Finite-time path following control for a stratospheric airship with input saturation and error constraint

This paper addresses the finite-time path following control problem for an under-actuated stratospheric airship with input saturation, error constraint, and external disturbances. To handle the adverse effect of input saturation, anti-windup compensators are employed and finite-time convergence of the saturated control solution is established. Error constraints of airship position and attitude are handled by incorporating a tan-type barrier Lyapunov function (TBLF) in guidance and attitude control schemes. Backstepping design is presented with the anti-windup compensators, the TBLF, and nonlinear disturbance observers which estimate the external disturbances. Stability analysis shows that the tracking errors of the airship position converge into a small set around zero within finite-time, the constrained requirements on the airship position and attitude are not violated during operation, and all closed-loop signals are guaranteed to be uniformly ultimately bounded. Compared with the conventional control scheme, simulation results illustrate that the proposed finite-time controller offers a faster convergence rate and a higher path following accuracy for the stratospheric airship.     

自治飞艇直接自适应模糊路径跟踪控制

针对具有模型不确定和未知外部干扰的自治飞艇, 提出了直接自适应模糊路径跟踪控制方法. 该方法由路径跟踪控制和自适应模糊控制两部分组成. 首先基于飞艇的平面运动模型设计路径跟踪控制律, 包括制导律计算、偏航角跟踪和速度控制3 部分; 然后构造直接自适应模糊控制器逼近路径跟踪控制律中的不确定项. 稳定性分析证明所设计的控制律能使飞艇跟踪给定的期望路径, 跟踪误差收敛到原点的小邻域内. 仿真结果验证了所提出方法的有效性.

     

Robust adaptive path following of underactuated ships

Robust path following is an issue of vital practical importance to the ship industry. In this paper, a nonlinear robust adaptive control strategy is developed to force an underactuated surface ship to follow a predefined path at a desired speed, despite the presence of environmental disturbances induced by wave, wind and ocean-current. The proposed controller is scalable and is designed using Lyapunov's direct method and the popular backstepping and parameter projection techniques. Along the way of proving closed-loop stability, we obtain a new stability result for nonlinear cascade systems with non-vanishing uncertainties. Interestingly, it is shown in this paper that our developed control strategy is easily extendible to situations of practical importance such as parking and point-to-point navigation. Numerical simulations using the real data of a monohull ship are provided to illustrate the effectiveness of the proposed methodology for path following of underactuated ships.     

Backstepping Sliding Mode Trajectory Tracking via Extended State Observer for Quadrotors with Wind Disturbance

To overcome nonlinear, underactuated and external wind disturbances problems for the 6-DOF (degrees of freedom) quadrotor unmanned aerial vehicle (UAV) system, a backstepping sliding mode control algorithm based on high-order extended state observer (ESO) is proposed. Based on the hierarchical control principle, the quadrotor UAV dynamic system is decomposed into position subsystem and attitude subsystem to facilitate the backstepping control design. Moreover, the EXO is used to estimate the remaining unmeasurable states and the external wind disturbances online. The advantages of the controllers are that they can not only ensure good tracking performance, but also deal with uncertain external disturbances. To imitate the real situation as much as possible, the external wind disturbances are composed of four basic wind models in this paper. The tracking error and estimate error of the design methods are shown to arbitrarily small by using Lyapunov theory. Finally, the effectiveness and superiority of the proposed control algorithm are proved by the simulation.

     

基于非线性迭代滑模的欠驱动UUV三维航迹跟踪控制

为实现欠驱动无人水下航行器(Unmanned underwater vehicle, UUV)在未知海流干扰作用下的三维航迹跟踪控制, 提出一种基于工程解耦思想设计的非线性迭代滑模航迹跟踪控制器. 基于虚拟向导的方法,建立UUV空间航迹跟踪误差方程;采用迭代方法设计非线性滑模控制器, 无需对UUV模型参数不确定部分和海流干扰进行估计,避免了舵的抖振现象以及减小了稳态误差与超调问题. 仿真实验表明,设计的控制器对欠驱动UUV系统的模型参数摄动及海流干扰变化不敏感、 且设计参数易于调节,可以实现三维航迹的精确跟踪.     

