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.     

Robust decomposed system control for an electro-mechanical linear actuator mechanism under input constraints

This paper aims to develop a robust decomposed system control (RDSC) strategy under input constraints for an electro-mechanical linear actuator (EMLA) facing model uncertainty and external disturbances. At first, a state-space model of a complex multi-stage gearbox EMLA system, driven by a permanent magnet synchronous motor (PMSM), is developed, and the non-ideal characteristics of the ball screw are presented through the model. The result is a four-order nonlinear strict-feedback form (NSFF) system decomposed into three subsystems. As the paper's main result, a novel RDSC strategy with uniform exponential stability for controlling subsystem states is presented. This developed controller avoids the "explosion of complexity" problem associated with backstepping by treating the time derivative of the virtual control input as an uncertain system term. The proposed method, despite assuming load disturbances and input constraints with arbitrary bounds, offers a straightforward control approach for a broader range of applications. Further, the controller's performance is evaluated by simulating two distinct duty cycles, each representing different levels of demand on the actuator facing load disturbances near the rated motor performance.     

多输入多输出最小相位系统的执行器故障自适应容错控制

针对一类具有执行器卡死或/和变执行器故障的多输入多输出(MIMO)非线性最小相位系统提出了自适应容错跟踪控制方案.结合系统特征对系统执行器进行分类,用神经网络逼近执行器未知故障函数,采用模型参考自适应容错控制方法设计控制律.所设计的控制律不仅保证闭环系统稳定,而且跟踪误差一致最终有界.仿真结果表明了所提出方法的有效性.     

Adaptive decentralized finite‐time output tracking control for MIMO interconnected nonlinear systems with output constraints and actuator faults

In this work, we present a novel adaptive decentralized finite‐time fault‐tolerant control algorithm for a class of multi‐input–multi‐output interconnected nonlinear systems with output constraint requirements for each vertex. The actuator for each system can be subject to unknown multiplicative and additive faults. Parametric system uncertainties that model the system dynamics for each vertex can be effectively dealt with by the proposed control scheme. The control input gain functions of the nonlinear systems can be not fully known and state dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, with the use of graph theory, finite‐time convergence of the system output tracking error into a small set around zero is guaranteed for each vertex, while the time‐varying constraint requirement on the system output tracking error for each vertex will not be violated during operation. An illustrative example on 2 interacting 2‐degree‐of‐freedom robot manipulators is presented in the end to further demonstrate the effectiveness of the proposed control scheme.     

饱和非线性时滞系统约束预测控制

针对一类具有执行器饱和与输出约束的离散非线性时滞系统,提出新的模糊预测控制方法。首先,采用T-S模糊模型来逼近实际非线性系统,运用平行分步补偿（PDC）原理将该系统转化为一系列线性系统的凸组合。其次,通过每个采样时刻优化无穷时域的“min-max”性能指标来求解状态反馈预测控制器,得到系统满足Lyapunov渐近稳定的充分条件,并进一步将该条件转化为基于线性矩阵不等式（LMI）技术的半正定规划（SDP）问题。最后,通过数值仿真验证该方法的有效性。     

Fault tolerant control for a class of nonlinear system with actuator faults

In this work, a fault tolerant control scheme is proposed for a class of nonlinear system with actuator faults. In this fault tolerant control strategy, an estimator is designed to estimate both the system states and the fault signal simultaneously. Based on these estimations, the control law is constructed to achieve the fault tolerant control for the nonlinear system considered. It is shown that the estimation error and the system state can be guaranteed to be bounded. The obtained theoretic results have been verified through the simulation examples on the three‐tank system.     

Design of a sliding mode control system for chemical processes

This paper considers the non-linear regulation control of chemical processes. A novel and systematic sliding mode control system design methodology is proposed, which integrates an identified second-order plus dead-time (SOPDT) model, an optimal sliding surface and a delay-ahead predictor. The convergence property of the closed-loop system is guaranteed theoretically by means of satisfying a sliding condition and the control system performance is examined with some typical chemical processes. Besides, with the concept of delay equivalent, the proposed sliding mode control scheme can be utilized directly to the regulation control of a non-minimum phase process. As a special case the proposed scheme is further extended to the control of chemical processes whose dynamics are simply described by a first-order plus dead-time (FOPDT) model. In addition, the decentralized sliding mode control scheme for multivariable processes is also explored in this paper. Extensive simulation results reveal that the proposed sliding mode control system design methodology is applicable and promising for the non-linear regulation of time-delay chemical processes.     

