Nonlinear Attitude Control Research Articles

Dynamics modeling and nonlinear attitude controller design for a rocket-type unmanned aerial vehicle

This paper presents an altitude and attitude control system for a newly designed rocket-type unmanned aerial vehicle (UAV) propelled by a gimbal-based coaxial rotor system (GCRS) enabling thrust vector control (TVC). The GCRS is the only means of actuation available to control the UAV’s orientation, and the flight dynamics identify the primary control difficulty as the highly nonlinear and tightly coupled control distribution problem. To address this, the study presents detailed derivations of attitude flight dynamics and a control strategy to track the desired attitude trajectory. First, a Proportional-Integral-Derivative (PID) control algorithm is developed based on the formulation of linear matrix inequality (LMI) to ensure robust stability and performance. Second, an optimization algorithm using the Levenberg–Marquardt (LM) method is introduced to solve the nonlinear inverse mapping problem between the control law and the actual actuator outputs, addressing the nonlinear coupled control input distribution problem of the GCRS. In summary, the main contribution is the proposal of a new TVC UAV system based on GCRS. The PID control algorithm and LM algorithm were designed to solve the distribution problem of the actuation model and confirm altitude and attitude tracking missions. Finally, to validate the flight properties of the rocket-type UAV and the performance of the proposed control algorithm, several numerical simulations were conducted. The results indicate that the tightly coupled control input nonlinear inverse problem was successfully solved, and the proposed control algorithm achieved effective attitude stabilization even in the presence of disturbances.

Nonlinear Attitude and Altitude Trajectory Tracking Control of a Bicopter UAV in Geometric Framework

In this paper, we deal with a Bicopter drone that has two thrusters and two tilting servos. Both the position and attitude dynamics of Bicopter are globally expressed on the Special Euclidean group SE3. A simple control allocation method is proposed to map between the control wrench and actuator inputs for the Bicopter. A geometric nonlinear attitude and altitude tracking controller is developed for the Bicopter and the asymptotic stability analysis is performed using the Lyapunov method for the closed-loop nonlinear system. The performance of the proposed altitude and attitude stabilization controller is validated through experimental hardware developed in-house. The attitude controller performance is validated through simulations and shown to be comparable against an linear matrix inequality-based control law.

Q-LEARNING, POLICY ITERATION AND ACTOR-CRITIC REINFORCEMENT LEARNING COMBINED WITH METAHEURISTIC ALGORITHMS IN SERVO SYSTEM CONTROL

This paper carries out the performance analysis of three control system structures and approaches, which combine Reinforcement Learning (RL) and Metaheuristic Algorithms (MAs) as representative optimization algorithms. In the first approach, the Gravitational Search Algorithm (GSA) is employed to initialize the parameters (weights and biases) of the Neural Networks (NNs) involved in Deep Q-Learning by replacing the traditional way of initializing the NNs based on random generated values. In the second approach, the Grey Wolf Optimizer (GWO) algorithm is employed to train the policy NN in Policy Iteration RL-based control. In the third approach, the GWO algorithm is employed as a critic in an Actor-Critic framework, and used to evaluate the performance of the actor NN. The goal of this paper is to analyze all three RL-based control approaches, aiming to determine which one represents the best fit for solving the proposed control optimization problem. The performance analysis is based on non-parametric statistical tests conducted on the data obtained from real-time experimental results specific to nonlinear servo system position control.

Intersatellite and Downlink Agile Attitude Maneuvers

This research is focused on the problem of agile attitude maneuvering, aimed at the precise pointing of a satellite forming a typical constellation in low Earth orbit. We consider two different operational scenarios: (a) pointing toward a specific ground station, located on the Earth surface (for downlink data routing), and (b) pointing toward a companion satellite (for establishing an intersatellite connection). The two preceding operational requirements can both be formulated as attitude tracking problems. In this study, we use an inertia-free nonlinear attitude control algorithm based on rotation matrices and possessing remarkable stability properties, in conjunction with a pyramidal array of single-gimbal control momentum gyroscopes. Numerical simulations, in both nominal and nonnominal flight conditions, demonstrate that the attitude control architecture proposed in this work is effective for the purpose of performing agile attitude maneuvering, aimed at precise pointing during downlink and intersat data routing.