Command filtered path tracking control of saturated ASVs based on time‐varying disturbance observer

This paper investigates the path‐tracking control problem for an autonomous surface vessel (ASV) with unknown time‐varying disturbances and input saturation. A robust nonlinear control law is proposed based on a disturbance observer and an auxiliary system in the context of command filtered control. The disturbance observer is constructed to estimate the unknown time‐varying disturbances, the auxiliary dynamic system is employed to handle input saturation, and the compensator based command filtered control technique makes the designed path‐tracking control law simple and easy to implement in practice. It is proved that the nonlinear control law can track the desired vessel's position and heading, while guaranteeing the uniform ultimate boundedness of all signals in the path‐tracking control system. Simulation results further demonstrate the effectiveness of the method.     

Stabilization and Tracking Control of X‐Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control

A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X‐Z inverted pendulum known as a special underactuated, non‐feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower‐order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X‐Z inverted pendulum, including a comparative simulation with an all‐state‐feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques.     

Dynamic modeling and nonlinear tracking control of a novel modified quadrotor

In this article, a nonlinear tracking controller is designed based on Lyapunov stability for a novel aerial robot. The proposed 6‐rotor configuration improves stability and payload lifting capacity of the robot compared with conventional quadrotors while avoiding further complexities in the robot dynamics and steering principles. The dynamical model of the robot is derived using Newton‐Euler method. The model represents a nonlinear, coupled, and underactuated system. The proposed control strategy includes 2 main parts: an attitude controller and a position controller. Both the attitude and position controls are Lyapunov‐based nonlinear tracking controllers that guarantee the asymptotic convergence of the states' tracking errors to zero. Simulation results are presented to illustrate appropriate performance of the closed‐loop system in terms of position/attitude tracking even in the presence of wind disturbance.     

Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method

We present an asymptotic tracking controller for an underactuated quadrotor unmanned aerial vehicle using the sliding mode control method and immersion and invariance based adaptive control strategy in this paper. The control system is divided into two loops: the inner‐loop for the attitude control and the outer‐loop for the position. The sliding mode control technology is applied in the inner‐loop to compensate the unmatched nonlinear disturbances, and the immersion and invariance approach is chosen for the outer‐loop to address the parametric uncertainties. The asymptotic tracking of the position and the yaw motion is proven with the Lyapunov based stability analysis and LaSalle's invariance theorem. Real‐time experiment results performed on a hardware‐in‐the‐loop‐simulation testbed are presented to validate the good control performance of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Autonomous airship path following control: Theory and experiments

A novel path following control method related to the planar and spatial motions for an underactuated autonomous airship is presented. First, the trajectory linearisation control (TLC) theory is briefly described and the dynamic model of the airship is introduced. Then, based on the model, a path following strategy that integrates the guidance-based path following principle and the TLC theory is deduced. The designed control system possesses a cascaded structure composed of a guidance loop, an attitude kinematics loop and a dynamics control loop. Stability analysis shows that the controlled closed-loop system is asymptotically stable. Finally, experimental flight results for the airship following typical paths are illustrated to verify the effectiveness of the proposed approach.     

A novel trajectory planning-based adaptive control method for 3-D overhead cranes

A three-dimensional (3-D) overhead crane is a complicated nonlinear underactuated mechanical system, for which high-speed positioning and anti-sway control are the kernel objective. Existing trajectory-based methods for 3-D overhead cranes focus on combining efficient and smooth trajectories with anti-sway tracking controllers without regard for payload motion; moreover, the exact value of plant parameters is required for accurate compensation during the control process. Motivated by these facts, we present a two-step design tracking strategy which consists of a trajectory planning stage and an adaptive tracking control design stage for 3-D overhead cranes. As shown by Lyapunov techniques and Barbalat's Lemma, the proposed controller guarantees asymptotic swing elimination and trolley positioning result in the presence of system uncertainties including unknown parameters and external disturbances. Simulation results also showed the applicability of the proposed method with good robustness against parameter uncertainties and external disturbances.     

