Attitude Stabilization Problem Research Articles

Geometric prescribed‐time control of quadrotors with adaptive extended state observers

AbstractThis article studies an adaptive extended state observer (AESO) based prescribed‐time geometric attitude stabilization problem of quadrotors with endogenous uncertainties, exogenous disturbances, and actuator saturation, which can be estimated and compensated by AESOs. The employment of the geometric representation method for system attitude can effectively avoid ambiguity or singularity problems that may arise with other representations. The temporal and scale transformations are employed to solve the global boundedness problem on infinite time instead of the prescribed‐time convergence problem on finite time. By integrating the proposed controller with the backstepping technique, the system of quadrotors can be prescribed‐time stable. Further, a prescribed‐time geometric attitude control technique is devised such that the control signal is bounded and the state signals converge to a small domain near the equilibrium point in the prescribed time. The prescribed time is determined by the user and is independent of the initial conditions. The comparative simulations with different initial information are performed to demonstrate the effectiveness of the proposed design technique.

Simple robust PD control for asymptotic stabilization of uncertain spacecraft with actuator constraints and disturbances

AbstractThis paper concerns the problem of asymptotic attitude stabilization for uncertain spacecraft subject to actuator constraints and bounded external disturbances. A simple model‐free saturated robust PD control is proposed within the framework of PD design methodology combining sliding mode control strategy. Asymptotic stabilization stability is proved in terms of Lyapunov's direct method and Barbalat's lemma. Advantages of the proposed control include the easy‐going implementation with simple and intuitive structure and explicit tuning procedure and abilities to guarantee the asymptotic attitude stabilization and bounded disturbance rejection and ensure the actuator constraint is not violated by selecting the control gains a priori. Simulation comparisons demonstrate the improved performance of the proposed approach.

Event‐driven fault‐tolerant attitude tracking control of spacecraft for noncooperative target interest surface

AbstractThis paper explores the problem of relative attitude stabilization between a noncooperative target interest surface (NCTIS) and a bandwidth‐restricted spacecraft subjected to parameter uncertainties, exogenous disturbance, actuator faults, and input saturation. The proposed angular velocity estimator provides the rotational angular velocity of NCTIS. The proposed control scheme uses a dynamic surface control framework with the finite time disturbance observer to attenuate multi‐source disturbances, and it deals with the restricted communication resources by employing a dynamic event‐triggered mechanism. The presented scheme relaxes the prior upper bound of total disturbance and improves the traditional event‐triggered technique. Stability analysis shows the ultimate uniform boundedness of the closed‐loop system's state trajectory. In addition, the Zeno‐free behavior can be guaranteed in the design. Comparing numerical simulation results with advanced techniques shows the effectiveness of the proposed scheme.

A Cubature Kalman Filter for parameter identification and output-feedback attitude control of liquid-propellant satellites considering fuel sloshing effects

The problem of parameter identification and output-feedback attitude stabilization is addressed for liquid-propellant satellites in the presence of fuel sloshing. The sloshing is described by a 2-degree-of-freedom pendulum. A torsional spring-damper system is utilized to model the flexibility of the diaphragm passive strategy and the fuel viscosity. By employing the control Lyapunov function methodology, a nonlinear backstepping-type state-feedback control law is constructed to stabilize the satellite and cancel the fuel sloshing. Then, to make the controller more feasible in practice, the required states of the controller, stiffnesses, and dampers are considered to be unavailable. Thus, a Cubature Kalman Filter is developed to estimate the system states and identify the fuel parameters. The state-feedback control law in conjunction with the Cubature Kalman Filter approach provides an output-feedback control law. This work owns the following two major novelties. One is identifying the stiffness and damping coefficients of the fuel and another is developing a Cubature Kalman Filter for estimating the resultant nonlinear system states. Lastly, comparative simulations verify and highlight the main results of the proposed methodology in relation to the existing methods. The findings suggest that the Cubature Kalman Filter offers potential advantages over the methods outlined in previous works, particularly in terms of reducing RMS error and improving state estimation convergence. The average reduction in RMS error for state convergence is 24 %, while the estimation process is found to be 63 % faster when compared to existing methods.