Nonlinear position control of electro-hydraulic servo system based on lyapunov robust integral backstepping controller

In electro-hydraulic servo systems (EHSS), high nonlinearity and time-varying features limit the hydraulic actuator performance. In feedback-based systems, linearization reduces nonlinearities. Their cancellation may produce instability when modeling uncertainty exists. This work uses a robust nonlinear controller based on Lyapunov theory to control the nonlinear position of the electro-hydraulic servo system (EHSS). The dynamics of the system were modeled as extensively as possible, and then a simplified mathematical model based on the EHSS dynamics was created for the controller design. Integral backstepping was used to design the nonlinear robust controller utilizing the Lyapunov theory of nonlinear systems. Lyapunov functions theoretically ensured closed-loop stability. Comparative simulation analysis and experimental investigation in real-time with the proportional integral derivative (PID) controller optimized offline for position tracking control were carried out. Besides tracking performance and steady-state error, the mean square error (MSE), the root mean square error (RMSE), the maximum absolute value of tracking errors and the standard deviation of tracking errors (σ) was utilized to evaluate the controllers’ performance. The simulation analysis and experimental verification were accomplished under various sinusoidal trajectories using different testing conditions (amplitudes, frequencies, and external disturbance), in all testing conditions the effectiveness of the robust nonlinear integral backstepping controller was demonstrated.

Nonlinear Dynamic Model-Based Position Control Parameter Optimization Method of Planar Switched Reluctance Motors

Currently, there are few systematic position control parameter optimization methods for planar switched reluctance motors (PSRMs); how to effectively optimize the control parameters of PSRMs is one of the critical issues that needs to be urgently solved. Therefore, a nonlinear dynamic model-based position control parameter optimization method of PSRMs is proposed in this paper. First, to improve the accuracy of the motor dynamics model, a Hammerstein–Wiener model based on the BP neural network input–output nonlinear module is established by combining the linear model and nonlinear model structures so that the nonlinear and linear characteristics of the system are characterized simultaneously. Then, a position control parameter optimization system of PSRMs is developed using the established Hammerstein–Wiener model. In addition, with a self-designed simulated annealing adaptive particle swarm optimization algorithm (SAAPSO), the position control parameter optimization system is performed offline iteratively to obtain the optimal position control parameters. Simulations and experiments are carried out and the corresponding results show that the optimal position control parameters obtained by the proposed method can be directly applied in the actual control system of PSRMs and the control performance is improved effectively using the obtained optimal control parameters.

UAS Control under GNSS Degraded and Windy Conditions

Multirotor Uncrewed Aircraft Systems (UAS), widely known as aerial drones, are increasingly used in various indoor and outdoor applications. For outdoor field deployments, the plethora of UAS rely on Global Navigation Satellite Systems (GNSS) for their localization. However, dense environments and large structures can obscure the signal, resulting in a GNSS-degraded environment. Moreover, outdoor operations depend on weather conditions, and UAS flights are significantly affected by strong winds and possibly stronger wind gusts. This work presents a nonlinear model predictive position controller that uses a disturbance observer to adapt to changing weather conditions and fiducial markers to augment the system’s localization. The developed framework can be easily configured for use in multiple different rigid multirotor platforms. The effectiveness of the proposed system is shown through rigorous experimental work in both the lab and the field. The experimental results demonstrate consistent performance, regardless of the environmental conditions and platform used.

Solving the Non-Linear Motion in a Micromanipulation System Powered by Thermocapillary Flows

Non-contact micromanipulation tools have emerged as a promising solution for manipulating small components. However, they are mainly based on non-linear actuation principles requiring ad-hoc control strategies. This paper proposes non-linear control laws to actuate a non-contact manipulation system based on thermocapillary flows for the manipulation of micro-objects on an air-water interface. The actuation system consists of steering a laser beam to locally heat the liquid surface, thus inducing a thermocapillary flow. The resulting flow propels floating objects away from the laser spot with a significant velocity (up to ten body-length per second) but the behavior is highly non-linear. Notably, small errors in the laser positioning are amplified and give place to non-linear motion. Therefore, we developed a control method consisting of a non-linear position controller including a laser position observer. We achieve stable 2D position control in this non-linear system, with a precision of 0.3 mm on a 0.5 mm object.

Hierarchical Control and Cooperative Disturbance Estimation for Multiple Drones: Towards Application to Micro-Meteorology Control

This paper deals with formation control and disturbance estimation problem for multiple drones in the presence of unknown disturbance forces. The unknown disturbance forces are assumed to be generated mainly by wind. In view of application to micro-meteorology control, a formation control law involving a cooperative disturbance estimation mechanism is proposed. The estimated disturbance can be used for meteorology control. The proposed control law consists of three parts: a hierarchical optimal feedback control law for translational motion, a cooperative update law for disturbance estimation, and a nonlinear attitude control law.

Increasing the dynamic accuracy of ball screw drives with quasi-sliding-mode (qSMC) position control

To increase the dynamics of ball screw drives, a nonlinear position controller based on sliding-mode control is presented along with its parameterization to ensure robust stability. The controller is validated experimentally on a ball screw axis and shown to increase the controller bandwidth from 8 Hz to 15.9 Hz in comparison to proportional (P) position control with feedforward. The mean absolute tracking error under high performance cutting forces is reduced by 24%. Under variation of the model parameters by 20%, the controller shows excellent robust performance with only 2.7% degradation of the tracking error.

