Static anti‐windup design for a class of nonlinear systems

This paper focuses on the problem of static anti‐windup design for a class of multivariable nonlinear systems subject to actuator saturation. The considered class regards all systems that are rational on the states or that can be conveniently represented by a rational system with algebraic constraints considering some variable changes. More precisely, a method is proposed to compute a static anti‐windup gain which ensures regional stability for the closed‐loop system assuming that a dynamic output feedback controller is previously designed to stabilize the nonlinear system. The results are based on a differential algebraic representation of rational systems. The control saturation effects are taken into account by the application of a generalized sector bound condition. From these elements, LMI‐based conditions are devised to compute an anti‐windup gain with the aim of enlarging the closed‐loop region of attraction. Several numerical examples are provided to illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust non‐fragile control for delayed singular Markovian jump systems with actuator saturation and partially unknown transition probabilities

The paper is devoted to the investigation of the problem of robust non‐fragile control for singular Markovian jump systems with time‐varying delay and saturating actuators under partially unknown transition probabilities. By employing a Lyapunow function, a mode‐dependent robust non‐fragile state feedback controller, as well as an estimate of the domain of attraction in the mean square sense, is derived to guarantee stochastic admissibility of the corresponding closed‐loop system with actuator saturation. The controller parameters can be obtained by solving a series of linear matrix inequalities. An illustrative example is provided to show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic anti‐windup design in anticipation of actuator saturation

In a traditional anti‐windup design, the anti‐windup mechanism is set to be activated as soon as the control signal saturates the actuator. A recent innovation of delaying the activation of the anti‐windup mechanism, both static and dynamic, until the saturation reaches a certain level of severity has led to a performance improvement of the resulting closed‐loop system. It has been shown that significant further performance improvements can be obtained by activating a static anti‐windup mechanism in anticipation of actuator saturation, instead of immediate or delayed activation. This paper demonstrates that anticipatory activation of a dynamic anti‐windup mechanism would also lead to significant performance improvements over both the immediate and delayed activation schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

随机非线性和部分转移概率未知时马尔科夫系统的H1控制

研究上述系统时: 1) 利用了非线性的概率分布信息; 2) 利用了转移概率中已知部分和未知部分的关系. 利用李雅普诺夫泛函方法和线性矩阵不等式方法, 本文得到了使得系统随机稳定的充分条件并得到了相应的反馈控制增益. 文中最后给出的例子表明了所建立模型和分析方法的有效性.     

Dynamic anti‐windup method for a class of time‐delay control systems with input saturation

An anti‐windup‐based approach is newly attempted to deal with time‐delay control systems with input saturation. Following the anti‐windup paradigm, we assume that controllers have been designed beforehand for time‐delay control systems based on existing design techniques which will show desirable performance. Then, an additional compensator is designed to provide graceful performance degradation under control input saturation. By taking the difference of controller states in the absence and presence of input saturation as a performance index, a dynamic compensator which minimizes it is derived. The resulting anti‐windup compensator is expressed in plant and controller parameters. The proposed method not only provides graceful performance degradation, but also guarantees the stability of the overall systems. Illustrative examples are provided to show the effectiveness of the proposed method. Copyright © 2000 John Wiley & Sons, Ltd.     

Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information

The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.     

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.     

A new view of anti‐windup design for uncertain linear systems in the frequency domain

This paper presents a new perspective on the stability problem for uncertain LTI feedback systems with actuator input amplitude saturation. The solution is obtained using the quantitative feedback theory and a 3 DoF non‐interfering control structure. Describing function (DF) analysis is used as a criterion for closed loop stability and limit cycle avoidance, but the circle or Popov criteria could also be employed. The novelty is the combination of a controller parameterization from the literature and describing function‐based limit cycle avoidance with margins for uncertain plants. Two examples are given. The first is a benchmark problem and a comparison is made with other proposed solutions. The second is an example that was implemented and tested on an X‐Y linear stage used for nano‐positioning applications. Design and implementation considerations are given. An example is given on how the method can be extended to amplitude and rate saturation with the help of the generalized describing function, and a novel anti‐windup compensation structure inspired by previous contributions. Copyright © 2015 John Wiley & Sons, Ltd.     

