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.     

Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.     

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ’large’ as possible. An example is provided to demonstrate the effectiveness of the new method.     

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.     

N4SID and MOESP algorithms to highlight the ill-conditioning into subspace identification

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.     

Design of a bilinear fault detection observer for singular bilinear systems

A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.     

Stability analysis and antiwindup design of uncertain discrete-time switched linear systems subject to actuator saturation

This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the switched Lyapunov function approach.Supposing that a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation,we design antiwindup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation.Then,in terms of a sector condition,the antiwindup compensation gains which aim to maximize the estimation of domain of attraction of the closed-loop system are presented by solving a convex optimization problem with linear matrix inequality(LMI)constraints.A numerical example is given to demonstrate the effectiveness of the proposed design method.     

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.     

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain.In order to better investigate uncertain suspension dynamics,the sampleddata Takagi-Sugeno(T-S)fuzzy half-car active suspension(HCAS)system is considered,which is further modelled as a continuous system with an input delay.Firstly,considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay,a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system.Secondly,since external disturbances often belong to a restricted frequency range,a finite frequency control criterion is presented for control synthesis to reduce conservatism.Thirdly,given a full information of state variables is hardly available in practical suspension systems,a two-stage method is proposed to calculate the static output feedback control gains.Moreover,an iterative algorithm is proposed to compute the optimum solution.Finally,numerical simulations verify the effectiveness of the proposed controllers.     

Generic regular decompositions for generic zero-dimensional systems

Two new concepts,generic regular decomposition and regular-decomposition-unstable(RDU)variety for generic zero-dimensional systems,are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously.The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety.The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm,which is based on the theories of subresultants.Furthermore,the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety.The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature.Empirical results are also presented to show the good performance of the algorithm.     

约束T-S模糊系统设计的模糊Lyapunov方法

通过引入模糊Lyapunov函数,研究一类执行器饱和的离散T-S模糊系统.对系统设计模糊抗积分饱和补偿器,得到系统稳定的充分条件,并扩大了系统的吸引域.这种方法避免了寻求一个满足系统所有模糊规则的公共正定矩阵P.最后,抗积分饱和补偿器增益通过迭代优化算法得到.     

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.     

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.     

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.     

A Switching Anti-windup Design Using Multiple Lyapunov Functions

This technical note proposes a switching anti-windup design, which aims to enlarge the domain of attraction of the closed-loop system. Multiple anti-windup gains along with an index function that orchestrates the switching among these anti-windup gains are designed based on the min function of multiple quadratic Lyapunov functions. In comparison with the design of a single anti-windup gain which maximizes a contractively invariant level set of a single quadratic Lyapunov function as a way to enlarge the domain of attraction, the use of multiple Lyapunov functions and switching in the proposed design allows the union of the level sets of the multiple Lyapunov functions, each of which is not necessarily contractively invariant, to be contractively invariant and within the domain of attraction. As a result, the resulting domain of attraction is expected to be significantly larger than the one resulting from a single anti-windup gain and a single Lyapunov function. Indeed, simulation results demonstrate such a significant improvement.      

Anti-windup design with guaranteed regions of stability for discrete-time linear systems

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.     

Incorporating anti-windup gain in improving stability of actuator constrained linear multiple state delays systems

This paper proposes the design of anti-windup compensator gain for improving stability of actuator input constrained linear multiple state delays systems. The system state delays are classified into mixed delay-dependent/delay-independent analysis and described by delay-differential equations. The real scalar delays are assumed to be fixed and unknown, but with known coefficient matrices. It is shown that the closed-loop system containing the controller plus the anti-windup gain can be modeled as a linear system with dead-zone nonlinearity. The formulation of anti-windup compensator gain is based on convex optimization using linear matrix inequalities (LMI) that ensure closed-loop asymptotic stability of the system while accounting upper-bound delays. The devised LMIs based on Lyapunov-Krasovskii functionals prove significantly less conservative in giving higher upper bounds delays in the formulation of anti-windup gain besides ensuring closed-loop asymptotic stability.     

高阶非线性系统状态反馈抗饱和跟踪控制

针对参数未知的高阶非线性系统,提出了一种简单有效的反馈抗饱和控制方法,并进行了状态反馈抗饱和控制吸引域估计.利用反馈控制思想,借助于李亚普诺夫稳定性理论,设计出了相应的状态抗饱和反馈控制器,并借助于Matlab进一步求出了控制器的参数.将所设计的抗饱和控制应用于Duffing混沌系统,仿真结果验证了该控制方法的有效性.     

Anti‐windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance

A novel anti‐windup design method is provided for a class of uncertain nonlinear systems subject to actuator saturation and external disturbance. The controller considered incorporates both an active disturbance rejection controller as well as an anti‐windup compensator. The dynamical uncertainties and external disturbance are treated as an extended state of the plant, and then estimate it using an extended state observer and compensate for it in the control action, in real time. The anti‐windup compensator produces a signal based on the difference between the controller output and the saturated actuator output, and then augment the signal to the control to deal with the windup phenomenon caused by actuator saturation. We first show that, with the application of the proposed controller, the considered nonlinear system is asymptotically stable in a region including the origin. Then, in the case that the controller in linear form, we establish a linear matrix inequality‐based framework to compute the extended state observer gain and the anti‐windup compensation gain that maximize the estimate of the domain of attraction of the resulting closed‐loop system. The effectiveness of the proposed method is illustrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.