Discrete Integral Optimal Controller for Quadrotor Attitude Stabilization: Experimental Results

The Unmanned Aerial Vehicle (UAV) attitude stabilization problem has been dealt with in many previous works through applying a vast range of philosophies of control strategies. In this paper, a discrete controller based on a Linear Quadratic Regulator (LQR) plus integral action is synthesized to stabilize the attitude and altitude of a quadrotor helicopter. This kind of control strategy allows us to reduce the energy consumption rate, and the desired UAV behavior is properly achieved. Experimental tests are conducted with external disturbances such as crosswinds deliberately added to affect the performance of the aerial vehicle. This provides experimental evidence that the integral part considered in the proposed control strategy contributes to improving the performance of the vehicle under external disturbances. In fact, a comparative analysis of potential and kinetic energy consumption is developed between the Optimal Integral Controller (OIC) and a Proportional Integral Derivative Controller (PID), allowing us to determine the level of improvement of the closed-loop system when the discrete Integral Optimal Controller is applied.

Appointed‐time nonsingular sliding mode control of spacecraft attitude stabilization

AbstractThis paper investigates the appointed‐time attitude stabilization problem of a rigid spacecraft under disturbance and parametric uncertainty. A continuous appointed‐time sliding mode disturbance observer is presented to observe the synthetical disturbance term. To circumvent the singularity problem in terminal sliding mode control, a new nonsingular appointed‐time sliding mode surface is designed by employing the concept of switching control. Based on the observation information deriving from the proposed disturbance observer, an observer‐based nonsingular sliding mode control scheme is developed to stabilize the attitude control system within appointed time which is given by the user. And also, the undesired control chattering phenomenon can be attenuated. The appointed‐time stability of the controlled attitude system is proved by the Lyapunov criteria. The simulation results show that the proposed attitude stabilization control scheme is valid.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Attitude Control for Fractionated Space Systems

This paper addresses the attitude stabilization problem for fractionated space systems where the onboard computers cannot run continuously. An auxiliary filter is constructed to imitate the intermittent computer or state acquisition of a small size, power, and weight constrained spacecraft such a CubeSat. The proposed controller does not require angular rate or inertia knowledge and guarantees attitude stabilization and boundedness for all closed loop signals for persistently excited gains driving the auxiliary filter. A novel Lyapunov function is constructed to guarantee stability including auxiliary functions for strictification of the controller. Simulation of a 3U form factor CubeSat example is carried out to demonstrate the feasibility of the controller.

Event‐driven fault‐tolerant attitude control of spacecraft with finite‐time disturbance observer under input saturation

AbstractThis paper investigates the attitude stabilization problem for a bandwidth‐constrained spacecraft subjected to model uncertainty, external disturbances, actuator faults, and saturated input. The proposed attitude controller is developed by combining the disturbance observer with an event‐trigger technique to provide disturbance attenuation meanwhile respecting the constraint on the wireless control network. The proposed disturbance observer estimates the lumped disturbance within a finite time, and its output is then fed to the composite control law. The presented control scheme relaxes the use of a priori upper bound knowledge of disturbance and resolves the unwinding problem in the quaternion‐based attitude representation. The closed‐loop stability analysis under the proposed algorithm shows the uniformly ultimately bounded convergence of state trajectories. Moreover, the designed event trigger approach avoids the Zeno behavior. The numerical simulation with comparative analysis illustrates the efficacy of the proposed controller in terms of convergence time, steady‐state bound, rate of control update, and energy consumption.

