Outer-loop Subsystem Research Articles

Adaptive sliding mode control for quadrotor transport systems with uncertain parameters and disturbances

SummaryQuadrotor transportation systems have been widely utilized in both commercial and civilian fields. However, challenges arise due to the variable payload mass and unpredictable wind disturbances during cargo transport, potentially leading to excessive payload swinging and system instability. To tackle this issue, this article proposes an adaptive sliding mode control approach that concurrently achieves trajectory tracking for the quadrotor and mitigates payload swinging. In the outer loop subsystem, the quadrotor dynamics model is partitioned into two components that is, actuated and underactuated components. Sliding surfaces are designed based on this divided system model, and two adaptive laws are designed to compensate for payload mass uncertainty and unknown wind disturbances. The system's asymptotic stability is assured through the application of the Lyapunov theorem. In the inner loop subsystem, a disturbance rejection controller is formulated. Comparative simulation results conclusively demonstrate the outstanding performance of the proposed method in terms of trajectory tracking and robustness.

Finite-time control based on RBF neural network for quadrotor UAVs with varied mass load

Aiming at the problem of the gradual reduction of the weight and the external wind disturbance affect flight performance of the quadrotor Unmanned Aerial Vehicle (UAV), a dual-loop finite time control strategy based on Radial Basis Function (RBF) neural network is proposed. The UAV model under disturbance is decoupled into position outer loop subsystem and attitude inner loop subsystem. In the outer loop, the changing weight and the external wind disturbance are approximated by using RBF neural network, command filter is used to avoid the “computing explosion” problem in the traditional backstepping method, and the finite-time control method is able to improve the convergence speed of the position. In the inner loop, the cascade RBF neural network PID control which relies on the self-learning of neural network to realize the dynamic tuning of PID parameters is adopted to achieve rapid convergence of the attitude angle. The simulation results show that compared with the traditional backstepping method and cascade PID control, the convergence time is reduced by 31% on average, which verifies the superiority and effectiveness of the proposed control strategy.

Antiswing Control for Aerial Transportation of the Suspended Cargo by Dual Quadrotor UAVs

Quadrotor unmanned aerial vehicles, with excellent maneuver performance and flexibility, are widely used in cargo transportation. Due to higher requirements for load capacity, dual quadrotors are expected to work cooperatively so as to transport heavy cargos. However, the aerial transportation system with dual quadrotors exhibits higher degrees of freedom, stronger nonlinearities, and more complex system couplings compared with the single quadrotor transportation system, which brings great challenges to the control of the system. This article focuses on the cooperative control of aerial transportation systems with dual quadrotors. Based on the Lagrange’s method, a redundant form of the dynamic model is constructed and presented, where the control inputs are decoupled with system dynamic. According to the cascade characteristics of the system, the inner loop subsystem on the attitude characteristics of the quadrotor, as well as the outer loop subsystem on the cargo’s swing motion and the quadrotor’s translational motion are defined. Then, a nonlinear hierarchical controller containing relative position constraints and cable tensions compensation is proposed. Specifically, by utilizing the energy-based analysis method, virtual control inputs are designed for the outer loop subsystem. Finally, LaSalle’s invariance principle is used to prove the stability of the closed-loop system. Experimental results show satisfactory control performance of the proposed controller.

Design and Implementation of a Fully-Actuated Integrated Aerial Platform Based on Geometric Model Predictive Control

Unlike individual unmanned aerial vehicles (UAVs), integrated aerial platforms (IAPs) containing multiple UAVs do not suffer from underactuation and can move omnidirectionally in six dimensions, providing a basis for constructing aerial manipulation platforms. Compared to single UAVs, multi-UAV IAPs are also advantageous in terms of payload and fault-tolerance capacity, making them promising candidates as platforms with integrated-response, observation, and strike capabilities. Herein, an IAP structure design containing three sub-UAVs connected in a star-like configuration is presented. This form of integration enables the IAP, as a whole, to simultaneously adjust its position and attitude in six dimensions. The dynamics of the overall system of the IAP are modeled. On this basis, an overall system controller is designed. To simplify control, based on stability of cascaded system, the rotational motion of the sub-UAVs is treated as a inner-loop subsystem, whereas the overall motion of the IAP is seen as a outer-loop subsystem. Because the configuration space of the sub-UAVs is non-Euclidean, a controller is designed for the outer-loop subsystem based on model predictive control on the manifold. Subsequently, the stability of the closed-loop system is demonstrated. Fieldbus technology is employed to design a real-time, scalable communication architecture for multiple sub-UAVs, followed by the development of a principle prototype of the multi-UAV IAP that consists of hardware and software systems. The effectiveness of the IAP design and control method is validated through simulation and real-world prototype-based tests. In the simulation and real-world tests, the proposed methodology can make the IAP system converge to the desired configuration at the presence of large initial configuration error. The same test scenario cannot be finished by a baseline PID controller. The advantage of the proposed control scheme in dealing with state and input constraints is shown via such tests.

