Design of multiple anti-windup loops for multiple activations

This paper considers anti-windup design for linear systems subject to actuator saturation.Three anti-windup gains are designed for activations immediately at the occurrence actuator saturation,after the saturation has reached a certain level and in anticipation of the occurrence of saturation,respectively.The design is based on the minimization of L 2 gain from the disturbance to the controlled output of the resulting closed-loop system.Traditional anti-windup scheme involves a single anti-windup loop for immediate activation.A recent innovation is to design a single anti-windup loop for delayed or anticipatory activation,as well as to design two anti-windup gains,one for immediate activation and one for delayed activation.Our design of three anti-windup gains for three different activations is shown through simulation to lead to significant further performance improvement over the previous activation schemes.     

Static anti‐windup design for a class of Markovian jump systems with partial information on transition rates

This paper investigates the problem of static anti‐windup design for uncertain continuous‐time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time‐varying and norm‐bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output‐feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti‐windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed‐loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.     

延迟不确定马尔科夫跳变系统的执行器和传感器故障同时估计方法

针对具有参数不确定和延迟环节的马尔科夫跳变系统,在状态转移概率矩阵（Transition probability matrix,TPM）不确定的情形下,讨论了其执行器和传感器故障同时估计的方法.通过扩展系统状态,将系统转换为一个具有马尔科夫跳变参数的广义描述系统,基于此广义描述系统设计马尔科夫跳变观测器实现对其状态和传感器故障的估计.与此同时,还设计了一组自适应律对执行器故障进行在线调节.通过求解一组线性矩阵不等式最优化问题,得到观测器存在的充分条件.最后,针对两个数值实例,验证了所设计方法的有效性.     

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm.      

Stabilisation for Markovian jump delta operator systems with time-varying delays and actuator saturation

In this paper, stochastic stabilisation is studied for Markovian jump delta operator systems with time-varying delays and actuator saturation. The transition probability rates in Markovian jump parameters are considered as partly known. Both lower and upper bounds are considered in the time-varying delays. Using Lyapunov–Krasovkii functional, a stochastic stabilisation condition is obtained for the closed-loop Markovian jump delta operator system with time-varying delays and actuator saturation. A numerical example is shown to illustrate the effectiveness and potential for the developed techniques.     

Dynamic anti-windup design for anticipatory activation：enlargement of the domain of attraction

Traditional anti-windup compensators are designed for activation immediately at the occurrence of actuator saturation.Recently,anti-windup compensators were designed for actuation either after the saturation has reached a certain level or in anticipation of its occurrence.In the case of static anti-windup compensators,it has been shown that an anti-windup compensator designed for activation in anticipation of actuator saturation would lead to better performance than those designed for immediate or delayed activation could,both in terms of transient performance and the size of the domain of attraction.More recently,it has been shown that a dynamic anti-windup compensator designed for anticipatory activation would also result in better transient performance than those designed for immediate or delayed activation could.In this paper,we design dynamic anti-windup compensators for the enlargement of the domain of attraction.These compensators are designed respectively for immediate,delayed and anticipatory activation.We will show by simulation that a dynamic anti-windup compensator designed for anticipatory activation would result in a larger domain of attraction than a dynamic anti-windup compensator designed for immediate or delayed activation could.     

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.     

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovian jump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality (LMI) conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.     

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.     

Robust control of uncertain discrete-time Markovian jump systems with actuator saturation

In this paper, the robust stochastic stabilization problem for the class of discrete-time uncertain Markovian jump linear systems (MJLS) with actuator saturation is considered. The definition of domain of attraction in mean square sense (DoA-MSS) is introduced to analyze the stochastic stability of the closed-loop system. By using a class of stochastic Lyapunov function which is dependent on the jump mode and saturation function, design procedures for both the mode-dependent and mode-independent state feedback controllers are developed based on the Linear Matrix Inequality (LMI) approach. Finally, a numerical example is provided to show the usefulness of the proposed techniques.     

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．     

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 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.     

Stability analysis and anti-windup design of switched systems with actuator saturation

The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Two numerical examples are given to show the effectiveness of the proposed method.     

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。     

一类饱和非线性系统抗饱和控制器设计

针对一类饱和非线性系统研究抗饱和控制器综合问题. 基于线性分式表示技术(LFR), 该类非线性系统可转化为带有满足扇形区间不等式条件的非线性函数及额外线性分式约束的饱和线性系统. 基于二次Lyapunov 方程并利用广义扇形区间不等式条件处理饱和非线性项, 提出了基于LMI 条件的非线性抗饱和控制器综合方法. 数值仿真验证了所提出方法的有效性.

     

基于扩张状态观测器的动态抗饱和补偿器设计方法

针对一类受外界扰动以及执行器饱和影响的不确定非线性系统,提出一种基于扩张状态观测器的动态抗饱和补偿器设计方法.首先通过将系统的不确定项以及外部扰动作为扩张状态,设计线性扩张状态观测器(ESO)对系统的总扰动进行估计;然后,在控制器中引入对扩张状态的估计值,对系统的总扰动进行补偿,设计了动态抗饱和补偿器,将控制器、观测器以及动态抗饱和补偿器的参数求解问题转化为基于LMI不等式组约束的优化问题,确保系统具有尽可能大的收敛域;最后通过数值仿真验证所提出设计方法的有效性.     

Anti-windup compensation for systems with sensor saturation: a study of architecture and structure

This article proposes a linear dynamic anti-windup strategy for the alleviation of performance and stability problems in systems which are linear apart from saturating sensors. Unlike anti-windup compensation for systems subject to actuator saturation, there is no agreed architecture for applying anti-windup to systems with sensor saturation and therefore attention is devoted to the discussion of various candidate configurations which can be interpreted as a particular choice of a static non-linear map. The main results of the article give existence conditions for compensators which yield global exponential stability and finite ?₂ gain of the overall non-linear closed-loop system. The existence conditions are different to those which have appeared hitherto in the literature.     

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.     

Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances

This paper considers the design of output tracking systems subject to actuator saturation and integrator windup. An optimization-based approach is developed to design feedback and anti-windup gains of a controller structure involving intelligent integrators. The design goal is to increase stability region and output tracking and disturbance rejection ability of the closed-loop system.