Thrust Saturation Research Articles

An improved convex optimization-based guidance for fuel-optimal powered landing

Convex optimization has great potential for onboard trajectory generation which can eliminate large state deviations and improve landing precision. In practical applications, the convex optimization problem is often infeasible under disturbances. In this paper, we analyze the reason for the infeasibility of the fuel-optimal trajectory optimization problem. The analysis result shows that the thrust saturation degrade the anti-disturbance performance and then lead to infeasibility. Based on this analysis, we improved the anti-disturbance performance of convex optimization-based guidance from two aspects: (1) a maximum-thrust regulation strategy is embedded into the original fuel-optimal problem to avoid thrust saturation; (2) a trajectory tracking method with a disturbance compensator is performed to attenuate disturbance effects and to make the initial state of each optimization cycle close to the existing feasible trajectory. Numerical simulations demonstrate that the proposed method can improve the infeasibility and can realize the high-precision landing under disturbances.

PSO and NNPC-based integrative control allocation for dynamic positioning ships with thruster constraints

In order to overcome the issues of thrust saturation, uneven energy consumption and suboptimal control associated with the traditional hierarchical control strategy employed in ship dynamic positioning (DP) systems, an integrative control allocation strategy is proposed by combining the low-level thrust allocation into the high-level motion controller. The proposed scheme is implemented via the neural network-based nonlinear predictive control (NNPC) and solved via an improved particle swarm optimization (PSO) algorithm. A data-driven recurrent neural network (RNN) ship motion and thrust allocation model is off-line identified based only on the current and historical measured output and thrust input data. Utilizing the established RNN model to predict the future multi-step outputs, and combining the motion control, the thruster energy consumption and the thruster wear and tear as an integrative control objective, the integrated NNPC online optimization problem with thruster constraints is established and solved by an improved evolution algorithm of PSO. Simulations are respectively carried out for setpoint regulation and trajectory tracking. Simulation results well demonstrate the feasibility and superiority of the proposed control strategy.

Experimental investigation on magnetic field strength providing thrust saturation in a magnetic nozzle radiofrequency plasma thruster

Magnetic field strength applied to a magnetic nozzle radiofrequency (rf) plasma thruster having a 10.5 cm diameter source tube is increased up to about 3 kG by pulsing the solenoid current. A target plate is installed at 30 cm downstream of the source and an impulse bit exerted to the target is measured to assess the thrust, where the thrust balance measurement was impossible due to the interaction between the pulsed magnetic fields and the eddy currents on surroundings. Since the diameter of the plasma plume at the target location is larger than the target diameter, a comparison between the thrust balance and target measurements under continuous magnetic field and rf power is performed prior to the pulsed magnetic field experiments, showing that about 65 percent of the plasma momentum is exerted to the target plate. Saturation of the impulse bit, being equivalent to the force multiplied by the rf pulse width, is clearly observed when increasing the magnetic field strength. The magnetic field providing the force saturation is found to be changed by the source diameter, which is qualitatively explained by considering a change in the plasma loss to the source wall in a thruster model containing the particle balance, power balance, and one-dimensional magnetic nozzle models. It is suggested that the magnetic field strength required for optimizing the force, i.e. the thrust, can be reduced when enlarging the source tube diameter.

Motion control for an open-frame work-class ROV in current using an adaptive super-twisting disturbance observer

Remotely operated vehicle (ROV) plays an important role in marine operation and maintenance for offshore facilities. Motion control design is one of the major challenges in the development of ROV, especially when the ROV is subjected to unstable sea currents, parametric uncertainty, hydraulic delay, and thrust saturations. In this study, an open-frame work-class ROV used for offshore structure surface cleaning is considered. The dynamic model of the ROV is established, based on the hydrodynamic properties obtained from CFD simulations. A sliding mode controller is designed for the ROV trajectory tracking, which is developed by the command filtered backstepping method. An adaptive super-twisting disturbance observer is employed to estimate and compensate the loading disturbances and modeling uncertainties. Stability analysis is performed and proves Lyapunov stability of the proposed controller. The effects of current, dynamics of the hydraulically-driven propellers, and thrust saturation are rigorously taken into account in this study. Various simulation cases are conducted using the Simulink software. The results have demonstrated that the superior robustness of the proposed control design against thrust saturation, modeling errors, and external disturbances.