基于离散滑模预测的欠驱动AUV三维航迹跟踪控制

针对欠驱动自主水下航行器（AUV）的模型不确定和外界海流干扰问题,为了实现欠驱动AUV的三维航迹跟踪控制,采用虚拟向导法建立空间运动误差离散化模型.基于递归滑模思想设计离散滑模预测控制器,利用滚动优化和反馈校正方法补偿了不确定项对滑模预测模型的影响.最后针对某欠驱动AUV进行了空间曲线跟踪控制仿真实验.结果表明,所设计的控制器可以较好地克服时变非线性水动力阻尼对系统的影响,并对外界海流干扰有较好的抑制作用,保证了欠驱动AUV三维航迹跟踪系统的鲁棒性,实现了三维航迹的精确跟踪.     

风浪流干扰及参数不确定欠驱动船舶航迹跟踪的滑模鲁棒控制

针对欠驱动船舶的模型参数不确定和外界风浪流干扰问题,为实现水平面的航迹跟踪控制,提出了一种基于上下界的滑模控制方法.首先利用反步法将控制器的设计分解为运动学回路和动力学回路.其次,在运动学回路中为实现位置跟踪误差的收敛,根据期望航迹与当前位置信息,设计船舶的纵向与侧移参考速度,并视为镇定位置误差的虚拟控制律;在动力学回路中,将虚拟控制律作为新的跟踪目标,利用滑模方法设计实际控制律实现对参考速度的跟踪控制,最终实现了欠驱动船舶的跟踪控制.最后对有无干扰下的欠驱动船模分别进行了仿真实验,仿真结果证明了控制律的有效性.     

Global robust adaptive path following of underactuated ships

We propose a method for designing a global robust adaptive controller that forces an underactuated ship to follow a reference path under both constant and time-varying disturbances induced by waves, wind and ocean-currents. Both linear and nonlinear damping terms are included to cover both low- and high-speed applications. All nonlinear damping coefficients are assumed unknown but lie in a known compact set. The new results are derived using a choice of an appropriate body-fixed frame origin, a smooth approximation of nonsmooth damping terms, several nonlinear coordinate changes, the backstepping technique, and utilization of the ship dynamic structure. Experiments on a model ship illustrate the results.     

带有未知参数和有界干扰的移动机器人轨迹跟踪控

针对模型参数未知和存在有界干扰的非完整移动机器人的轨迹跟踪控制问题,本文提出了一种鲁棒自适应轨迹跟踪控制器方法.非完整移动机器人的控制难点在于它的运动学系统是欠驱动的.针对这一难点,本文利用横截函数的思想,引入新的辅助控制器,使得非完整移动机器人系统不再是一个欠驱动系统,缩减了控制器设计的难度,进而利用非线性自适应算法和参数映射方法构造李雅谱诺夫函数.通过李雅普诺夫方法设计控制器和参数自适应器,从而使得非完整移动机器人的跟随误差任意小,即可以任意小的误差来跟随任意给定的参考轨迹.仿真结果证明了方法的有效性.     

