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.     

Dynamic anti‐windup compensator for fractional‐order system with time‐delay

This paper describes the results of introducing an additional dynamic element to an anti‐windup compensator from control quality and stability area anslysis viewpoint. The analyzed system consists of a first‐order plant with time delay and a fractional‐order PI controller, to present the discussed approach. The controller is tuned based on Hermite‐Biehler and Pontryagin theorems. In the paper, the stability analysis and tracking performance are presented based on both simulation and experimental results. The experiments have been performed using Inteco Modular Servo System with performance evaluated on the basis of the selected performance criterion, namely the Integral of Absolute Error, to verify the applicability of the proposed method. The results have proven that use of the additional dynamic element provides a wider range of controller parameters to ensure stability of the closed‐loop system and better tracking performance in comparison to the system without anti‐windup compensation or system with a standard anti‐windup compensator. It is actually the first time that this type of analysis for dynamic element compensation in anti‐windup framework has been presented for fractional‐order systems. In addition, all the obtained results are referred to the experimental data.     

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.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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     

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.     

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.     

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.     

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.     

An alternative approach to anti‐windup in anticipation of actuator saturation

Traditionally, an anti‐windup compensator is activated when control signal saturation occurs. An alternative approach is to activate the compensator at a level below that of the physical control constraints: the anti‐windup compensator is activated in anticipation of actuator saturation. Recent studies have proposed systematic methods for the construction of such anticipatory anti‐windup compensators, but a pseudo‐LPV representation of the saturated system has been central to these results. This paper approaches the anticipatory anti‐windup problem for open‐loop stable plants using a ‘non‐square’ sector condition, which is associated with a combination of deadzone nonlinearities. The advantage of this approach is that it leads to synthesis routines, which bear a close resemblance to those associated with traditional immediately activated anti‐windup compensators. A by‐product of this approach also appears to be that the arising compensators are better numerically conditioned. Some simulation examples illustrating the effectiveness of anticipatory anti‐windup compensators and some comments on their wider use complete the paper. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust quantized output feedback control for uncertain discrete time‐delay systems with saturation nonlinearity

This paper is concerned with robust quantized output feedback control problems for uncertain discrete‐time systems with time‐varying delay and saturation nonlinearity. It is assumed that the quantizer is of the saturating type. A new framework for the local boundedness stabilization of quantized feedback systems is developed. Attention is focused on finding a quantized static output feedback controller such that all trajectories of the resulting closed‐loop system starting from an admissible initial basin converge to a bounded region strictly within the initial basin. A quantized feedback controller is proposed, which comprises output feedback and the exogenous signal parts. Simulation examples are given to illustrate the effectiveness and advantage of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Improved delay‐dependent stabilization of time‐delay systems with actuator saturation

This paper addresses the controller synthesis problem of linear time‐delay systems subjected to saturating control. Delay‐dependent regional stabilization criteria are derived based on Lyapunov–Krasovskii approach by using both the polytopic or dead‐zone representation of the saturation function. The main contribution of the paper lies in developing less conservative convex criterion in terms of LMIs to obtain superior results. On the basis of the derived stabilization criterion, an optimization problem is defined to compute the stabilizing state feedback gains with an aim to maximize the stabilizing region while guaranteeing the asymptotic stability of the closed‐loop system. Considering three numerical examples, an assessment of the polytopic and dead‐zone nonlinearity approaches is made. Copyright © 2012 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.     

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.     

Reliable control for a class of uncertain singular systems with interval time‐varying delay

This paper is concerned with the reliable controller design problem for a class of singular systems with interval time‐varying delay and norm‐bounded uncertainties. A more practical model of actuator failures than outages is considered. First, by constructing a novel Lyapunov–Krasovskii functional combined with Finsler's Lemma, an improved delay‐range‐dependent stability criterion for the nominal unforced singular time‐delay system is established in terms of linear matrix inequality (LMI). Then, based on this criterion, an LMI condition for the design of a reliable state feedback controller is presented such that, for all parameter uncertainties and actuator failures, the resultant closed‐loop system is regular, impulse‐free and stable. Numerical examples are proposed to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Extended anti‐windup control schemes for LTI and LFT systems with actuator saturations

In this paper, the popular anti‐windup control scheme will be extended in two important directions. The first scenario is the control of LTI systems subject to actuators with both magnitude and rate constraints. The second case of extension is LFT systems with input saturations. Based on the extended Circle criterion, we will develop convex anti‐windup control synthesis conditions in the form of LMIs for each class of systems. The explicit anti‐windup controller formula are also provided to facilitate compensator construction. The effectiveness of proposed anti‐windup control schemes will be demonstrated using a flight control example. Copyright © 2004 John Wiley & Sons, Ltd.     

A delay‐independent output feedback for linear systems with time‐varying input delay

It is well known that a delay‐dependent or delay‐independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of a time‐varying or unknown delay, delay‐independent feedback laws are preferable over delay‐dependent feedback laws as the former provide robustness to the uncertainties in the delay. In the light of few results on the construction of delay‐independent output feedback laws for general linear systems with input delay, we present in this paper a delay‐independent observer–based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through the Razumikhin‐type stability analysis. An implication of the delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open‐loop poles at the origin or in the open left‐half plane. Compared with that of the delay‐dependent output feedback laws in the literature, this same level of stabilization result is not sacrificed by the absence of the prior knowledge of the delay.     

Modified static anti‐windup for saturated systems with sector‐bounded and slope‐restricted nonlinearities

This paper proposes modified static anti‐windup techniques for saturated systems with sector‐bounded and slope‐restricted nonlinearities by augmenting the pre‐designed controller with the so‐called differential compensator to process the slope restriction. By using a purely quadratic Lyapunov function and with a modified sector condition dealing with actuator saturation, LMI‐based synthesis conditions are presented to address the problems of the estimates of the region of attraction and performance analysis of the closed‐loop system. Numerical examples illustrate the effectiveness of the proposed approaches. Copyright © 2016 John Wiley & Sons, Ltd.