Model predictive control using LPV approach for trajectory tracking of quadrotor UAV with external disturbances

PurposeThe rotorcraft technology is very interesting area since last few decades due to variety of applications. One of the rotorcrafts is the quadrotor unmanned aerial vehicle (QUAV), which contains four rotors mounted on an airframe with an onboard controller. The QUAV is a highly nonlinear system and underactuated. Its controller design is very challenging task, and the need of controller is to make it autonomous based on mission planning. The purpose of this study is to design a controller for quadrotor UAV for attitude stabilization and trajectory tracking problem in presence of external environmental disturbances such as wind gust.Design/methodology/approachTo address this problem, the model predictive control has been designed for attitude control and feedback linearization control for the position control using the linear parameter varying (LPV) approach. The trajectory tracking problem has been addressed using the circular trajectory and helical trajectory.FindingsThe simulation results show the efficient performance with good trajectory tracking even in presence of external disturbances in both the scenarios considered, one for circular trajectory tracking and other for helical trajectory tracking.Originality/valueThe novelty of the work came from using the LPV approach in controller design, which increases the robustness of the controller in presence of external disturbances.

Robust Fixed-Time Sliding Mode Attitude Control of Tilt Trirotor UAV in Helicopter Mode

In this article, we address the problem of robust fixed-time attitude stabilization for tilt trirotor unmanned aerial vehicle subjects to parameter uncertainties and external disturbances. First, a novel fixed-time stable system with a faster convergence rate is proposed. Second, a nonsingular fixed-time sliding mode surface is developed, which has better convergence performance than existing methods. Third, a continuous fast fixed-time sliding mode control law is proposed by applying the developed sliding mode surface and adaptive technique. As a result, the convergence time of the closed-loop system is bounded and independent of the initial conditions. Simulation and experiments are presented to verify that the proposed scheme can effectively and rapidly achieve attitude stabilization while maintaining high control precision and robustness.

Attitude Stabilization of a Satellite Having Only Electromagnetic Actuation Using Oscillating Controls

We consider the problem of attitude stabilization for a low Earth orbit satellite having only electromagnetic actuation. Such a satellite is not fully actuated, as the control torque is the cross-product of magnetic moment due to magnetorquers and the geomagnetic field. The aim of this work is to study whether oscillating controls can be designed such that a satellite actuated via magnetorquers alone can achieve full three-axis control irrespective of the position of the satellite. To this end, we propose considering oscillating feedback controls which generate the motion of the closed-loop system in the direction of appropriate Lie brackets. Simulation studies show that the proposed control scheme is able to stabilize the considered system.

Constrained multi‐observer‐based fault‐tolerant disturbance‐rejection control for rigid spacecraft

AbstractThis article develops a multi‐observer‐based fault‐tolerant disturbance‐rejection control strategy to solve the attitude stabilization problem of spacecraft subject to multisource complex disturbances, for example, external disturbance, measurement error, actuator fault, input constraint. First, two intermediate variables are introduced for multi‐observer design, so that the synergistic estimations of attitude information, actuator fault and external disturbance are obtained simultaneously. Then, a fault‐tolerant disturbance‐rejection control strategy is proposed based on the estimations, and an augmented closed‐loop system is derived. Afterwards, Lyapunov stability analysis is performed to prove the quadratic stability and robust performance, and corresponding conditions in terms of linear matrix inequalities (LMIs) is proved, where the input constraint is satisfied as well. Finally, numerical simulations of a spacecraft attitude control system are performed which demonstrate the effectiveness and superiority of the proposed multi‐observer‐based control strategy.

Performance-Boosting Attitude Control for 2-DOF Helicopter Applications via Surface Stabilization Approach

This study solves the attitude stabilization problem of 2-degree-of-freedom (2-DOF) helicopters by robustly assigning the variable-performance to the closed-loop system in the presence of the model-plant mismatches and load variations. The proposed approach reformulates the original problem to a surface stabilization one which yields three contributions: a) the proposed attitude velocity observer forms a conventional Luenberger-type observer incorporating the parameter-independence and estimation gains specifically designed for causing the pole-zero cancellation, b) the pole-zero cancellation velocity control loop makes it possible to accomplish the surface stabilization task with the first-order closed-loop order, and c) the closed-loop analysis results demonstrate the attractive properties of the exponential performance recovery and convergence. The effectiveness of the proposed technique is verified using the experimental platform provided by the Quanser AERO.

