Simultaneous Linear and Anti‐Windup Controller Synthesis: Delayed Activation Case

In this paper, we present a method for the synthesis of a delayed anti‐windup scheme in which the anti‐windup compensator is activated only when the degree of saturation reaches a certain level. Unlike the traditional two‐step anti‐windup design procedure, our method synthesizes entire parameters of the nominal controller and the delayed anti‐windup compensator simultaneously. In this simultaneous design, the trade‐offs between the linear and the constrained closed‐loop response are carried out, for the anti‐windup compensator retrofits to the “existing” nominal controller. Sufficient conditions for guaranteeing global stability and minimizing the induced gain performance for exogenous input are formulated and solved as some linear matrix inequality (LMI) optimization problems. Effectiveness of the proposed method is illustrated with a well‐known example.     

Controller Reset Strategy for Anti‐Windup Based on Switching Gain Analysis

When the calculated value of a control input approaches its limitations, resets of controllers are often used to prevent windup. However, an automatic reset should only be performed after confirmation that it will not adversely affect the transient performance and lead to another windup. In this study, we apply a switching gain analysis to a more appropriate evaluation of transient responses after a reset in order to propose an improved strategy for the automatic resets of controllers, such that windup does not accompany resets.     

Simultaneous Design of Parallel Distributed Output Feedback and Anti‐windup Compensators for Constrained Takagi‐Sugeno Fuzzy Systems

This paper is devoted to developing a novel approach to deal with constrained continuous‐time nonlinear systems in the form of Takagi‐Sugeno fuzzy models. Here, the disturbed systems are subject to both input and state constraints. The one‐step design method is used to simultaneously synthesize the dynamic output feedback controller and its anti‐windup strategy. A parameter‐dependent version of the generalized sector condition is used together with Lyapunov stability theory to derive linear matrix inequality design conditions. Based on this result and for different design specifications, the synthesis of an anti‐windup based dynamic output feedback controller is expressed on the form of convex optimization problems. A physically motivated example is given to illustrate the effectiveness of the proposed method.     

Synthesis of a static anti‐windup compensator via linear matrix inequalities

In this paper, we propose a design method of a static anti‐windup compensator that guarantees robust stability subject to input saturation and suppresses the degradation of robust performance during the saturation period. In previous studies, this problem has been considered to be equivalent to a static output feedback design problem, which is essentially a non‐convex problem. We show that this problem can be reduced to an equivalent convex problem by using an appropriate sector transformation. The numerical solution can be obtained efficiently by solving linear matrix inequalities (LMIs). Further, a constant scaling matrix is introduced to the condition in order to reduce the conservativeness. In this case, since the design problem is no more LMIs, an algorithm for solving the problem by LMI iterations is presented. Four numerical examples are given to illustrate the effectiveness of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Modified dynamic anti‐windup through deferral of activation

We consider the dynamic anti‐windup design problem for linear systems with saturating actuators. The basic idea proposed here is to apply anti‐windup only when the performance of saturated system faces substantial degradation. We provide synthesis LMIs to obtain the gains of the dynamic anti‐windup compensator in a structure that delays the activation of the anti‐windup. Benefits of the proposed design method over the immediate activation of the anti‐windup are demonstrated using a well‐known example. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.     

切换系统的无扰切换控制及其在航空发动机中的应用

利用多Lyapunov函数方法, 本文研究了一类切换线性系统的状态跟踪无扰切换控制问题.首先, 刻画了控制信号在切换时刻处的抖振抑制水平.其次, 通过控制器与切换律的同时设计, 实现了系统的状态跟踪和控制信号抖振抑制.最后, 将所提出的状态跟踪无扰切换控制策略应用于一个涡扇航空发动机模型的控制设计上, 说明了所提出方法的有效性.     

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.     

Robust sampled‐data model predictive control for networked systems with time‐varying delay

In this paper, the problem of sampled‐data model predictive control (MPC) is investigated for linear networked control systems with both input delay and input saturation. The delay‐induced nonlinearity is overapproximatively modeled as a polytopic inclusion. The nonlinear behavior of input saturation is expressed as a convex polytope. The resulting closed‐loop systems are represented as linear systems with polytopic and additive norm‐bounded uncertainties. The aim is to determine a robust MPC controller that asymptotically stabilizes the uncertain system at the origin with a certain level of quadratic performance. The effectiveness of the proposed algorithm is demonstrated by a numerical example.     