Fault-Tolerant Control of a Variable-Pitch Quadrotor under Actuator Loss of Effectiveness and Wind Perturbations

The actuator fault-tolerant control problem for a variable-pitch quadrotor is addressed under uncertain conditions. Following a model-based approach, the plant nonlinear dynamics are faced with a disturbance observer-based control and a sequential quadratic programming control allocation, where only kinematic data of the onboard inertial measurement unit are required for the fault-tolerant control, i.e., it does not require the measurement of the motor speed nor the current drawn by the actuators. In the case of almost horizontal wind, a single observer handles both faults and the external disturbance. The estimation of the wind is fed forward by the controller, while the actuator fault estimation is exploited in the control allocation layer, which copes with the variable-pitch nonlinear dynamics, thrust saturation, and rate limits. Numerical simulations in the presence of measurement noise show the capability of the scheme to handle multiple actuator faults in a windy environment.

Adaptive Anti-Saturation Prescribed-Time Control for Payload Retrieval of Tethered Space System

This work presents an adaptive anti-saturation prescribed-time control scheme for the stable payload retrieval of a two-body tethered space system following the desired libration state. The tethered payload is retrieved at the analytical speed function corresponding to the desired stable libration state. At the same time, the thrust at the payload is applied with the proposed adaptive anti-saturation prescribed-time control scheme to closely track the desired state to eliminate any deviation from the desired libration state due to external disturbances. The influence of the thrust saturation is minimized by a neural dynamics-based adaptive anti-saturation compensator that quickly drives the control system away from the saturated region. The Lyapunov stability of the proposed control scheme is proved analytically. Numerical simulations validate the effectiveness of the proposed prescribed-time strategy and the adaptive anti-saturation compensator.

Adaptive prescribed performance second-order sliding mode tracking control of autonomous underwater vehicle using neural network-based disturbance observer

For trajectory tracking control problem of autonomous underwater vehicle (AUV) with model uncertainties, unknown nonlinear external disturbances, and input saturation, an observer-based adaptive second-order sliding mode control scheme with prescribed performance is proposed. Firstly, a finite time performance function (FTPF) is constructed to constrain the tracking error to the prescribed precision within the preset finite time, and achieve the prescribed dynamic convergence performance and tracking accuracy. Then, a neural network-based disturbance observer (NNDO) is designed to deal with model uncertainties and external disturbances, respectively. Based on prescribed performance control and sliding mode control technique, an adaptive prescribed performance second-order sliding mode control strategy was proposed. In addition, we construct an auxiliary system to overcome the effect of thrust saturation. Lyapunov method is applied to demonstrate the stability of the closed-loop system. Finally, the validity of the proposed control law is verified by numerical simulations.

Passivity-based adaptive tracking control of spacecraft line-of-sight relative motion with thrust saturation

This paper considers the control problem of spacecraft line-of-sight (LOS) relative motion with thrust saturation in the presence of unmodeled dynamics, external disturbance and unknown mass property. By using skew-symmetric property, reference trajectory generator and anti-windup technique, a novel passivity-based adaptive sliding mode control (SMC) scheme is proposed without prior knowledge of uncertainty/disturbance bound. Within the Lyapunov framework, the establishment of a real sliding mode (which induces the practical stability of closed-loop error system) is validated. The main contributions are that a new control gain adaptive algorithm is adopted to attenuate the overestimation of switching gain and a differentiable projection-based parameter adaptive algorithm is proposed to force the mass approximator to remain in a desired domain, then the adaptive control law is modified by the reference trajectory generator and anti-windup technique to compensate for the effect of thrust saturation. Finally, simulations are conducted to show the fine performance of proposed control scheme.

