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.     

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.     

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.     

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.     

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.     

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.     

Stability Analysis and Design of Uncertain Discrete‐time Switched Systems with Actuator Saturation Using Antiwindup and Multiple Lyapunov Functions Approach

The stability analysis and anti‐windup design problem is investigated for a class of discrete‐time switched systems with saturating actuators by using the multiple Lyapunov functions approach. Firstly, we suppose that a set of linear dynamic output controllers have been designed to stabilize the switched system without input saturation. Then, we design anti‐windup compensation gains and a switching law in order to enlarge the domain of attraction of the closed‐loop system. Finally, the anti‐windup compensation gains and the estimation of domain of attraction 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.     

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.     

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.     

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.     

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     

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.     

Dynamic output feedback control with output quantizer for nonlinear uncertain T‐S fuzzy systems with multiple time‐varying input delays and unmatched disturbances

The dynamic output feedback control problem with output quantizer is investigated for a class of nonlinear uncertain Takagi‐Sugeno (T‐S) fuzzy systems with multiple time‐varying input delays and unmatched disturbances. The T‐S fuzzy model is employed to approximate the nonlinear uncertain system, and the output space is partitioned into operating regions and interpolation regions based on the structural information in the fuzzy rules. The output quantizer is introduced for the controller design, and the dynamic output feedback controller with output quantizer is constructed based on the T‐S fuzzy model. Stability conditions in the form of linear matrix inequalities are derived by introducing the S‐procedure, such that the closed‐loop system is stable and the solutions converge to a ball. The control design conditions are relaxed and design flexibility is enhanced because of the developed controller. By introducing the output‐space partition method and S‐procedure, the unmatched regions between the system plant and the controller caused by the quantization errors can be solved in the control design. Finally, simulations are given to verify the effectiveness of the proposed method.     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 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.     

Output feedback control of a class of nonminimum‐phase nonlinear systems

The problem of global stabilization by output feedback is investigated in this paper for a class of nonminimum‐phase nonlinear systems. The system under consideration has a cascade configuration that consists of a driven system known as the inverse dynamics and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonminimum‐phase system if both driven and driving systems have a lower‐triangular form and satisfy a Lipschitz‐like condition, and the inverse dynamics satisfy a stronger version of input‐to‐state stabilizability condition. A design procedure is provided for the construction of an n‐dimensional dynamic output feedback compensator. Examples and simulations are also given to validate the effectiveness of the proposed output feedback controller. Copyright © 2016 John Wiley & Sons, Ltd.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance

In this paper, we investigate the problem of output‐feedback tracking control for a class of nonlinear SISO systems in the strick‐feedback form, which are subject to both uncertain delay‐related functions and disturbances. A reduced‐order observer is first introduced to provide the estimates of the unmeasured states. Then, an output‐feedback controller is recursively designed based on the backsteppng method. By constructing an appropriate Lyapunov–Krasovskii functional, we prove that all the signals in the closed‐loop system are bounded. The tracking performance is guaranteed by suitably choosing the design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm. Copyright © 2009 John Wiley & Sons, Ltd.