带执行器饱和的柔性关节机器人位置反馈动态面控制

针对带有执行器饱和的柔性关节机器人系统,提出一种位置反馈动态面控制,以实现机器人连杆的角位置跟踪.在一般动态面控制的设计框架下,设计观测器重构系统未知速度状态,利用径向基函数神经网络学习饱和非线性特性,结合“最小参数学习”算法减轻计算负担.通过Lyapunov方法证明得出闭环系统所有信号半全局一致有界,跟踪误差可以通过调节控制器参数达到任意小.仿真结果表明,控制系统能够克服外界干扰,有效补偿系统存在的执行器饱和,实现柔性关节机器人的准确跟踪控制.该方法避免了传统反演设计存在的“微分爆炸”现象,简化了设计过程.     

具有执行器故障的不确定多智能体系统自适应动态面控制

本文研究了一类具有输入量化、未建模动态和执行器故障的非线性多智能体系统的一致跟踪问题.引入一个可量测的动态信号消除未建模动态对系统的影响.利用Young’s不等式和高斯函数的性质,有效地处理了多智能体邻居节点在设计的第一步中对子系统的耦合作用.通过将滞回量化器表示为具有有界系数和有界扰动的输入线性函数,并利用动态面控制方法,提出一种自适应神经网络动态面控制方案,简化了控制器的设计,保证了闭环系统的所有信号都是半全局一致终结有界的,所有跟随者都能实现期望的一致性.最后,仿真结果验证了所提出的自适应控制策略的有效性.     

Active vibration control for nonlinear vehicle suspension with actuator delay via I/O feedback linearization

The problem of nonlinear vibration control for active vehicle suspension systems with actuator delay is considered. Through feedback linearization, the open-loop nonlinearity is eliminated by the feedback nonlinear term. Based on the finite spectrum assignment, the quarter-car suspension system with actuator delay is converted into an equivalent delay-free one. The nonlinear control includes a linear feedback term, a feedforward compensator, and a control memory term, which can be derived from a Riccati equation and a Sylvester equation, so that the effects produced by the road disturbances and the actuator delay are compensated, respectively. A predictor is designed to implement the predictive state in the designed control. Moreover, a reduced-order observer is constructed to solve its physical unrealisability problem. The stability proofs for the zero dynamics and the closed-loop system are provided. Numerical simulations illustrate the effectiveness and the simplicity of the designed control.     

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints, for cases where the state constraints need to be enforced at all times (hard constraints) and where they can be relaxed for some time (soft constraints). We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time during which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.     

Globally linearized control system design of a constrained multivariable distillation column

The goal of this paper is to develop a discrete-time multivariable globally linearized control (GLC) algorithm, which provides low computational requirements with constraint handling ability. The control strategy is constructed with four elements: a transformer that accounts for process nonlinearities; an estimator, which observes the required unmeasured states; a variable constraint mapping optimizer that transforms the input constraints of the nonlinear process into constraints on the manipulated inputs of the globally linearized system and a quadratic dynamic matrix controller (QDMC) that provides constraints handling ability. The effectiveness of the designed controller has been tested on a multi-input multi-output (MIMO) nonlinear distillation column through extensive numerical simulations. The control law showed a high quality performance for set point tracking and disturbance rejection in presence of parametric uncertainty. The effect of unmeasured disturbance also has been studied through the simulation experiment. In the comparative study, the proposed GLC-QDMC control technique outperformed the GLC-DMC control law.     

Nonsingular predefined-time dynamic surface control of a flexible-joint space robot with actuator constraints

To achieve predefined-time trajectory tracking control of a flexible-joint space robot(FJSR) with actuator constraints, a nonsingular predefined-time dynamic surface control scheme is developed. The input saturation caused by actuator constraints is addressed via the designed predefined-time anti-saturation compensator. On this basis, two different control laws are designed for such high-order nonlinear systems by utilizing the backstepping technique, and a novel nonlinear filter is constructed to filter the virtual control signals, thus avoiding the “differential expansion” phenomenon. Moreover, a singularity-free auxiliary function is designed to solve the singularity issue generated by the derivative of fractional power terms in the predefined-time control algorithm framework. The closed-loop system is proven to be semi-globally predefined-timely uniformly ultimately bounded (SGPTUUB) via constructing the suitable Lyapunov function. The difference and effectiveness of the two designed control laws are illustrated by the conducted simulations. Both of them allow the FJSR system to track the desired trajectory in a reasonably predefined time.     

