具有输入饱和的近空间飞行器鲁棒控制

针对近空间飞行器这一类存在外部扰动,输入饱和和参数不确定的多输入多输出线性系统,提出了一种基于干扰观测器的抗饱和鲁棒控制方案.将干扰观测器与抗饱和控制技术相结合,从而消除系统存在的未知外部扰动、输入饱和和不确定性对系统控制的影响.首先,设计干扰观测器对线性外部系统产生的未知扰动进行估计.然后根据干扰观测器输出,通过超前抗饱和方法设计抗饱和补偿器,并将其加入到鲁棒控制器的设计中,保证闭环系统存在输入饱和、未知外部扰动和参数不确定情况下的稳定性.为便于设计,干扰观测器、抗饱和补偿器和控制器设计矩阵均通过求解线性矩阵不等式得到.最后,将提出的鲁棒抗饱和控制方法应用于近空间飞行器,仿真结果验证了该控制方案的有效性.     

Anti-windup controller design using linear parameter-varying control methods

In this paper, we seek to provide a systematic anti-windup control synthesis approach for systems with actuator saturation within a linear parameter-varying (LPV) design framework. The closed-loop induced L2 gain control problem is considered. Different from conventional two-step anti-windup design approaches, the proposed scheme directly utilizes saturation indicator parameters to schedule accordingly the parameter-varying controller. Hence, the synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved very efficiently. The resulting gain-scheduled controller is non-linear in general and would lead to graceful performance degradation in the presence of actuator saturation non-linearities and linear performance recovery. An aircraft longitudinal dynamics control problem with two input saturation non-linearities is used to demonstrate the effectiveness of the proposed LPV anti-windup scheme.     

轮式移动机器人的数据驱动轨迹跟踪滑模约束控制

针对有输入饱和约束的轮式移动机器人(WMR)的轨迹跟踪问题,提出一种抗饱和无模型自适应积分终端滑模控制方案.该方案基于紧格式动态线性化技术,构建WMR系统的在线数据驱动模型.在积分终端滑模控制器设计过程中,引入动态抗饱和补偿器,以解决WMR系统轨迹跟踪过程中执行器饱和问题.控制器设计仅利用控制系统的输入输出数据,与WMR系统模型信息无关.因此,针对不同类型的WMR系统,该方案均可实现.最后,通过仿真实验将所提出的方法与PID方法的控制效果进行对比,仿真结果表明,所提出的控制算法的跟踪误差更小且响应速度更快.     

Nonlinear scheduled anti-windup design for linear systems

The nonlinear L/sub 2/ anti-windup framework introduced in Teel and Kapor (1997) reduces the anti-windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched L/sub 2/ disturbances. In this note, based on the structure proposed in that previous paper, we provide a linear matrix ineqaulity (LMI) formulation of high-performance anti-windup design for control systems with linear asymptotically stable plants. In particular, we first give a linear quadratic-based formulation of linear anti-windup compensation, in terms of the solution of a set of (always feasible) LMI constraints. Then, we propose a nonlinear scheduling technique, where hysteresis switching among a family of linear gains is employed for performance improvement. Both design techniques are demonstrated on an academic example.     

单输入线性系统的改进型动态抗饱和设计

本文基于状态重置的改进型动态抗饱和补偿方案, 研究了具有单输入的线性饱和系统的抗饱和控制问题. 相比较于传统的动态抗饱和补偿方案, 当执行器不饱和时, 改进的动态抗饱和补偿方案把动态抗饱和补偿器的状态重置为零. 所以当执行器不饱和时, 改进的动态抗饱和补偿器将不会对控制器进行补偿. 进一步的, 提出了一个时间依赖的Lyapunov函数来分析闭环系统的稳定性, 并以LMIs的形式给出了闭环系统的控制综合条件. 最后, 通过压电纳米运动平台验证了所提出的改进型动态抗饱和补偿方案的有效性。     

Model recovery anti-windup for output saturated SISO linear closed loops

We define model recovery anti-windup for SISO linear control systems with output saturation. We address the problem by relying on a hybrid modification of the linear closed loop which employs a suitable logic variable to activate/deactivate various components of a control scheme. The scheme relies on a finite-time observation law, an open-loop observer and an open-loop input generator which is capable of driving the plant output within the saturation limits. Then the control scheme is based on suitable (hybrid) resetting laws allowing the controller to operate on the artificial output signal generated by the open-loop observer when the actual plant output is outside the saturation limits. Unlike existing results, not only we prove uniform global asymptotic stability of the closed loop, but we also prove the local preservation and global recovery properties, typical of model recovery anti-windup paradigms. We also illustrate the proposed technique on an example study.     

