Observer-based Adaptive Fuzzy Backstepping Tracking Control of Quadrotor Unmanned Aerial Vehicle Powered by Li-ion Battery

In this paper, an Adaptive Fuzzy Backstepping Control (AFBC) approach with state observer is developed. This approach is used to overcome the problem of trajectory tracking for a Quadrotor Unmanned Aerial Vehicle (QUAV) under wind gust conditions and parametric uncertainties. An adaptive fuzzy controller is directly used to approximate an unknown nonlinear backstepping controller which is based on the exact model of the QUAV. Besides, a state observer is constructed to estimate the states. The stability analysis of the whole system is proved using Lyapunov direct method. Uniformly Ultimately Bounded (UUB) stability of all signals in the closed-loop system is ensured. The proposed control method guarantees the tracking of a desired trajectory, attenuates the effect of external disturbances such as wind gust, and solves the problem of unavailable states for measurement. Extended simulation studies are presented to highlight the efficiency of the proposed AFBC scheme.     

Disturbance observer based backstepping for position control of electro-hydraulic systems

We propose a disturbance observer (DOB) based backstepping control which improves the position tracking performance in the presence of both friction and load force in an electro-hydraulic systems. The DOB is designed to estimate the disturbance including friction and load force, while avoiding amplification of the measurement noise. We use an auxiliary state variable to avoid the use of the derivative of the measured signal. This results in the avoidance of the amplification of the measurement noise. For position tracking with compensation of disturbances, a backstepping controller is design. The backstepping controller guarantees the ultimate boundedness of the tracking error in the presence of both friction and load force. The closed-loop stability is proven using Lyapunov’s theory.

     

Novel smooth sliding mode attitude control design for constrained re-entry vehicle based on disturbance observer

This paper investigates the attitude tracking control system design for reusable launch vehicle (RLV) in re-entry phase with input constraint, model uncertainty and external disturbance. The novel control scheme is designed via combining the advantages of the robust property of sliding mode control (SMC), the compensation ability of disturbance observer (DOB) and the systematic design procedure of backstepping technique. By applying DOB technique to estimate the lumped uncertainty, there is no need to choose the switch gain larger than the bound of uncertainty. Through designing the exponential form sliding surface and smooth sliding mode controller, the chattering and discontinuous problem inherent in the traditional SMC is alleviated. An additional system is constructed to handle input constraint. Based on Lyapunov theory, the asymptotic stability of the closed-loop system is proven. At last, compared simulations are presented to verify the effectiveness of the proposed control approach.     

主旋翼升力和机身姿态受限的模型直升机非线性控制（英文）

A nonlinear control is proposed for trajectory tracking of a 6-DOF model-scaled helicopter with constraints on main rotor thrust and fuselage attitude. In the procedure of control design, the mathematical model of helicopter is simplified into three subsystems: altitude subsystem, longitudinal-lateral subsystem and attitude subsystem. The proposed control is developed by combining the sub-controls for the corresponding subsystems. The sub-controls for altitude subsystem and longitudinal-lateral subsystem are designed with hyperbolic tangent functions to satisfy the constraints; the sub-control for attitude subsystem is based on backstepping technique such that fuselage attitude tracks the virtual control for longitudinallateral subsystem. It is proved theoretically that tracking errors are ultimately bounded, and control constraints are satisfied.Performances of the proposed controller are demonstrated by simulation results.     

主旋翼升力和机身姿态受限的模型直升机非线性控制

针对主旋翼升力和机身姿态受限的6自由度模型无人直升机的轨迹跟踪控制问题设计了一种非线性控制器.在控制器设计过程中,直升机的数学模型被简化为三个子系统: 姿态子系统,纵-侧向子系统和高度子系统,所设计的控制器由针对这三个子系统的子控制器组成.纵-侧向和高度子控制器基于双曲正切函数进行设计,以保证满足受限条件; 姿态子控制器利用反步法设计,使得机身姿态能够跟踪纵-侧向和高度子系统的虚拟控制.本文在理论上证明了闭环系统跟踪误差最终有界,并且控制器满足受限条件.仿真结果证实了所设计控制器的性能.     