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 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     

Anti‐windup synthesis for nonlinear dynamic inversion control schemes

A general anti‐windup (AW) compensation scheme is provided for a class of input constrained feedback‐linearizable nonlinear systems. The controller considered is an inner‐loop nonlinear dynamic inversion controller, augmented with an outer‐loop linear controller, of arbitrary structure. For open‐loop globally exponentially stable plants, it is shown that (i) there always exists a globally stabilizing AW compensator corresponding to a nonlinear generalization of the Internal‐Model‐Control (IMC) AW solution; (ii) important operator theoretic parallels exist between the AW design scheme for linear control and the suggested AW design scheme for nonlinear affine plants and (iii) a more attractive AW compensator may be obtained by using a nonlinear state‐feedback term, which plays a role similar to the linear state‐feedback term in linear coprime factor‐based AW compensation. The results are demonstrated on a dual‐tank simulation example. Copyright © 2009 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.     

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.     

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

In this paper, a simple derivation for an all‐stabilizing proportional controller set for first‐order bi‐proper systems with time delay is proposed. In contrast to proper systems, an extremely limited number of studies are available in the literature for such bi‐proper systems. To fill this gap in the literature, broader aspects of the stabilizing set are taken into consideration. The effect of zero on the stabilizing set is clearly discussed and we also prove that, when their zeros are placed symmetrically to the origin, the stabilizing set of non‐minimum phase plant is always smaller than that of the minimum phase one. Moreover, for an open‐loop unstable plant, maximum allowable time delay (MATD) is explicitly expressed as a function of the locations of the pole and zero. From that function, it is shown that for a minimum phase plant, the supremum of the MATD is two times that of the time constant of the plant and the infimum of the MATD is the time constant of the plant. We also prove that the supremum is the time constant and the infimum is zero for a non‐minimum phase plant.     

Robust consensus tracking of linear multiagent systems with input saturation and input‐additive uncertainties

The problem of robust global consensus tracking of linear multiagent systems with input saturation and input‐additive uncertainties is investigated in this paper. By using the parametric Lyapunov equation approach and an existing dynamic gain scheduling technique, a new distributed nonlinear‐gain scheduling consensus‐trackining algorithm is developed to solve this problem. Under the assumption that each agent is asymptotically null controllable with bounded control, it is shown that the robust global consensus tracking can be achieved under the undirected graph provided that its generated graph contains a directed spanning tree. Compared with the existing algebraic Riccati equation approach, which requires the online solution of a parameterized algebraic Riccati equation, all the parameters in the proposed nonlinear algorithm are offline determined a priori. Finally, numerical examples are provided to validate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Anti‐Synchronization and Intermittent Anti‐Synchronization of Two Identical Delay Hyperchaotic Chua Systems Via Linear Control

This work is concerned with anti‐synchronization and intermittent anti‐synchronization of two identical delay hyperchaotic Chua systems with linear control approaches. In the first two schemes, based on Lyapunov stability theory, some sufficient conditions for achieving anti‐synchronization of two identical delay hyperchaotic Chua systems are derived, numerical simulation results are presented to demonstrate the effectiveness of the proposed anti‐synchronization schemes. In the third scheme, the anti‐synchronization conditions are obtained by numerical method. In the fourth scheme, only one state of the response system is controlled via linear control, we report an interesting phenomenon of intermittent anti‐synchronization.     

An improvement to the low gain design for discrete‐time linear systems in the presence of actuator saturation nonlinearity

A low‐gain design for linear discrete‐time systems subject to input saturation was recently developed to solve both semi‐global stabilization and semi‐global output regulation problems. This paper proposes an improvement to the low‐gain design and determines controllers with the new design that achieve semi‐global output regulation. The improvement is reflected in better utilization of available control capacity and consequently better closed‐loop performance. Copyright © 2000 John Wiley & Sons, Ltd.