H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities

This paper focuses on mode‐dependent H_∞ state‐feedback control for a class of discrete‐time Markovian jump systems (MJSs) with partial information on transition probabilities (TPs). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma (BRL) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H_∞ controllers are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.     

Delay‐dependent anti‐windup strategy for linear systems with saturating inputs and delayed outputs

This paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti‐windup strategies. A method for synthesizing anti‐windup gains aiming at maximizing a region of admissible states, for which the closed‐loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed‐loop system resulting from the controller plus the anti‐windup loop as a linear time‐delay system with a dead‐zone nonlinearity, constructive delay‐dependent stability conditions are formulated by using both quadratic and Lure Lyapunov–Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti‐windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.     

Stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities

This paper considers the stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities. Firstly, a set of necessary and sufficient conditions for the stochastic stability is proposed in terms of LMIs, then a set of sufficient conditions is proposed for the design of a state feedback controller to guarantee that the corresponding closed‐loop systems are regular, causal, and stochastically stable by employing the LMI technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

L2‐gain analysis and anti‐windup design of switched linear systems subject to input saturation

The problem of L₂‐gain analysis and anti‐windup compensation gains design is studied for a class of switched linear systems with actuator saturation via the multiple Lyapunov functions approach. When a set of anti‐windup compensation gains are given, a sufficient condition on tolerable disturbances is obtained, under which the state trajectory starting from the origin will remain inside a bounded set. Then over this set of tolerable disturbances, we obtain the upper bound of the restricted L₂‐gain. Furthermore, the anti‐windup compensation gains and the switched law, which aim to determine the maximum disturbance tolerance capability and the minimum upper bound of the restricted L₂‐gain, are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Finally we give a numerical example to demonstrate the effectiveness of the proposed method.     

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.     

Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

This article is devoted to provide further criterion for stochastic stability analysis of semi‐Markovian jump linear systems (S‐MJLSs), in which more generic transition rates (TRs) will be studied. As is known, the time‐varying TR is one of the key issues to be considered in the analysis of S‐MJLS. Therefore, this article is to investigate general cases for the TRs that covered almost all types, especially for the type that the jumping information from one mode to another is fully unknown, which is merely investigated before. By virtue of stochastic functional theory, sufficient conditions are developed to check stochastic stability of the underlying systems via linear matrix inequalities formulation combined with a maximum optimization algorithm. Finally, a numerical example is given to verify the validity and effectiveness of the obtained results.     

Moment exponential stability analysis of Markovian jump stochastic differential equations with uncertain transition jump rates

This paper is concerned with the moment exponential stability analysis of Markovian jump stochastic differential equations. The equations under consideration are more general, whose transition jump rates matrix Q is not precisely known. Sufficient conditions for testing the stability of such equations are established, and some numerical examples to illustrate the effectiveness of our results are presented.     

Finite‐time guaranteed cost control for Itô Stochastic Markovian jump systems with incomplete transition rates

This paper is concerned with the finite‐time guaranteed cost control problem for stochastic Markovian jump systems with incomplete transition rates. By a mode‐dependent approach (MDA), several new sufficient conditions for the existence of state and output feedback finite‐time guaranteed cost controllers are provided, and the upper bound of cost function is more accurately expressed. Moreover, these results' superiorities are analyzed and shown. A new N‐mode optimization algorithm is given to minimize the upper bound of cost function. Finally, a detailed example is utilized to demonstrate the merit of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.     

A new anti‐windup strategy for PID controllers with derivative filters

This paper presents a new strategy for suppressing the windup effect caused by actuator saturation in proportional–integral–derivative (PID) controlled systems. In the proposed approach, the windup effect is modeled as an external disturbance imported to the PID controller and an observer‐based auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal in accordance with an H‐infinite optimization criterion. It is shown that the proposed anti‐windup (AW) scheme renders the performance of the controlled system more robust toward the effects of windup than conventional PID AW schemes and provides a better noise rejection capability. In addition, the proposed PID AW scheme is system independent and is an explicit function of the parameters of the original PID controller. As a result, the controller is easily implemented using either digital or analog circuits and facilitates a rapid, on‐line tuning of the controller parameters as required in order to prevent the windup effect. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society