In-Orbit Three-Axis Spacecraft Orbit Control Based on Neural Networks via Limited Thrust Budget

The problem of spacecraft orbit control is divided into coplanar and non-coplanar control algorithms. The general case of an orbital manoeuvre for a low earth orbit spacecraft is represented by a mixed planar and non-coplanar manoeuvre. Several algorithms for developing non-coplanar orbital manoeuvre exist in the literature. These algorithms usually require intensive calculations, representing a severe problem for application on-board a spacecraft in-orbit. In this research article, a spacecraft orbit control algorithm is developed based on Neural Networks. The developed orbit control algorithm has numerous advantages over the ones found in the literature. Various sources of nonlinearities such as plant nonlinearity, disturbance nonlinearity, and thrust saturation level are taken into consideration during the controller design process. Random disturbances are also considered during the controller design process. Training data is provided by a PD control algorithm with proven stability. The Stability of the learning algorithm is also proven. The developed controller can mimic the performance of the PD control algorithm, which is used for training. The developed algorithm can completely control the spacecraft’s orbit during the manoeuvre and avoid collision with the surface of the earth while the PD control algorithm has failed. This has assured the superior performance of the developed control algorithm.

Robust Synchronization for Under-Actuated Vessels Based on Disturbance Observer

This work focuses on the robust leader-follower synchronization navigation for the under-actuated vessels with only independent the surge control force and the yaw moment. The ocean disturbances and thruster saturation are simultaneously addressed. A virtual vessel placed at the relative distance with the moving main vessel alleviates the requirements on main vessel’s velocity measurements. The disturbance estimation performance is achieved by utilizing the disturbance observer. The additional controls produce the filtered non-achievable command control signals due to the thrust saturation effects. The filtered signals correct feedback errors for avoiding disturbance estimation and rejection compromise. The dynamic surface control technique is employed to derive the under-actuated synchronization control laws. By employing first-order filters, the differential terms are replaced by the algebraic operations such that the control is convenient to implement. It is analyzed that the supply vessel control system is semi-globally stable and the synchronization navigation along with the main vessel is ensured with the small errors. Simulations in the different disturbance cases validate the synchronization scheme.

Adaptive Asymptotic Tracking Control Without Singularity for a Class of Uncertain Quadrotors With Thrust Saturation

A novel adaptive tracking control strategy without singularity is proposed for quadrotor systems subject to uncertain dynamic parameters. Based on the design technique of bounded control, a new differentiable saturated function is proposed and subsequently adopted to ensure that the developed translational thrust remains within the preassigned range in the position control loop. A technical lemma is established to analyze the relationship between the convergence of the attitude tracking error and the position tracking error in the presence of thrust saturation. Then, by the compensation term in the form of an attitude error function, a singularity-free torque controller, which can avoid analytic calculations involving the desired attitude derivative, is presented in the attitude control loop. Finally, we prove that the proposed method can achieve asymptotic tracking without singularity. Simulation results illustrating the effectiveness of the proposed strategy are exhibited.

An approximation-free simple controller for uncertain quadrotor systems in the presence of thrust saturation

In this paper, a new simple tracking control scheme is presented for quadrotor systems with uncertain dynamics. It precludes the necessity for prohibitive analytic computation of the derivatives of the desired (virtual) attitude that is typically employed in controlling quadrotor systems. Moreover, this control scheme is approximation-free in the sense that it does not incorporate any adaptive laws, observers, or command filters to compensate for unknown parameters in the dynamics and the absence of the analytic differentiation, thus exhibiting remarkably low complexity levels and making its implementation straightforward. The thrust saturation is approached in the position control design, which also enables the singularity in desired attitude extraction to be avoided entirely. It is demonstrated that based on the proposed scheme, the tracking errors can be made arbitrarily small by appropriately selecting design parameters. Extensive simulations and experiments are performed to verify the effectiveness of our method.