Adaptive event-triggered global asymptotic full-state stabilization of under-actuated surface vessels with unknown model parameters

This paper studies an adaptive event-triggered controller (ETC) for global asymptotic full-state stabilization of under-actuated surface vessels (USVs) with unknown model parameters. Applying an inner–outer loop structure, desired linear and angular velocities regarded as control inputs of the outer loop subsystem are designed free of any model parameters, such that the outer loop subsystem is globally asymptotically stabilized. The generated desired velocities are assigned as the reference signals for the inner loop subsystem, thereby the actual adaptive ETC is designed to track the reference velocities and to compensate for the effect of the unknown model parameters. The proposed scheme guarantees global asymptotic stability of the closed-loop system proved by the Lyapunov-based analysis. The switching threshold event-triggering mechanism (SWT-ETM) is introduced to alleviate the system’s burden requiring less resources for communication and actuator execution. Simulation results show the effectiveness of the proposed method.

Fixed-time disturbance observer-based nearly optimal control for reusable launch vehicle with input constraints

In this paper, a fixed-time disturbance observer-based nearly optimal control (FTDO-NOC) scheme is proposed for reusable launch vehicle (RLV) subject to model uncertainties, input constraints, and unknown mismatched/matched disturbances. The dynamics of RLV attitude motion are divided into outer-loop subsystem and inner-loop subsystem. For the outer-loop subsystem, to address the problems of unknown mismatched disturbances and model uncertainties, a novel adaptive-gain multivariable generalized super-twisting (AMGST) controller is proposed. Two modified gain-adaptation laws are derived for tuning the control gains of AMGST controller, which attenuates chattering efficiently. For the inner-loop subsystem, considering the effect of unknown matched disturbances, a fixed-time disturbance observer (FTDO) is utilized to estimate the matched disturbances and the time derivative of virtual control input. Incorporated with the designed FTDO, a nearly optimal controller (NOC), which is based on the critic–actor neural networks (NNs), is utilized to generate the approximate optimal control moments satisfying the input constraints. The tracking errors of inner-loop subsystem and the weight estimation errors of the critic–actor NNs are proved to be uniformly ultimately bounded (UUB) via Lyapunov technique. Finally, we provide simulation results to validate the effectiveness and superiority of the proposed control scheme.

Global event-triggered inner–outer loop stabilization of under-actuated surface vessels

An event-triggered controller (ETC) for global full-state stabilization of under-actuated surface vessels (USVs) is proposed. Based on an inner–outer loop structure with Lyapunov control design technique, the USV dynamics are separated into two subsystems to facilitate the design and stability analysis. A time-varying variable is constructed to design the desired velocities used as virtual control inputs to stabilize the under-actuated outer loop subsystem. For the fully-actuated inner loop subsystem, the actual control force and moment inputs are designed using a switching threshold event-triggering mechanism (SWT-ETM) to drive the actual velocities to the desired ones, thereby the inner loop subsystem and the closed-loop system are stabilized. The proposed ETC guarantees global asymptotical convergence of the stabilization error by choosing proper control parameters. It also significantly reduces the times for communication and the actuator burden while provides stable and accurate control performance. Simulation results are carried out to illustrate the effectiveness of the proposed scheme.

A Novel Robust Observer-Based Nonlinear Trajectory Tracking Control Strategy for Quadrotors

In this article, a novel robust observer-based nonlinear control approach is proposed for quadrotors with unmodeled dynamics and external disturbances, wherein the tracking errors are restricted effectively. Two nonlinear disturbance observers are proposed to deal with uncertainties in the inner and outer loops, respectively. On this basis, a robust observer-based nonlinear control approach is put forward for quadrotor systems. Specifically, in the outer loop subsystem, a robust observer-based control scheme is proposed, which can reduce unexpected tracking errors for quadrotors effectively. Subsequently, based upon the geometric methods, the coordinate-free attitude controller and the nonlinear disturbance observer are integrated as a robust controller in the inner loop subsystem. Based upon full nonlinear dynamics, the solutions of the closed-loop system are proven to be uniformly ultimately bounded by means of rigorous Lyapunov analysis. A series of comparative experiments consisting of the implementation of a nonlinear proportional-integral-derivative (PID)-type controller, an observer-based sliding mode controller, and the proposed controller are conducted to demonstrate the remarkable performance of the proposed method in terms of higher tracking accuracy and stronger robustness.

Fully distributed time-varying formation tracking control for multiple quadrotor vehicles via finite-time convergent extended state observer

This paper investigates a time-varying anti-disturbance formation problem for a group of quadrotor aircrafts with time-varying uncertainties and a directed interaction topology. A novel Finite-Time Convergent Extended State Observer (FTCESO) based fully-distributed formation control scheme is proposed to enhance the disturbance rejection and the formation tracking performances for networked quadrotors. By adopting the hierarchical control strategy, the multi-quadrotor system is separated into two subsystems: the outer-loop cooperative subsystem and the inner-loop attitude subsystem. In the outer-loop subsystem, with the estimation of disturbing forces and uncertain dynamics from FTCESOs, an adaptive consensus theory based cooperative controller is exploited to ensure the multiple quadrotors form and maintain a time-varying pattern relying only on the positions of the neighboring aircrafts. In the inner-loop subsystem, the desired attitude generated by the cooperative control law is stably tracked under a FTCESO-based attitude controller in a finite time. Based on a detailed algorithm to specify the cooperative control protocol, the feasibility condition to achieve the time-varying anti-disturbance formation tracking is derived and the rigorous analysis of the whole closed-loop multi-quadrotor system is given. Some numerical examples are conducted to intuitively demonstrate the effectiveness and the improvements of the proposed control framework.

