presented. As compared with current adaptive sliding mode control, a much smaller switching gain is produced. Then, a disturbance observer-based adaptive integral sliding mode control design is proposed to further enhance the result. To this end, the joint effect caused by external disturbance and inertia matrix uncertainty, referred as lumped uncertainty, is divided into a slow varying part and a rapid varying part. By compensating the slow varying component via a disturbance observer, the switching ...