基于非线性干扰观测器的高超声速飞行器滑模反演控制

针对高超声速飞行器非线性、强耦合和参数不确定弹性体模型,提出了一种基于非线性干扰观测器的滑模反演控制方法.将飞行器曲线拟合模型分解为速度子系统和高度相关子系统并表示为严格反馈形式,分别采用滑模和反演方法设计实际控制量与虚拟控制量.采用1阶低通滤波器获取虚拟控制量的导数,解决了传统反演控制方法"微分项膨胀"问题.基于改进滑模微分器设计了一种新型非线性干扰观测器,以此对模型不确定项进行估计和补偿.仿真结果表明,该控制器对模型不确定性和气动弹性影响具有鲁棒性,且实现了对速度和高度参考输入的稳定跟踪.     

Tracking control of second‐order chained form systems by cascaded backstepping

A design methodology is presented for tracking control of second‐order chained form systems. The methodology separates the tracking‐error dynamics, which are in cascade form, into two parts: a linear subsystem and a linear time‐varying subsystem. The linear time‐varying subsystem, after the first subsystem has converged, can be treated as a chain of integrators for the purposes of a backstepping controller. The two controllers are designed separately and the proof of stability is given by using a result for cascade systems. The method consists of three steps. In the first step we apply a stabilizing linear state feedback to the linear subsystem. In the second step the second subsystem is exponentially stabilized by applying a backstepping procedure. In the final step it is shown that the closed‐loop tracking dynamics of the second‐order chained form system are globally exponentially stable under a persistence of excitation condition on the reference trajectory. The control design methodology is illustrated by application to a second‐order non‐holonomic system. This planar manipulator with two translational and one rotational joint (PPR) is a special case of a second‐order non‐holonomic system. The simulation results show the effectiveness of our approach. Copyright © 2002 John Wiley & Sons, Ltd.     

水上无人机自主着水控制系统设计

针对水上无人机在高海况下的着水问题,本文在分析了不同着水阶段特性的基础上,提出了一种自主着水控制系统设计方案.该方案将整个系统分为速度控制子系统和姿态控制子系统.速度控制子系统包含速度动态逆控制器和油门切换模块,姿态控制子系统包含海浪滤波器俯仰角反步控制器、高度PID控制器、俯仰角切换模块和T-S模糊推理模块.其中,海浪滤波器能有效滤除受扰姿态角中的海浪高频扰动,避免了着水之后舵面的频繁抖动;俯仰角反步控制器采用指令滤波的反步法设计,有效缓解了高海况下的舵面饱和问题.最后,在不同海况条件下进行了仿真.仿真结果表明所设计的控制系统具有良好的控制性能.     

Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding‐Mode Neural Network

In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual‐arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding‐mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding‐mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e‐modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method.     

四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性集总未知非线性的四旋翼飞行器,提出了一种采用自适应不确定性补偿器的自适应动态面轨迹跟踪方法.通过将四旋翼飞行器系统分解为位置、欧拉角和角速率3个动态子系统,使各子系统虚拟控制器设计能充分考虑欠驱动约束;结合动态面控制技术,通过采用一阶低通滤波器,避免对虚拟控制信号求导;进而设计自适应不确定性补偿器,处理未知外界扰动和系统不确定性,最终确保闭环控制系统的稳定性、跟踪误差一致最终有界和系统所有状态信号有界.仿真研究和实验结果验证了本文提出控制方法的有效性和优越性.     

Optimal control of non-minimum phase integrating processes with time delay using disturbance observer-based control scheme

A systematical design method of optimal control for non-minimum phase integrating processes with time delay using disturbance observer-based (DOB) control scheme is presented. All stabilising controllers and the filter of DOBs for integrating plants are developed. Then the optimal set-point tracking controller and the optimal filter of DOB are systematically derived by minimising the H₂ norm performance specifications. The proposed design method has three main advantages. First, the design procedure is systematical and simple. Specified weight functions are chosen for step inputs and inputs similar to steps. The designed set-point tracking controller and the filter of DOB are given in analytical forms. Second, the designed set-point tracking controller and the filter of the DOB are optimal. They are derived from minimising the performance indexes of set-point tracking and input load disturbance rejection (ILDR). Finally, the set-point tracking performance specification and ILDR specification can be quantitatively achieved by conveniently tuning the adjustable parameters. Numerical simulations are given to illustrate the effectiveness of the proposed method.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.     