Super-Twisting direct torque optimal L2 -gain control for self-excitation induction generation system

The use of self-excitation induction generation system (SEIGs) was identified by many researchers as an important way to construct the high power density isolated power supply system (IPSS). However, for the wide variation range of the prime mover speed and the load power, the majority of the researchers consider it’s important to improve the power supply performance of the SEIGs. This research contributes to propose a new Super-Twisting direct torque optimal L2-gain control (ST-OP-L2-DTC) method for the SEIGs. In order to enhance the torque response speed, the Super-Twisting space vector direct torque control method is adopted in the voltage-linkage outer loop subsystem, comparing with sinusoidal angular modulation, which can improve 13.5 percent of the voltage usage ratio and raise the DC rectifier voltage. For minimizing disturbance influence, the optimal L2-gain control method is used in the current inner loop subsystem, which can minimize the impact of disturbance by solving the Linear Matrix Inequality (LMI) to obtain the optimal control law against the worst disturbance. Results of simulation and experiment show that, under the load power and the speed varying condition, comparing with traditional voltage outer loop-current inner loop (VOL-CIL) control method, ST-OP-L2-DTC method can enhance the DC output voltage transient stability, realize the derivative convergence of the sliding mode surface, shorten the stability time of the electromagnetic torque.

Nonlinear Hierarchical Control for Unmanned Quadrotor Transportation Systems

An unmanned quadrotor presents excellent mobility to fly freely in complex environments, which makes it an ideal choice for aerial transferring tasks. During the transferring process, it is very challenging to eliminate the swing, since there is no direct control on the payload. The quadrotor transportation system presents the great challenge of the cascaded underactuated–underactuated property, which makes it extremely difficult to simultaneously implement accurate quadrotor positioning and efficient payload swing suppression. In this paper, a nonlinear hierarchical control scheme is proposed for a quadrotor transportation system, which takes full advantage of the cascade property of the system and separates the controller design for the inner loop and the outer loop, respectively, to facilitate the design procedure. More specifically, for the outer loop subsystem, based on the proposed energy storage function, a virtual control vector is designed, which introduces a saturation function to make the desired attitude free of any singularities. For the inner loop, a coordinate-free geometric attitude tracking controller is designed on the Lie group to drive the quadrotor to its desired attitude. It is shown theoretically by Lyapunov techniques and LaSalle's invariance theorem that the equilibrium point of the overall system is asymptotically stable. As illustrated by experimental results, the proposed control law presents advantages such as high control precision, effective payload swing suppression, and so on.

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations.

Disturbance rejection control for attitude control of air-breathing hypersonic vehicles with actuator dynamics

A novel disturbance rejection control scheme is proposed to address the robust attitude control problem for the air-breathing hypersonic vehicle with actuator dynamics and disturbances based on predictive sliding mode control and nonlinear disturbance observer. To achieve attitude control subtly and precisely, the attitude control system is decomposed into two subsystems: the outer-loop subsystem and inner-loop subsystem. Different control schemes are taken to attenuate or reject model uncertainties and external disturbances, whose influences on the two subsystems are different. The predictive sliding mode control is first utilized to attenuate model uncertainties imposed on the outer-loop subsystem. Then, a novel nonlinear disturbance observer–based predictive sliding mode control is proposed to tackle the mismatched disturbances with remarkable influence on the inner-loop subsystem. Afterward, both the effectiveness and stability of the proposed nonlinear disturbance observer–based predictive sliding mode control disturbance rejection control scheme are demonstrated from the theoretical prospective. Finally, simulation results are given to present the effectiveness and robustness of the proposed disturbance rejection control scheme.

Integrated Finite-Time Disturbance Observer and Controller Design for Reusable Launch Vehicle in Reentry Phase

AbstractAn integrated finite-time disturbance observer (FDO) and attitude controller is designed for a reusable launch vehicle (RLV) in this paper. In accordance with the multiple-timescale features, RLV attitude dynamics are divided into an outer-loop subsystem and an inner-loop subsystem. Based on the recently developed sliding mode control (SMC), a novel multivariable supertwisting sliding mode controller driven by a FDO is designed to achieve a fast and accurate reentry attitude tracking. This integrated design can generate a continuous control law which has excellent robustness to uncertainty and disturbances with known bounds while achieving an arbitrarily fast convergence. The finite-time stability of the overall system is proved by using the Lyapunov function technique and the multiple-timescale separation principle. In addition, an optimal control allocation for allocating torque commands into aerodynamic surface deflection commands with constraints is also proposed. Finally, the effectiveness an...