H ∞ inverse optimal attitude tracking on the special orthogonal group SO(3)

The problem of attitude tracking in the presence of disturbances is addressed by combining inverse optimality and disturbance attenuation. Conditions are provided which ensure that an inverse optimal nonlinear attitude control problem is solved and a meaningful cost function is minimised. The approach results in a PD-type attitude control law on the Special Orthogonal Group which guarantees that, for almost all initial conditions, the energy gain from an exogenous disturbance to a specified error signal respects a given upper bound. For numerical simulations, a satellite attitude tracking problem from literature is considered. The controller gains are tuned using a decoupled linearised single-axis model and the structured control synthesis method. Results indicate that the proposed controller has good tracking and disturbance attenuation capability. In particular, for the problem under consideration, the inverse optimal controller is seen to have better transient performance than its continuous-time quaternion counterpart. Moreover, for initial errors up to radians, it has comparable performance to the shortest-path quaternion PD controller.

Attitude control method for compound multi-rotor UAV

To control the flight of the compound multi-rotor UAV which is a combination of coaxial rotor and quad-rotor, the attitude control method is proposed. The nonlinear attitude control dynamic model of the compound multi-rotor UAV is given. The Proportion-Proportion Integration Differentiation (P-PID) control method is used for the attitude control module and obtaining the virtual control values. The control values distribution matrix is used to realize mapping between the virtual control values and the multi-actuator. The rotation rate-blade pitch integration control method is used to coordinate the rotor’s rotation rate and blade pitch, which ensure fast response of the UAV’s attitude stabilization control. Simulation results show that the attitude controller can realize the UAV’s pitch, roll, yaw attitude motion control, and do well in attitude angle stability control when periodic change attitude angles is tracked.

Multiplexed MPC attitude control of a moving mass satellite using dual-rate piecewise affine model

This paper proposes a Multiplexed MPC algorithm for the dual-rate piecewise affine (PWA) model to control the attitude of a low-Earth-orbit (LEO) moving mass satellite. Although still facing an inherent inertial disturbance problem, the moving mass technology is a promising way to counter the strong aerodynamic torques in LEO. To make the satellite attitude fully actuated, a magnetorquer is used to cooperate with the moving mass system, resulting in a two-input control system. Through a strategy that updates inputs asynchronously, the proposed algorithm effectively balances the inertial disturbances caused by mass motions, the system's dynamic performance, and the controller's computational complexity. Error attitude kinematic and dynamic equations are derived, to convert the tracking problem into an equivalent regulation problem. The PWA approximation is used to transform the nonlinear attitude control equations described by error modified Rodrigues parameter to a linear state-space model for MPC design. Then, a new form of Multiplexed MPC, namely dual-rate PWA-MMPC, is developed for this dual-rate PWA model, which updates two control inputs at different rates. Despite only finding sub-optimal solutions to the original problem by stability analysis, this algorithm outperforms other control strategies through its ability to coordinate multiple inputs, deal with constraints, and reduce computational complexity. Hardware-in-the-loop simulations are conducted to demonstrate the effectiveness of the proposed methodology for the attitude control.

Verification framework for control theory of aircraft

AbstractA control system verification framework is presented for unmanned aerial vehicles using theorem proving. The framework’s aim is to set out a procedure for proving that the mathematically designed control system of the aircraft satisfies robustness requirements to ensure safe performance under varying environmental conditions. Extensive mathematical derivations, which have formerly been carried out manually, are checked for their correctness on a computer. To illustrate the procedures, a higher-order logic interactive theorem-prover and an automated theorem-prover are utilised to formally verify a nonlinear attitude control system of a generic multi-rotor UAV over a stability domain within the dynamical state space of the drone. Further benefits of the procedures are that some of the resulting methods can be implemented onboard the aircraft to detect when its controller breaches its flight envelope limits due to severe weather conditions or actuator/sensor malfunction. Such a detection procedure can be used to advise the remote pilot, or an onboard intelligent agent, to decide on some alterations of the planned flight path or to perform emergency landing.

Nonlinear Slewing Control of a Large Flexible Spacecraft Using Reaction Wheels

Reorientation maneuvers represent a key task for large satellites. This work considers a space vehicle with solar panels and reaction wheels as actuation devices. Solar panels are modeled as flexural beams, using the modal decomposition technique. An inertia-free nonlinear attitude control algorithm, which enjoys quasi-global stability properties, is employed for the numerical simulation of a large reorientation maneuver. Preliminary analysis with ideal actuation allows sizing the control system and identifying the expected elastic displacements. Then, the actuation dynamics is included, and the actual torque transferred to the vehicle no longer coincides with the commanded one, supplied by the nonlinear control algorithm. Moreover, the solar panels are designed to rotate, in order to maximize the power storage during the maneuver. The numerical results prove that the slewing maneuver is successfully completed in reasonable time and without any saturation of the actuation devices, while the elastic displacements remain modest, in spite of the solar panel rotation aimed at pursuing the Sun direction.

