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     

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 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.     

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.     

Beyond equidistant sampling for performance and cost: A loop‐shaping approach applied to a motion system

Nonequidistant sampling potentially enhances the performance/cost trade‐off that is present in traditional equidistant sampling schemes. The aim of this paper is to develop a systematic feedback control design approach for systems that go beyond equidistant sampling. A loop‐shaping design framework for such nonequidistantly sampled systems is developed that addresses both stability and performance. The framework only requires frequency response function measurements of the LTI system, whereas it appropriately addresses the linear periodically time‐varying behavior introduced by the nonequidistant sampling. Experimental validation on a motion system demonstrates the superiority of the design framework for nonequidistantly sampled systems compared to traditional designs that rely on equidistant sampling.     

Robust observer–controller compensator design using the loop shaping design procedure and the algebraic method

This paper investigates robust observer‐controller compensator design using Vidyasagar's structure (VS). VS has a unit matrix parameter H similar to the Q parameter for the Youla–Kucera parameterization. VS can be designed based on the left coprimeness of the central controller in the H_∞‐loop shaping design procedure (H_∞‐LSDP) and therefore can preserve the intrinsic properties of the H_∞‐LSDP. This paper introduces algebraic methods to simplify the design of H in the VS controller by solving specific algebraic equations. In particular, the algebraic design of H can achieve two things. First, a dynamic H adjusts the tracking performance and yields the integral action. Second, a dynamic H rejects the input and output sinusoidal disturbances with known frequencies. These attributes are indications of the flexibility of the proposed method since the output‐feedback controller design of the H_∞‐LSDP cannot easily deal with such conditions. This paper discusses the achieved loop and the closed‐loop behavior of the system with VS, and also gives two numerical examples. The first example shows that the proposed method results in a better design in many aspects than the resulting from H_∞‐LSDP. The second example shows the application of the proposed method to rejecting input and output step disturbances, and input and output multiple sinusoidal disturbances, for which the H_∞‐LSDP can hardly be used. Copyright © 2009 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.     

Closed‐loop input shaping control of vibration in flexible structures using discrete‐time sliding mode

Input shaping technique is widely used in reducing or eliminating residual vibration of flexible structures. It is easy to implement and achieve the exact elimination of the residual vibration if the dynamics of the system are known accurately. However, it is not very robust to parameter uncertainties and external disturbances. In this paper, a closed‐loop input shaping method is developed for reducing or eliminating residual vibration of flexible structure systems with parameter uncertainties and external disturbances. The algorithm is based on input shaping control and discrete‐time sliding mode control. It is shown that the proposed scheme guarantees closed‐loop system stability, and yields good performance and robustness in the presence of parameter uncertainties and external disturbances as well. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. The knowledge of upper bound of uncertainties is not required. Furthermore, it is shown that increasing the robustness to parameter uncertainties does not lengthen the duration of the impulse sequence. Simulation results demonstrate the efficacy of the proposed closed‐loop input shaping control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Reference shaping for model-based control of biomass grate boilers

An established control strategy for biomass grate boilers based on a low-order nonlinear model is considered. Under ideal conditions, it achieves decoupled control of desired outputs by means of input–output linearization. The decoupling is gradually reduced and control performance deteriorates when actuator saturation occurs. This may be avoided by appropriately shaping the control strategy’s reference values. This contribution presents a method to do so by solving a sequence of linear programs. Its implementation requires the knowledge of typically unknown limits of mass-flows fed into the plant. An estimation strategy for these limits based on measurable quantities is thus proposed. Experimental data from three different scenarios is presented, in which the reference shaping improves tracking, mitigates wind-up phenomena and reduces emissions, respectively.     

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.     

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.     

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.     

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.     

An iterative algorithm for maximizing robust performance in loop‐shaping design

In this paper, an algorithm that gives the best achievable performance bound on a given control problem is proposed using the loop‐shaping design framework. In view of standard design requirements, the robust performance is maximized at low and high frequencies while keeping the robust stability margin above a specified level, and the robust stability margin is directly improved at mid frequencies (around crossover). The proposed frequency‐dependent optimization problem is cast in an LMI framework. The resulting solution algorithm simultaneously synthesizes loop‐shaping weights and a stabilizing controller that achieve the maximum performance for a given level of robust stability margin corresponding to sufficient gain and phase margins of the closed‐loop system. Copyright © 2012 John Wiley & Sons, Ltd.     

Pole placement with sensitivity function shaping using 2nd order digital notch filters

This technical note deals with the design of robust digital controllers using pole placement with sensitivity shaping by means of the use of digital notch (band-stop) filters. The use of this type of filters drastically simplifies the effective shaping of the sensitivity functions and the resulting procedure competes with the procedure based on the use of Q-parameterization combined with convex optimization (Automatica 35 (1999) 1111). The feasibility of the technique is illustrated by its application to the control of a very flexible arm.     

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.     

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.     

Microstrip dual‐band bandpass filters using parallel‐connected open‐loop ring resonators

This article proposes a microstrip dual‐band bandpass filter that uses parallel‐connected open‐loop ring resonators. Compared to many microstrip dual‐band filters, the advantages of using microstrip open‐loop ring resonators are easy calculation (half‐guided‐wavelength), easy fabrication (equal width for all 50‐Ω lines and without grounding holes), and direct connection to external feed lines (reducing insertion loss caused by gap couplings). Another advantage of the filter is an asymmetrical feed on the ring resonator that provides sharp rejections at its adjacent bands. The input and output matches of resonators to the external feed lines are derived using a simple transmission‐line theory. The results of the derivation provide a simple design rule for filter designers. Simulated and measured results are presented with good agreement. The filter has minimum insertion loss of 1.25 dB at 1.85 GHz and 1.6 dB at 2.33 GHz. The 3‐dB fractional bandwidths are 5.9% for the 1.9‐GHz bandpass filter and 4.7% for the 2.4‐GHz bandpass filter, respectively. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

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.     

Effectiveness and limitation of circle criterion for LTI robust control systems with control input nonlinearities of sector type

This paper considers linear time invariant systems with sector type nonlinearities and proposes regional ??₂ performance analysis and synthesis methods based on the circle criterion. In particular, we consider the effect of non‐zero initial states and/or an ??₂ disturbance inputs on the ??₂ norm of a selected performance output. We show that both analysis and synthesis problems can be recast as linear matrix inequality (LMI) optimization problems, where, for synthesis, the outputs of the nonlinear elements are assumed available for control. Moreover, it is shown when the circle criterion does or does not help to improve the performance bound in robust control synthesis when compared with the existing linear analysis method. Copyright © 2005 John Wiley & Sons, Ltd.