A Saturating Extension of an Output Feedback Controller for Internally Damped Euler‐Lagrange Systems

In this research, a novel extension of the passivity‐based output feedback trajectory tracking controller is developed for internally damped Euler‐Lagrange systems with input saturation. Compared with the previous output feedback controllers, this new design of a combined adaptive controller‐observer system will reduce the risk of actuator saturation effectively via generalized saturation functions. Semi‐global uniform ultimate boundedness stability of the tracking errors and state estimation errors is guaranteed by Lyapunov stability analysis. An application of the proposed saturated output feedback controller is the stabilization of a nonholonomic wheeled mobile robot with saturated actuators towards desired trajectories. Simulation results are provided to illustrate the efficiency of the proposed controller in dealing with the actuator saturation.     

Error-constrained path-following control for a stratospheric airship with actuator saturation and disturbances

This paper is concerned with the path-following control problem for an under-actuated stratospheric airship with error constraint, actuator saturation, and external disturbances. To address the tracking error-constrained requirements of airship position and attitude, novel tan-type barrier Lyapunov functions are proposed and incorporated with the guidance and attitude control schemes, which calculate the desired attitude and angular velocity. An auxiliary design system in the form of anti-windup compensator is employed to deal with actuator saturation, and the stability of the saturated control solution is verified. Nonlinear disturbance observer is developed to estimate the unknown external disturbances. Rigorous stability analysis shows that the constrained requirements on the airship position and attitude will not be violated under the proposed control method and all closed-loop signals are uniformly ultimately bounded, despite the presence of actuator saturation and disturbances. Simulation results and comparisons illustrate the effectiveness of the proposed controller.     

一类具有执行器饱和的非线性系统抗饱和方法研究

针对一类具有执行器饱和的非线性控制系统, 提出了一种双环路的动态抗饱和补偿方案, 为执行器输出受限的非线性系统提供了新思路. 与现有结果相比, 所提方案能更好地改善闭环系统控制性能. 考虑执行器饱和约束, 通过优化执行器饱和发生前后控制器的状态误差的积分性能指标, 综合设计一类同时包含传统抗饱和及延迟抗饱和补偿器两个环路的改进抗饱和补偿器, 这类补偿器有效地抑制了饱和现象对控制器的影响, 从而降低了执行器饱和对控制系统性能的影响. 当系统存在高饱和度现象时, 利用该双环路抗饱和补偿器, 可以最大程度弱化饱和对系统性能的影响. 最后, 利用输入状态稳定 (Input state stability, ISS) 定理分析和证明了该闭环系统全局一致有界稳定. 并通过舵机执行器受约束的舵减横摇系统的仿真试验, 验证了该方案的有效性及优越性.     

基于输出反馈的欠驱动TORA系统的有界输入控制

针对欠驱动TORA (Translational oscillations with a rotational actuator)系统, 设计了一种具有执行器饱和约束的输出反馈控制器.与其他现有方法相比, 本文方法不仅考虑了执行器饱和约束和速度信号不可测情形, 而且考虑了旋转小球可能存在的循环行为.具体而言, 首先根据TORA系统模型分析了TORA系统的控制目标; 随后, 构造了一种新颖的能量函数, 在此基础上设计了一种考虑执行器饱和约束的输出反馈控制器, 并通过严格的数学分析证明了闭环系统关于平衡点的稳定性; 最后, 借助数值仿真测试检验了所提控制器的控制性能, 并与已有方法进行了对比.仿真测试结果表明本文所提方法具有更好的控制性能.     

Fixed-structure controller design for systems with actuator amplitude and rate non-linearities

In this paper we develop output feedback controllers and fixed-order (i.e., full- and reduced-order) dynamic compensators for systems with actuator amplitude and rate saturation constraints. The proposed design methodology employs a rate limiter as part of the controller architecture. The problem of simultaneous control amplitude and rate saturation is embedded within an optimization problem by constructing a Riccati equation whose solution guarantees closed-loop global/local asymptotic stability in the face of sector bounded actuator amplitude and rate non-linearities. Application of the proposed framework is demonstrated via a flight control example involving actuator amplitude and rate saturation constraints.     

Stability of Switched Positive Linear Systems with Actuator Saturation under Mode-dependent Average Dwell Time

The stability problem is investigated for switched positive linear systems (SPLS) with unstabilized subsystem and actuator saturation. By using Lyapunov functions method and mode-dependent average dwell time (MDADT) strategy, sufficient conditions of the stability for the considered systems are established. We also give an estimate of the attraction domain. The convex hull represent approach is used to deal with actuator saturation. Finally, two examples are carried out to show the validity of results, which is less conservative than the average dwell time (ADT) switching.