Globally Stable Attitude Control and Quasi-Static Disturbance Estimation in the Presence of Aerodynamic Dissipation

In this letter, we design and verify a novel nonlinear attitude controller for small fixed-wing unmanned aerial vehicles (UAVs) in the presence of dissipation. The attitude controller is designed using quaternions, which provide the physical insight for the control design by relating it to the geometry of rotations. We also show how the controller can be suitably modified to adaptively estimate quasi-static disturbances and compensate for aerodynamic damping by incorporating suitable refinements to the controller. The performance of the controller is then verified using simulations that demonstrate global stability against arbitrarily large initial attitude errors.

Vision‐based tracking control of quadrotor for a moving target with nonlinear angular velocity observer

AbstractIn this article, an automatic tracking process for unmanned aerial vehicle (UAV) system to follow the target with maneuverability is developed, and a vision‐based control method is proposed. At first, the image‐based visual servoing (IBVS) position control technology is applied without any prior target information for the algorithm practicability. Besides, consider the situation with unavailable angular velocity measurement, a thorough nonlinear attitude controller with an observer based on contraction is proposed. Finally, the whole UAV system stability is demonstrated to be uniformly ultimately bounded, and the bound can be arbitrarily small. Simulation and experiment results are presented to show effectiveness of the designed controller.

Синтез нелинейного прогнозирующего управления вентильным электроприводом оптико-механических комплексов

The paper proposes a method to synthesize the nonlinear discrete predictive position controller in tracking electric drive control system of optical-mechanical complexes based on permanent-magnet synchronous motor. The technique for constructing mathematical discrete nonlinear vector-matrix model of permanent-magnet synchronous motor in rotor rotating coordinate for vector control is given. The permanentmagnet synchronous motor is operated under conditions of two-mass elastic load. The steps to synthesize nonlinear predictive control algorithms by using extended linearization technique and optimization objective function with convex quadratic programming method are analyzed. Computer simulation results are carried out on MATLAB / Simulink environment. In carried out simulation, the performance of discrete predictive controller in the position loop of optical-mechanical complexes tracking control system is assessed with different kind of control signals and under the influence of external disturbance.

Force/Torque-Based Impedance Control With Perturbation Observer—Toward High Payload System Robust Trajectory Tracking

This paper presents a robust force/torque-based impedance control that reacts to deviated motion by generating forces to achieve the desired impedance, particularly for high payload systems. One of the special cases of such systems is an assistive robot for paraplegics (ARP) with a sit-stand mechanism (STSM) and, therefore, its control is investigated. Recently, a nonlinear robust position control known as sliding mode control with sliding perturbation observer (SMCSPO) was implemented on STSM and proven its effectiveness. However, with increasing subject body mass, high switching control gains are required which consequently either result in increased tracking error or chattering in control performance. In this regard, a new framework of integrated control was proposed which combines the feature of impedance control with estimated information from SMCSPO resulting in an enhanced control algorithm. The advantage of this impedance control is that because of SMCSPO, it utilizes the linear system information with position feedback only to estimate the states and perturbation (nonlinearities, uncertainties, and disturbance). This estimated perturbation then helps in compensating the actual perturbation effect from the system response. Moreover, the impedance control excludes the saturation function which helps prevent the chattering with low control gains. The comparison simulation and experiment results of the proposed impedance control with SMCSPO validated the proposed algorithm which enhances the transient response with minimized estimation error and better perturbation estimation.

Nonlinear Optimal Position Control with Observer for Position Tracking of Surfaced Mounded Permanent Magnet Synchronous Motors

Previous control methods were designed based on cascade structure and consist of position and current controllers for permanent magnet-synchronous motors (PMSMs). Thus, the structures of the previous methods are necessarily complex although the stability is guaranteed. Thus, the gain tuning is difficult to obtain for the desired control performance for the PMSMs. To overcome this problem, this paper proposes a nonlinear optimal position control method with an observer to improve the position tracking performance of PMSMs. The proposed method consists of a desired state generator, controller, and nonlinear observer. The desired states and inputs are derived using the PMSM model. Then, the state feedback controller is designed based on the whole tracking error dynamics including both mechanical and electrical dynamics. The nonlinear observer is designed to estimate the velocity and load torque. The closed-loop stability is proven using the input-to-state stability. The proposed method is not designed based on the cascade structure. Furthermore, the control and observer gains are chosen using an optimal control method to obtain the desired performance for the PMSMs. This approach simplifies the design process such that the control algorithm is suitable for real-time control. The performance of the proposed method is validated via simulations and experiments.