Synchronized adaptive control for coordinating manipulators with time‐varying actuator constraint and uncertain dynamics

This paper addresses the control issue for cooperative visual servoing manipulators on strongly connected graph with communication delays, in which case that the uncertain robot dynamics and kinematics, uncalibrated camera model, and actuator constraint are simultaneously considered. An adaptive cooperative image‐based approach is established to overcome the control difficulty arising from nonlinear coupling between visual model and robot agents. To estimate the coupled camera‐robot parameters, a novel adaptive strategy is developed and its superiority mainly lies in the containment of both individual image‐space errors and the synchronous errors among networked robots; thus, the cooperative performance is significantly strengthened. Moreover, the proposed cooperative controller with a Nussbaum‐type gain is implemented to both globally stabilize the closed‐loop systems and realize the synchronization control objective under the existence of unknown and time‐varying actuator constraint. Finally, simulations are carried out to validate the developed approach.     

一类MISO 最小相位系统的执行器故障自适应容错控制

针对一类具有执行器卡死或/和变执行器故障的多输入单输出(MISO)非线性最小相位系统,提出一种自适应容错跟踪控制方案.采用自适应算法估计系统的不确定性,利用神经网络逼近执行器未知故障函数,以完成执行器组合故障状态下的跟踪控制.所设计的控制律不仅保证了闭环系统稳定,而且所有状态均有界,跟踪误差一致最终有界.仿真结果表明了所提出方法的有效性.     

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

In the above paper Makoudi and Radouane, 2000 [A robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay. Automatica, 36, 1057-1065.], a model reference adaptive control (MRAC) algorithm is presented for non-minimum phase systems with unknown or time-varying delays. Unfortunately, this paper contains several mathematical mistakes that render the proofs of the claimed results erroneous. Furthermore, there are no obvious ways to correct these errors, so that the results presented in this paper are questionable.     

Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness‐based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger‐type observer within the two degrees‐of‐freedom control concept. The asymptotic stability of the closed‐loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C₀‐semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive compensation control for special actuator circumstances with input quantization

In this article, considering actuator constraints and possible failures, an adaptive compensation control scheme is developed to realize tracking control for a class of uncertain nonlinear systems with quantized inputs. A new variable is generated to evaluate the effect of actuator saturation and is used in the process of controller design to compensate for the influence of actuator saturation constraint. Moreover, the controller is able to show certain accommodation capability to tolerate possible actuator failures and input quantization error via integrating parameter update process of unknown fault constants into adaption of parametric uncertainties under the backstepping procedure. Specifically, actuator saturation effect and possible actuator failures as well as input quantization error can be dealt with uniformly under the framework of the proposed scheme and the control system has certain robustness to external disturbances. It is proved that all the signals of the closed‐loop system are ensured to be bounded and the tracking error is enabled to converge toward a compact set, which is adjustable by tuning design parameters. Finally, experiments are carried out on an active suspension plant to illustrate the effectiveness of the proposed control scheme.     

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

In this work, we propose a novel iterative learning control algorithm to deal with a class of nonlinear systems with system output constraint requirements and quantization effects on the system control input. Actuator faults have also been considered, which include multiplicative, additive, and stuck actuator faults. To the best of our knowledge, this is the first reported work in the iterative learning control literature to deal with quantization effects for the control input of nonlinear systems under the effects of actuator faults and system output constraints. Under the proposed scheme, using backstepping design and composite energy function approaches in the analysis, we show that uniform convergence of the state tracking errors can be guaranteed over the iteration domain, and the constraint requirement on the system output will not be violated at all time. In the end, a simulation study on a single‐link robot model is presented to demonstrate the effectiveness of the proposed scheme.     

直升机执行器故障的双时标容错控制系统设计

针对直升机的执行器故障,本文提出了一种基于双时标模型的自适应容错控制方法.根据直升机的不同状态变量响应时间不同的特点和时标分离理论,将直升机模型划分为快速(姿态动力学)和慢速(平移动力学)两种时标模型.反步控制方法和逆动力学控制方法分别被用于进行快慢两种模型控制器的设计,并在控制过程中采用了不同的控制周期.在双时标模型中,引入了执行器效率因子(actuator effectiveness factors,AEFs)用于表示执行器的健康情况.利用无色卡尔曼滤波(unscented Kalman filter,UKF)对AEFs进行了在线估计,估计结果用于快速和慢速模型控制器的自适应重构.仿真结果表明,该自适应容错控制方法,能够有效的消除执行器故障(包括常值和时变故障)对直升机飞行性能的影响,并取得良好的控制效果.