     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed using a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimization problem. Numerical examples are presented to show the effectiveness of the proposed method.     

Fault‐Tolerant Control for Flutter of Airfoil Subject to Input Saturation

In this paper, a fault tolerant control is studied for a two‐dimensional airfoil with input saturation and actuator fault. The dynamic equation of airfoil flutter is firstly established, in which the cubic hard spring nonlinearity of pitch stiffness is considered. Then, an adaptive sliding mode fault tolerant control is derived by using an on‐line updating law to estimate the bound of the actuator fault such that no information about the fault is needed. Furthermore, an auxiliary design system is introduced to resolve actuator saturation in control. Next, Lyapunov stability analysis is carried out to prove that the system is asymptotically stable. Finally, the effectiveness of the proposed controller is verified through numerical simulations. Simulation results indicate that the adaptive sliding mode fault tolerant controller is effective in suppressing airfoil flutter under partial loss of actuator effectiveness performance and input saturation.     

Actuator fault‐tolerant control of ocean surface vessels with input saturation

In this paper, an actuator robust fault‐tolerant control is proposed for ocean surface vessels with parametric uncertainties and unknown disturbances. Using the backstepping technique and Lyapunov synthesis method, the adaptive tracking control is first developed by incorporating the actuator configuration matrix and considering actuator saturation constraints. The changeable actuator configuration matrix caused by rotatable propulsion devices is considered. Next, the actuator fault‐tolerant control is developed for the case when faults occur in propulsion devices of the ocean surface vessel. Rigorous stability analysis is carried out to show that the proposed fault‐tolerant control can guarantee the stability of the closed‐loop system under certain actuator failure. Finally, simulation studies are given to illustrate the effectiveness of the proposed adaptive tracking control and fault‐tolerant control. Copyright © 2015 John Wiley & Sons, Ltd.     

Switching event-triggered control of switched systems with actuator saturation

This paper focuses on switching event-triggered controller design for switched continuous-time systems with actuator saturation. First, we revisit the switching event-triggered sampled-data mechanism (ETSDM) to adapt it to the state feedback control of switched systems with actuator saturation. Then, by thinking of the ETSDM as a switching between periodic sampling and continuous ETSDM, constructing a switching multiple Lyapunov functions to give the analysis and design, and adopting the sector conditions to deal with the saturation, the sufficient conditions and the initial region ensuring the exponential stability of the switched system are proposed. Furthermore, the corresponding solvable conditions for the switching event-triggered controller and the triggering parameter matrices are established. Finally, a circuit example is given to illustrate the validity of the proposed results.     

Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults

This article investigates the stability analysis and control design of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults and saturation. It is assumed that the actuator faults of each subsystem are varying and governed by a Markovian process. The nonlinear term is located in a sector. First, sufficient conditions for stochastic stability of the underlying systems are established using a stochastic copositive Lyapunov function. Then, a family of reliable L₁‐gain controller is proposed for nonlinear positive Markovian jump systems with actuator faults and saturation in terms of a matrix decomposition technique. Under the designed controllers, the closed‐loop systems are positive and stochastically stable with an L₁‐gain performance. An optimization method is presented to estimate the maximum domain of attraction. Furthermore, the obtained results are developed for general Markovian jump systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.     

Wavelet based control for a class of delayed nonlinear systems with input constraints

In this paper, a delay independent adaptive control strategy is presented for a class of uncertain, delayed nonlinear system subjected to actuator saturation. In proposed control scheme wavelet networks are used for approximation of unknown system dynamics as well as a wavelet based compensator is designed to deal with actuator saturation. Delayed wavelet networks are used for identification of unknown system dynamics having state delayed terms, thereby the approximation capabilities of delayed wavelet network are utilized. Adaptation laws are developed for the online tuning of wavelet parameters. Adaptation singularity problem is solved by employing a switching scheme. The stability of closed loop system and ultimate upper boundedness all closed loop signals is proved by constructing a Lyapunov–Krasovskii functional.     

A practical PID regulator with bounded torques for robot manipulators

This paper proposes a saturated nonlinear PID regulator for industrial robot manipulators. Our controller considers the natural saturation problem given by the output of the control computer, the saturation phenomena of the internal PI velocity controller in the servo driver, and the actuator torque constraints of the robot manipulator. An approach based on the singular perturbations method is used to analyze the exponential stability of the closed-loop system. Experimental essays show the feasibility of the proposed controller. Furthermore, the theoretical results justify why the classical PID used in industrial robots preserves its exponential stability despite the saturation effects of the electronic control devices and the actuator torque constraints.     