Geometric Attitude and Position Control of a Quadrotor in Wind

This paper addresses flight stability and performance in wind of a quadrotor equipped with custom flow probes that measure the wind velocity. Wind-velocity measurements are used in the attitude and position control through the use of principled models that estimate the aerodynamic forces and moments. The aerodynamic moment is caused primarily by propeller blade flapping, whereas the aerodynamic force includes the induced drag from the rotors and drag over the body. A feedback-linearization controller prescribes inputs based on the aerodynamic models and quadrotor kinematics, which are developed on the special Euclidean group. The controller also addresses the thrust saturation using a variable-gain algorithm. Simulated and experimental results highlight the benefits of flow feedback and the variable-gain algorithm for the inner- and outer-loop control of attitude and position, respectively.

Attitude Stabilization of Tug–Towed Space Target by Thrust Regulation in Orbital Transfer

This paper studies the stability control of a target towed by a space-tug via a tether in orbital transfer. The attitude of the towed target is controlled by thrust regulation at the tug with the consideration of the coupling effect between the attitudes of the tug and towed target and the motion of the flexible and elastic tether. A model-based control scheme is proposed, where the tug and towed target are assumed as rigid bodies and the tether is approximated as a series of extensible but incompressible rods connected by spherical hinges. The governing equations of motion of the coupled rigid–flexible multibody system are derived based on the recursive dynamics algorithm. The attitude motion of the tug with the presence of tether tension disturbance is controlled by a simple proportional–derivative torque controller. The attitude motion of the towed target and the elongation oscillation of the tether are stabilized simultaneously via the tether tension by regulating the thrust at the tug. The thrust control is achieved by first designing an optimal trajectory considering the system constraints based on a reference model, and then the trajectory is tracked by a robust global terminal sliding-mode controller with the consideration of thrust saturation and tether slackness avoidance. Finally, numerical simulation is carried out to demonstrate the effectiveness of the proposed attitude control law based on the thrust regulation.

Nonlinear DOB-based explicit NMPC for station-keeping of a multi-vectored propeller airship with thrust saturation

ABSTRACTA nonlinear station-keeping control method for a multi-vectored propeller airship under unknown wind field with thrust saturation is developed, which is composed of three modules: nonlinear model predictive controller (NMPC), disturbance observer (DOB) and tracking differentiator (TD). The nonlinear kinematics and dynamics models are introduced, and the wind effect is considered by the wind-induced aerodynamic force. Based on both models, an explicit NMPC is designed. Then a nonlinear DOB is introduced to estimate the wind disturbance. A TD, showing the relationship between the maximum propulsion force and the maximum flight acceleration, is proposed to handle the thrusts’ amplitude saturation. Stability analysis shows that the closed-loop system is globally asymptotically stable. Simulations for a multi-vectored propeller airship are conducted to demonstrate the robustness and effectiveness of the proposed method.

SOS Based Robust Control for Dynamic Positioning System Subject to Actuator Saturation

In this paper, the problem of thruster saturation is considered for dynamic positioning systems of offshore platforms, specifically, a state feedback controller is developed for polynomial systems subject to actuator saturation. The sufficient conditions of stabilization problem are formulated in the form of sum of squares to ensure the desired H infinity performance, which can be numerically solved via the SOSTOOLS.For the modeling uncertainty problem caused by the uncertain hydrodynamic parameter, the results are extended to the uncertain system for the consideration of wider applications. Finally, simulations are conducted for a system with parameter uncertainties and thrust saturation in dynamic positioning system to illustrate the effectiveness and advantages of the proposed control strategy.

