Stability of non-linear QFT designs based on robust absolute stability criteria

Baños, Alfonso; Barreiro, Antonio

doi:10.1080/002071700219957

Cited by 23 publications

(14 citation statements)

References 14 publications

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“…Thus, if a nonlinear QFT design is made without a non-expected disturbance as input, the feedback system can become unstable. Alternative approaches to nonlinear stability in QFT have been developed recently in References [27][28][29], based on absolute stability results such as the Circle and Popov criteria, or stability multipliers. They have been adapted as synthesis tools, generating stability bounds.…”

Section: Nonlinear Quantitative Feedback Theory 199mentioning

confidence: 99%

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Nonlinear quantitative feedback theory

Baños

2006

Intl J Robust & Nonlinear

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SUMMARYThis work revises the original nonlinear quantitative feedback theory (QFT) techniques of Prof. Horowitz, trying to contribute to the systematization of the field and reviewing some of the contributions made over the last three decades. The material is presented in a tutorial style, simplifying the exposition to mathematics, and using very simple examples that are expected to reveal the internal mechanisms of nonlinear QFT, basically based on a clever application of Schauders principle.

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Section: Nonlinear Quantitative Feedback Theory 199mentioning

confidence: 99%

“…By simplicity, the specification with a unique step reference rðsÞ ¼ 1=s is analysed. Thus, only one set of acceptable outputs A is defined by Equation (27). In this case u ¼ W …”

Section: The Second Nonlinear Qft Techniquementioning

confidence: 99%

Nonlinear quantitative feedback theory

Baños

2006

Intl J Robust & Nonlinear

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“…Goal The problem to be solved is closed loop stability and limit cycle avoidance in systems with actuator input amplitude saturation taking into account uncertainty in the plant, while retaining given specifications if the control signal does not saturate. Our solution can be viewed as a new extension to [9,12] and as a complement to [10,13,[21][22][23].…”

Section: Problem Statementmentioning

confidence: 99%

“…Nichols plot for five P C C H cases, and 1=¹N º with 12 dB margin, where P , C , and H are given inFigure 12and(20)and(21), respectively. The circle criterion loci arg.1=.1 C .P C C H // D .…”

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confidence: 99%

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

Berger

Gutman

2015

Int. J. Robust. Nonlinear Control

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Summary 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.

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“…This work does not explicitly consider the nonlinear stability problem of the closed-loop system, in the sense of guarantying bounded loop signals for any bounded input entering additively in the loop. Some recent work about stability of nonlinear QFT designs can be found in Reference [13].…”

Section: The Robust Control Problemmentioning

confidence: 99%

Some results in nonlinear QFT

Baños

Bailey

Montoya

2001

Intl J Robust & Nonlinear

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Nonlinear QFT (quantitative feedback theory) is a technique for solving the problem of robust control of an uncertain nonlinear plant by replacing the uncertain nonlinear plant with an &equivalent' family of linear plants. The problem is then "nding a linear QFT controller for this family of linear plants. While this approach is clearly limited, it follows in a long tradition of linearization approaches to nonlinear control (describing functions, extended linearization, etc.) which have been found to be quite e!ective in a wide range of applications. In recent work, the authors have developed an alternative function space method for the derivation and validation of nonlinear QFT that has clari"ed and simpli"ed several important features of this approach. In particular, single validation conditions are identi"ed for evaluating the linear equivalent family, and as a result, the nonlinear QFT problem is reduced to a linear equivalent problem decoupled from the linear QFT formalism. In this paper, we review this earlier work and use it in the development of (1) new results on the existence of nonlinear QFT solutions to robust control problems, and (2) new techniques for the circumvention of problems encountered in the application of this approach. statement is found in the work of Isaac Horowitz [1}7]. Since the late 1950s his work has focused on the control of systems with parametric uncertainty. The linear case was considered in Reference [1] and later considerably expanded and clari"ed in Reference [2]. Later work in the 1970s [3, 4] also considered robust control of some nonlinear and/or time-varying systems with parametric uncertainty. In that work, Horowitz developed a technique for translating a nonlinear and/or time-varying problem to an equivalent linear problem that, at least in some cases, can be solved using his earlier linear robust design techniques. All of these early ideas were then expanded and integrated by Horowitz and coworkers, leading to a set of control design methods including scalar/multivariable, linear/nonlinear, time-invariant/time-varying, single-loop/multiple-loops systems, now referred to as quantitative feedback theory [7].Here our main interest is in the scalar nonlinear and/or time-varying (NLTV) design problem of QFT. The "rst results of Horowitz [3,4] for this case were based on the translation of the uncertain NLTV dynamics of the plant into an &equivalent family' of ("nite-dimensional) linear time-invariant (LTI) plants. The success of the method relied upon the fact that under some circumstances a feasible controller for the equivalent linear family (ELF), computed according to linear QFT, is also a feasible controller for the original uncertain NLTV system, thus the nonlinear design is &validated'. However, in its initial formulation the proof of this validation procedure was extremely complicated and very dependent on the QFT framework. The basic idea was that in the control system design process a NLTV plant could be treated as a LTI plant, at the price of introducing uncerta...

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Stability of non-linear QFT designs based on robust absolute stability criteria

Cited by 23 publications

References 14 publications

Nonlinear quantitative feedback theory

Nonlinear quantitative feedback theory

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

Some results in nonlinear QFT

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