Robust fuzzy 3D path following for autonomous underwater vehicle subject to uncertainties

This paper addresses a three-dimensional (3D) path following control problem for underactuated autonomous underwater vehicle (AUV) subject to both internal and external uncertainties. A two-layered framework synthesizing the 3D guidance law and heuristic fuzzy control is proposed to achieve robust adaptive following along a predefined path. In the first layer, a 3D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the second layer, a heuristic adaptive fuzzy algorithm based on the guidance command and feedback linearization Proportional-Integral-Derivative (PID) controller is developed in the dynamics stage to account for the nonlinear dynamics and system uncertainties, including inaccuracy modelling parameters and time-varying environmental disturbances. Furthermore, the sensitivity analysis of the heuristic fuzzy controller is presented. Against most existing methods for 3D path following, the proposed robust fuzzy control scheme reduces the design and implementation costs of complicated dynamics controller, and relaxes the knowledge of the accuracy dynamics modelling and environmental disturbances. Finally, numerical simulation results validate the effectiveness of the proposed control framework and illustrate the outperformance of the proposed controller as well.     

Intelligent trajectory tracking of an aircraft in the presence of internal and external disturbances

This research deals with developing an intelligent trajectory tracking control approach for an aircraft in the presence of internal and external disturbances. Internal disturbances including actuators faults, unmodeled dynamics, and model uncertainties as well as the external disturbances such as wind turbulence significantly affect the performance of the common trajectory tracking control approaches. There are several fault‐tolerant control approaches in the literature to overcome the effects of specific actuator or sensor faults during the flight. However, trajectory tracking control of an air vehicle in the presence of unexpected faults and simultaneous presence of wind turbulence is still a challenging problem. In this paper, an intelligent neural network‐based model predictive control structure is proposed, where the prediction model is updated in each iteration based on a novel proposed online sequential multimodel structure. A hybrid offline‐online learning algorithm is adopted in the introduced online sequential multimodel structure to identify the time‐varying dynamics of the system. The proposed control structure can satisfactorily deal with unexpected actuator faults and structural damages as well as unmodeled dynamics and wind turbulence. The stability of the closed‐loop system is proved under some realistic assumptions. The simulation results demonstrate the high capability of the proposed approach for trajectory tracking control of a conventional aircraft in the simultaneous presence of system faults and external disturbances.     

An Enhanced Coupling Nonlinear Tracking Controller for Underactuated 3D Overhead Crane Systems

An enhanced coupling nonlinear tracking control method for an underactuated 3D overhead crane systems is set forth in the present paper. The proposed tracking controller guarantees a smooth start for the trolley and solves the problem of the payload swing angle amplitude increasing as the transferring distance gets longer for the regulation control methods. Different from existing tracking control methods, the presented control approach has an improved transient performance. More specifically, by taking the operation experience, mathematical analysis of the overhead crane system, physical constraints, and operational efficiency into consideration, we first select two desired trajectories for the trolley. Then, a new storage function is constructed by the introduction of two new composite signals, which increases the coupling behaviour between the trolley movement and payload swing. Next, a novel tracking control strategy is designed according to the derivation form of the aforementioned storage function. Lyapunov techniques and Barbalat's Lemma are used to demonstrate the stability of the closed‐loop system without any approximation manipulations to the original nonlinear dynamics. Finally, some simulation and experiments are used to demonstrate the superior transient performance and strong robustness with respect to different cable lengths, payload masses, destinations, and external disturbances of the enhanced coupling nonlinear tracking control scheme.     

Stabilization of an underactuated bottom‐heavy airship via interconnection and damping assignment

This paper focuses on feedback stabilization of a neutrally buoyant and bottom‐heavy airship actuated by only five independent controls (with the rolling motion underactuated). The airship is modelled as an eudipleural submerged rigid body whose dynamics is formulated as a Hamiltonian system with respect to a Lie–Poisson structure. By exploiting the geometrical structure and using the so‐called interconnection and damping assignment (IDA) passivity‐based methodology for port‐controlled Hamiltonian systems, state feedback control laws asymptotically stabilizing two typical motions are designed via La Salle invariance principle and Chetaev instability theorem. Simulation results verify the control laws. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust Backstepping Control Based on Integral Sliding Modes for Tracking of Quadrotors

Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results. Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem. However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants. In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton–Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model. Representative simulations are presented and discussed.