Application of a PID-like control to the problem of triaxial electrodynamic attitude stabilization of a satellite in the orbital frame

The problem of triaxial attitude stabilization of a satellite in the orbital frame is considered. The problem is raised about the possibility of implementing such a system of electrodynamic attitude control by the type of a PID controller in which the restoring component of the control torque contains a distributed delay. A constructive analytical approach to the nonlinear stability analysis in the problem of triaxial attitude stabilization of a satellite is presented. A theorem on the asymptotic stability of the stabilized angular position of the satellite is proved. The theorem substantiates the possibility of constructing the indicated control system. Nonlinear analysis is based on the Lyapunov direct method and an original construction of Lyapunov–Krasovskii functional. The effectiveness of the designed attitude control with a distributed delay is confirmed by a computer modeling.

NI-based static output feedback control for attitude stabilization of post-capture flexible spacecraft

This paper investigates the attitude stabilization problem of post-capture flexible spacecraft with non-cooperative target in the presence of input fault and saturation. In modeling, these non-cooperative characteristics are often manifested in uncertain and unknown inertia, model parameter uncertainty, input faults, etc. In this paper, aiming at the attitude stabilization problem of such post-capture flexible spacecraft, the attitude dynamics modeling is completed by introducing the nominal inertia to construct the comprehensive disturbance term including external disturbance, inertia uncertainty and actuator failure. Then, a static output feedback controller is applied to convert the closed-loop attitude control system to a stable negative imaginary system with H∞ performance constraints according to negative imaginary theory. As long as the optimization variables approach zero, the iterative algorithm can find such a static output feedback controller to achieve attitude stabilization of post-capture flexible spacecraft. It is worth mentioning that an event-triggered mechanism is introduced into the control scheme to reduce the communication pressure. Finally, the numerical simulation is performed in the presence of model parameter uncertainty and controller gain perturbations. Simulation results demonstrate the effectiveness, robustness and non-fragility of the control method.

Global finite-time set stabilization of spacecraft attitude with disturbances using second-order sliding mode control

The performance of attitude stabilization control algorithms for rigid spacecraft can be limited by disturbances. In this paper, the global finite-time attitude stabilization problem with disturbances is investigated and handled by constructing a second-order sliding mode controller. Firstly, a virtual controller based on set stabilization idea is constructed to globally finite-time stabilize the system. Then, a relay polynomial second-order sliding mode controller is constructed to guarantee that the tracking error toward the virtual controller will converge to zero in finite-time. Finite-time Lyapunov theory is applied to support the proof and stability analysis. The global finite-time stability holds even with bounded disturbances. The effectiveness and feasibility of the controller are illustrated by the numerical simulations.

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

Velocity-Free State Feedback Fault-Tolerant Control for Satellite with Actuator and Sensor Faults

A velocity-free state feedback fault-tolerant control approach is proposed for the rigid satellite attitude stabilization problem subject to velocity-free measurements and actuator and sensor faults. First, multiplicative faults and additive faults are considered in the actuator and the sensor. The faults and system states are extended into a new augmented vector. Then, an improved sliding mode observer based on the augmented vector is presented to estimate unknown system states and actuator and sensor faults simultaneously. Next, a velocity-free state feedback attitude controller is designed based on the information from the observer. The controller compensates for the effects of actuator and sensor faults and asymptotically stabilizes the attitude. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

Attitude stabilization of rigid spacecraft with angular velocity and torque limitations

An adaptive backstepping control scheme has been put forward to investigate the attitude stabilization problem for a spacecraft with modeling uncertainties, external disturbances, actuator failures, angular velocity limitations and actuator limitations simultaneously. Based on the active disturbance rejection concept (ADRC), a positive definite diagonal matrix is selected by the designer to separate a control item from the system. Then, an extended state observer is constructed to deal with the total uncertain item including actuator failure. In order to deal with the limitation of torques, a saturation coefficient is introduced and its adaptive law is obtained. Meanwhile, a command filter and the compensation signal are constructed to handle the angular velocity limitations. Finally, the stability of the closed-loop system is analyzed. Simulation results are given to verify the effectiveness of the proposed scheme.