An adaptive fuzzy design for fault-tolerant control of MIMO nonlinear uncertain systems

This paper presents a novel control method for accommodating actuator faults in a class of multiple-input multiple-output (MIMO) nonlinear uncertain systems.The designed control scheme can tolerate both the time-varying lock-in-place and loss of effectiveness actuator faults.In each subsystem of the considered MIMO system,the controller is obtained from a backstepping procedure;an adaptive fuzzy approximator with minimal learning parameterization is employed to approximate the package of unknown nonlinear functions in each design step.Additional control effort is taken to deal with the approximation error and external disturbance together.It is proven that the closed-loop stability and desired tracking performance can be guaranteed by the proposed control scheme.An example is used to show the effectiveness of the designed controller.     

基于有限时间预设性能的高超声速飞行器反演控制

针对存在参数不确定以及外界干扰的高超声速飞行器跟踪性能问题,提出一种基于有限时间预设性能的反演控制方案.首先,为便于控制器设计,将高超声速飞行器模型划分为速度和高度子系统,针对子系统分别设计预设性能控制器以提高系统的瞬态和稳态性能;然后,通过设计一种有限时间性能函数,使得跟踪误差能够在预设时间内收敛至稳态值;接着,考虑到反演设计中虚拟指令导数难以获取以及干扰项对系统的影响,基于干扰观测器提出一种扰动估计方法,目的是在取得良好的观测扰动效果的同时,使得控制器设计流程简化、复杂度降低;最后,基于Lyapunov稳定理论证明系统的跟踪误差最终一致有界,并通过仿真验证该方法的有效性.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance

In order to accommodate actuator failures which are uncertain in time, pattern and value, we propose two adaptive backstepping control schemes for parametric strict feedback systems. Firstly a basic design scheme on the basis of existing approaches is considered. It is analyzed that, when actuator failures occur, transient performance of the adaptive system cannot be adjusted through changing controller design parameters. Then we propose a new controller design scheme based on a prescribed performance bound (PPB) which characterizes the convergence rate and maximum overshoot of the tracking error. It is shown that the tracking error satisfies the prescribed performance bound all the time. Simulation studies also verify the established theoretical results that the PPB based scheme can improve transient performance compared with the basic scheme, while both ensure stability and asymptotic tracking with zero steady state error in the presence of uncertain actuator failures.     

Global stable tracking control of underactuated ships with input saturation

In this paper, tracking control of underactuated ship in the presence of input saturation is addressed. By dividing the tracking error dynamic system into a cascade of two subsystems, the torques in surge and yaw axes are designed separately using the backstepping technique. More specifically, we design the yaw axis torque in such a way that its corresponding subsystem is finite time stable, which makes it to be de-coupled from the second subsystem after a finite time. This enables us to design the torque in the surge axis independently. It is shown that the closed-loop system is stable and the mean-square tracking errors can be made arbitrarily small by choosing design parameters. Simulation results also verify the effectiveness of the proposed scheme.     

输出误差约束下四旋翼无人机预定性能反步控制

针对外界干扰和输出误差约束条件下的四旋翼无人机的跟踪控制问题,提出预定性能反步跟踪控制策略.首先,将四旋翼无人机动力学模型转换为带有外界干扰的严反馈形式;然后,利用反步法设计控制器,通过引入障碍Lyapunov函数保证跟踪误差的预定性能,设计干扰观测器对外界干扰进行估计,并通过滤波器估计姿态子系统中部分虚拟控制输入的导数;通过稳定性分析说明所设计的控制器可以保证跟踪误差的有界稳定性,且跟踪误差一直处于预设边界内;最后,通过仿真验证所设计控制策略的有效性.     

一类直接模型参考Backstepping自适应控制

提出一种新的直接模型参考Backstepping自适应控制系统结构:谈系统在直接模型参考卓适应控制(MRAC)结构的基础上,增加了Beckstepping控制信号发生器,通过Backstepping方法的灵活设计获得良好的过渡过程品质,得到直接MRAC在稳定性和鲁棒性设计等方面的优点.采用高阶调节器设计了未具规范化的直接模型参考Backstepping自适应律,克服了传统自适应律引入规范化信号后使系统过渡过程品质下降的缺点.     

Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.