An approximated scalar sign function approach to optimal anti-windup digital controller design for continuous-time nonlinear systems with input constraints

This article presents an approximated scalar sign function-based digital design methodology to develop an optimal anti-windup digital controller for analogue nonlinear systems with input constraints. The approximated scalar sign function, a mathematically smooth nonlinear function, is utilised to represent the constrained input functions, which are often expressed by mathematically non-smooth nonlinear functions. Then, an optimal linearisation technique is applied to the resulting nonlinear system (with smooth nonlinear input functions) for finding an optimal linear model, which has the exact dynamics of the original nonlinear system at the operating point of interest. This optimal linear model is used to design an optimal anti-windup LQR, and an iterative procedure is developed to systematically adjust the weighting matrices in the performance index as the actuator saturation occurs. Hence, the designed optimal anti-windup controller would lie within the desired saturation range. In addition, the designed optimal analogue controller is digitally implemented using the prediction-based digital redesign technique for the effective digital control of stable and unstable multivariable nonlinear systems with input constraints.     

Anti-windup design of uncertain discrete-time Markovian jump systems with partially known transition probabilities and saturating actuator

This paper carries out a study on the design of anti-windup gains for uncertain discrete-time Markovian jump systems subject to both actuator saturation and partially known transition probabilities. The parameter uncertainties appearing in both the state and input matrices are assumed to be time-varying and norm-bounded. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilise the Markovian jump system in the absence of actuator saturation, anti-windup compensation gains are designed for maximising the domain of attraction of the closed-loop system with actuator saturation. Then, by solving a convex optimisation problem with constraints of a set of linear matrix inequalities, the anti-windup compensation gains are obtained. A simulation example is provided to illustrate the effectiveness of the proposed technique.     

基于系统输出的嵌套饱和系统抗饱和补偿器设计

针对嵌套输入饱和系统的吸引域扩大问题,本文提出了一种基于系统输出的抗饱和补偿器激发策略,将被控系统输出信号经性能补偿器馈入到抗饱和补偿器激发环节中,形成蕴含系统实时性能信息的抗饱和激发新机制,克服了传统抗饱和激发机制无法直接反映系统性能的缺点.基于上述抗饱和控制新框架,本文建立了抗饱和补偿器及性能补偿器存在的充分条件,并依此构建了优化问题求解最优补偿器增益以实现扩大闭环系统吸引域的目的.仿真结果表明本文方法的有效性.     

非合作目标绕飞任务的航天器鲁棒姿轨耦合控制

本文研究了非合作目标强迫绕飞过程中存在外部干扰和参数不确定性以及控制输入饱和约束下的航天器鲁棒姿轨耦合控制问题.首先,根据视线坐标系下的轨道动力学方程和本体坐标系下的姿态动力学方程,建立了满足视线指向要求的航天器相对姿轨耦合动力学模型.其次,针对姿轨耦合模型,基于反步法设计了具有抗饱和能力的鲁棒自适应姿轨耦合控制律,其中利用抗饱和技术设计了饱和补偿器,并结合自适应方法对未知参数和扰动上界进行估计,并基于Lyapunov方法给出了闭环系统的稳定性证明.最后,将提出的控制方案进行了数值仿真和比较,验证了其有效性.     

共轴八旋翼无人飞行器的偏航静态抗饱和补偿控制

设计了一种共轴八旋翼无人飞行器,与四旋翼飞行器相比,其具有更大的驱动能力、更强的带载能力和一定的冗余能力．首先,建立了飞行器的动力学模型．针对共轴八旋翼飞行器偏航运动能力比俯仰、滚转运动能力弱,偏航容易出现执行器饱和现象的问题,从实际工程出发提出了基于线性自抗扰控制器的静态抗饱和补偿器．线性自抗扰算法易于工程调节,能够实时估计与补偿外界扰动．静态抗饱和补偿器不增加系统阶次,有效抑制偏航执行器饱和．利用李亚普诺夫稳定理论证明了基于线性自抗扰控制器的静态抗饱和偏航控制系统的稳定性．最后,通过共轴八旋翼飞行器的仿真实验与原型机比较实验验证了算法的有效性与鲁棒性．原型机实验结果表明：在室内固定干扰下,执行器退出饱和的最长时间约为4 s,偏航角误差收敛到±0.085 rad;在室外变干扰下,执行器退出饱和的最长时间约为9 s,偏航角误差收敛到±0.127 rad．基于线性自抗扰控制器的静态抗饱和补偿器在外界干扰情况下能够有效地抑制执行器饱和,具有良好的偏航控制性能与强鲁棒性．     

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.     

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.     

A switching anti-windup design based on partitioning of the input space

This paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti-windup compensator. The closed-loop system consisting of the plant, the controller and the anti-windup compensator is first equivalently formulated as a linear system with input deadzone. We then partition the input space into several regions. In one of these regions, all inputs saturate with the time-derivative of the saturated input being zero. In each of the remaining regions, there is a unique input that does not saturate. The time derivative of the deadzone function associated with the unsaturating input is zero. By utilizing these special properties of the inputs on an existing piecewise Lyapunov function of the augmented state vector containing the deadzone function of inputs, we design a separate anti-windup gain for each region of the input space. The switching from one anti-windup gain to another is activated when the input signals leave one region for another, which can be implemented online since only the measurement of the input signals is required. Simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches.     

Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization

We present a method for the synthesis of a control law for input constrained linear systems that incorporates both a traditional linear output-feedback controller as well as a static anti-windup compensator. Unlike traditional two-step anti-windup controller designs in which the linear controller and anti-windup compensator are designed sequentially, our method synthesizes all controller parameters simultaneously. This one-step design retains the anti-windup structure, thus providing structurally ‘a priori’ compensation for saturation. We derive sufficient conditions for guaranteeing global quadratic stability and for satisfying multiple, possibly conflicting, performance objectives on the constrained and unconstrained closed-loop dynamics. The resulting synthesis problem is recast as an optimization over linear matrix inequalities (LMIs). We demonstrate the proposed method on a benchmark problem.     

具有输入饱和的电液伺服位置系统自适应动态面控制

针对具有非线性、参数不确定性及输入饱和问题的电液伺服位置系统,提出了一种自适应动态面控制器的设计方法.该方法充分考虑饱和特性,利用双曲正切函数和辅助控制信号对系统非线性模型进行等价变换,进而采用动态面方法设计抗饱和控制器.设计过程中引入Nussbaum函数,以补偿输入饱和引起的非线性项.通过构造合适的Lyapunov函数,证明闭环系统的所有信号一致最终有界.仿真结果表明,所设计的控制器具有良好的跟踪效果,并有效地削弱了输入饱和对系统造成的不良影响.     

Guaranteed Cost Anti-windup Stabilization of Discrete Delayed Cellular Neural Networks

This paper studies the problem of guaranteed cost anti-windup stabilization of discrete delayed cellular neural networks. Saturation degree function is initially presented and the convex hull theory is applied to handle the saturated terms of discrete delayed cellular neural networks. Accordingly, after choosing a common quadratic performance function, the paper designs a guaranteed cost stabilization controller in the absence of input saturation on the basis of Lyapunov–Krasovskii theorem and linear matrix inequality formulation. Then a static state feedback anti-windup compensation is derived, which guarantee a guaranteed cost and the estimation of the asymptotic stability region for the closed-loop system. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed design technique.     

Dynamic anti-windup scheme for feedback linearizable nonlinear control systems with saturating inputs

This paper proposes a dynamic compensation scheme for input-constrained feedback linearizable nonlinear systems to cope with the windup phenomenon. Given a dynamic feedback linearizing controller designed without considering its input constraint, an additional dynamic compensator is proposed to account for the constraint. This dynamic anti-windup is based on the minimization of a reasonable performance index. The proposed strategy is a nonlinear extended version of [Park, J.-K., & Choi, C.-H. (1995). Dynamic compensation method for multivariable control systems with saturating actuators. IEEE Transactions on Automatic Control, 40(9), 1635–1640] with simplified derivation of an optimization solution under relaxed assumptions. The parameter matrices and structure of the solution are explicitly decided by mathematical optimization for infinite horizon without tuning of design parameters unlike previous schemes. During input saturation, the role of the anti-windup scheme with the proposed dynamic feedback compensator is to maintain the controller states to be exactly the same as those without input saturation. The local asymptotic stability and the total stability of the resulting systems are proved. The usefulness of the proposed design method is illustrated by comparative simulations for a constrained control system.     

Stabilization of nonlinear time-delay systems with input saturation via anti-windup fuzzy design

This investigation considers stability analysis and control design for nonlinear time-delay systems subject to input saturation. An anti-windup fuzzy control approach, based on fuzzy modeling of nonlinear systems, is developed to deal with the problems of stabilization of the closed-loop system and enlargement of the domain of attraction. To facilitate the designing work, the nonlinearity of saturation is first characterized by sector conditions, which provide a basis for analysis and synthesis of the anti-windup fuzzy control scheme. Then, the Lyapunov–Krasovskii delay-independent and delay-dependent functional approaches are applied to establish sufficient conditions that ensure convergence of all admissible initial states within the domain of attraction. These conditions are formulated as a convex optimization problem with constraints provided by a set of linear matrix inequalities. Finally, numeric examples are given to validate the proposed method.     

Gain-scheduled, model-based anti-windup for LPV systems

The aim of this paper is to show that a recently proposed technique for anti-windup control of exponentially unstable plants can be easily extended to solve the corresponding robust anti-windup problem for linear parameter varying systems, for which the time varying parameters are measured online. The proposed technique is minimally conservative with respect to the size of the resulting operating region (which coincides, up to an arbitrarily small quantity, with the largest set on which asymptotic stability can be guaranteed for the considered plant with the given saturation level and uncertainty characteristics), and is not limited to plants having only small uncertainties or being open-loop stable.