Distributed Formation Control for Multiple Vertical Takeoff and Landing UAVs With Switching Topologies

This paper proposes a distributed formation control approach for a team of vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) subject to switching topologies. The communication topology among UAVs is allowed to be with weak connectivity, in the sense of satisfying a uniformly jointly connected assumption. Since VTOL UAV systems are typically underactuated, a hierarchical framework is introduced such that a distributed control scheme can be established using neighboring positions and velocities. In particular, a distributed command force is developed to fulfill the formation objective, and an applied torque is synthesized for the attitude to track the command attitude. This command attitude is extracted from the command force by using a backstepping idea. In addition, an auxiliary system with appropriate parameters is introduced to preserve thrust saturation constraint, to guarantee nonsingular command attitude extraction and to avoid usage of neighboring acceleration information. With proper choices of Lyapunov functions, explicit selection criteria for the control parameters are formulated to ensure the asymptotic stability of the closed-loop system. Simulations and experiments are provided to validate the proposed theoretical results.

Robust nonlinear control design for dynamic positioning of marine vessels with thruster system dynamics

Considering the dynamics characteristics of thruster systems for dynamically positioned marine vessels with model parameter uncertainties and unknown time-varying ocean disturbances, the dynamic positioning (DP) control problem becomes a mismatched nonlinear control problem. To solve this problem, a DP robust nonlinear control law is developed using the command filtered vectorial backstepping combined with a disturbance observer (DO) and an auxiliary dynamic system (ADS). The DO provides the estimates of mismatched compound disturbances induced by model parameter uncertainties and unknown ocean disturbances. The ADS addresses the effects of thrust saturation constraints. The command filtered vectorial backstepping obviates differentiations of intermediate control function vectors due to introducing command filters and compensates for filtering errors of intermediate control function vectors caused by command filters by means of designed dynamic systems. The developed DP control law is computationally simple and the DP control performance is improved. Under the developed DP control law, the positioning errors of vessels are made as small as desired and all signals in the DP closed-loop control system are uniformly ultimately bounded. The high-fidelity simulation results on a supply vessel validate the developed DP control law.

Software-in-the-loop simulation of a quadcopter portion for hybrid aircraft control

In this paper, we present the design of the software-in-the-loop simulation framework for a quadcopter that is incorporated in our hybrid aircraft. The hybrid aircraft comprises a quad-copter and a fixed wing with one forward thrust rotor. We need to develop a split control system that utilizes a typical quadcopter controller to control four motors/propellers and a supervisor controller to control a forward thrust rotor. The supervisor controller shall take feedback signals from the quadcopter and will command the fifth rotor for stabilizing the hybrid aircraft and resolves problems like thrust saturation. The simulation simulates the control algorithm and verifies the quadcopter’s behavior using MATLAB and Simulink together. Achieving these results, we come to know how our hybrid controller will be implemented, what results to expect once the forward thrust rotor is attached to the quadcopter. The software-in-the-loop simulation of a quadcopter is one of the most effective methods for verifying overall control performance and safety of the hybrid aircraft before actual hardware implementation and flight test.

A novel adaptive dynamic surface control scheme of hypersonic flight vehicles with thrust and actuator constraints

In this paper, the nonlinear adaptive velocity and altitude tracking controller is developed for the longitudinal dynamics of generic air-breathing hypersonic flight vehicles. The proposed control scheme is designed using dynamic surface control method. The velocity and altitude subsystems are transformed into the linearly parameterized form for the convenience of adaptive law design. Both of the thrust and actuator constraints are explicitly considered. For thrust constraint, two cases are analyzed when the fuel-to-air ratio reaches its max and min values. A novel adaptive law is proposed to avoid over or less estimation in thrust saturation occasion. For actuator constraint, a magnitude and rate limiting filter is incorporated. The filter guarantees that the control signal is applicable for the actuator. It is shown that with the application of the proposed control scheme, all signals of the closed-loop system are uniformly ultimately bounded and the velocity and altitude tracking errors converge to a residual set which is arbitrarily small. Simulation results are demonstrated to show the effectiveness and superiority of the proposed control scheme.