Adaptive fuzzy neural network finite-time command filtered control of n-link robotic systems with actuator saturation

The finite time tracking control of n-link robotic system is studied for model uncertainties and actuator saturation. Firstly, a smooth function and adaptive fuzzy neural network online learning algorithm are designed to address the actuator saturation and dynamic model uncertainties. Secondly, a new finite-time command filtered technique is proposed to filter the virtual control signal. The improved error compensation signal can reduce the impact of filtering errors, and the tracking errors of system quickly converge to a smaller compact set within finite time. Finally, adaptive fuzzy neural network finite-time command filtered control achieves finite-time stability through Lyapunov stability criterion. Simulation results verify the effectiveness of the proposed control.     

带执行器饱和的N 连杆机械臂输出反馈动态面控制

针对带执行器饱和的多关节刚性机械臂系统,提出一种基于RBF神经网络补偿的输出反馈动态面控制.通过观测器实现角速度的观测,采用RBF网络实现执行器饱和的补偿;通过Lyapunov方法证明闭环系统的稳定性,实现高精度的角度和角速度跟踪.仿真结果表明,所提出的方法能够有效补偿系统存在的执行器饱和,显著减小跟踪误差,并且对于外界干扰具有一定的鲁棒性.     

Fault-tolerant Control for Linear System Under Sensor Saturation Constraint

An observer-based fault-tolerant control method is proposed for a linear system with sensor saturation constraint. Considering the linear system with simultaneous actuator faults and sensor faults, the sensor saturation would bring the output measurement error of the system, which would result in the estimation performance degradation. Firstly, the intermediate estimator is modified to estimate the system states and fault signals at the simultaneous time, and the fault-tolerant controller is designed based on the estimation to compensate the effect of actuator faults effectively. Through Lyapunov stability analysis, the sufficient conditions are obtained to ensure the states of closed-loop system to be uniformly ultimately bounded. The effect of sensor saturation error can be suppressed by adjusting some specified parameters directly without introducing any performance index. Finally, the effectiveness and superiority of the proposed method are verified by a simulation example.

     

Neural network control of a class of nonlinear systems with actuator saturation

A neural net (NN)-based actuator saturation compensation scheme for the nonlinear systems in Brunovsky canonical form is presented. The scheme that leads to stability, command following, and disturbance rejection is rigorously proved and verified using a general "pendulum type" and a robot manipulator dynamical systems. Online weights tuning law, the overall closed-loop system performance, and the boundedness of the NN weights are derived and guaranteed based on Lyapunov approach. The actuator saturation is assumed to be unknown and the saturation compensator is inserted into a feedforward path. Simulation results indicate that the proposed scheme can effectively compensate for the saturation nonlinearity in the presence of system uncertainty.     

Actuator saturation and anti-windup compensation in event-triggered control

Event-triggered control aims at reducing the communication load over the feedback link in networked control systems by sending information only if certain event conditions, which guarantee a desired control performance, are satisfied. This article investigates the consequences of actuator saturation on the behavior of the event-triggered control loop in terms of its stability and information exchange. Stability properties are derived using linear matrix inequalities (LMIs) which show how the stability of the event-triggered control loop depends on the selection of the event threshold. Moreover, it is shown that a lower bound on the minimum inter-event time exists being likewise affected by the event threshold. As actuator saturation might severely degrade the performance of the event-triggered closed-loop system, the scheme is extended by incorporating an anti-windup mechanism in order to overcome this problem. The results are illustrated by simulations and experiments.     

考虑状态约束与执行器饱和的水下机器人轨迹跟踪控制

针对执行器饱和、模型参数不确定以及海流干扰等因素影响下的水下机器人,提出一种考虑状态约束以及执行器饱和的轨迹跟踪控制器.首先,构建水下机器人水平面轨迹跟踪误差方程;然后,对载体模型参数不确定性产生的模型误差以及海流干扰,设计一个非线性观测器进行估计并用于对控制器进行扰动补偿;接着,引入执行器饱和补偿系统、二阶滤波器以及滤波器误差补偿系统,设计命令滤波反步滑模控制器来控制水下机器人的水平面轨迹跟踪;最后,严格验证命令滤波反步滑模控制器的稳定性并进行数值仿真,验证所提出控制器的有效性.