A steady state approach to the theory of saturable servo systems

Lozier, J. C.

doi:10.1109/tac.1956.1100815

Cited by 53 publications

(20 citation statements)

References 1 publication

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“…Since (22) coincides with (10) with the selection for (16)- (18), then provided the matrix satisfies expression (38), the proof of the sufficiency of item 1) can be followed verbatim to show that (22) is solvable with (16)- (18). To show that the construction (16)- (18) for satisfies (38), note that by the formulae for the inversion of block matrices [31, p. 23], the upper left block of needs to satisfy which, when premultiplied and postmultiplied by and substituting the selection (17) for , becomes which, by (16), is always satisfied.…”

Section: Conditions (11e) and (11f)mentioning

confidence: 96%

“…Assume that, according to (18), the matrix is partitioned as where Then, inequality (31a) can be computed explicitly based on (35) and (21a) Using the partition of the matrix we can compute explicitly the inequality (31b) based on the definitions (36) and (37) and substituting (19a) and (19c) into the entries of . After some computations it follows that coincides with the inequality in (11b), as desired.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Among early control algorithms, those that were most seriously affected by input saturation were those that contained integral action, e.g., PI or PID controllers. It was observed that, due to input saturation, the state of the integrator would "wind up" to excessively large values, leading to sluggish performance of the closed-loop control system [18]. It is for this reason that the phrase "antiwindup augmentation" is used to describe the problem of synthesizing controllers, subject to a local specification (called the unconstrained controller), for linear systems with input saturation.…”

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confidence: 99%

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Antiwindup for stable linear systems with input saturation: An LMI-based synthesis

Grimm

Hatfield

Postlethwaite

et al. 2003

IEEE Trans. Automat. Contr.

488

347

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Abstract-This paper considers closed-loop quadratic stability and 2 performance properties of linear control systems subject to input saturation. More specifically, these properties are examined within the context of the popular linear antiwindup augmentation paradigm. Linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification, called the "unconstrained closed-loop behavior." Building on known results on and LPV synthesis, the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem, which has an attractive system theoretic interpretation: the lower bound on the achievable 2 performance is the maximum of the open and unconstrained closed-loop 2 gains. In the special cases of zero-order (static) and plant-order antiwindup compensation, the feasibility conditions become (convex) linear matrix inequalities. It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwindup compensation is always feasible for large enough 2 gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists. Using the solutions to the matrix feasibility problems, the synthesis of the antiwindup augmentation achieving the desired level of 2 performance is then accomplished by solving an additional LMI.Index Terms-Antiwindup analysis, antiwindup synthesis, control systems, cost optimal control, finite 2 gain, linear matrix inequalities (LMIs), linear parameter varying (LPV).

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Section: Conditions (11e) and (11f)mentioning

confidence: 96%

Section: Proof Of Theoremmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Antiwindup for stable linear systems with input saturation: An LMI-based synthesis

Grimm

Hatfield

Postlethwaite

et al. 2003

IEEE Trans. Automat. Contr.

488

347

View full text Add to dashboard Cite

show abstract

“…In particular the socalled anti-windup approach arose in those early years as a possible response to the need of not sacrificing the small signal behavior to obtain a satisfactory large signal behavior [15]. An important peculiarity of the saturation phenomenon is that for small enough signals its effects are invisible, so if that is the only nonlinearity in an otherwise linear control scheme, small signal responses are fully linear and controllers can be conveniently designed using linear tools to guarantee desirable and well characterized performance properties of the closed-loop.…”

Section: Introductionmentioning

confidence: 99%

An almost Anti-Windup scheme for plants with magnitude, rate and curvature saturation

Forni

Galeani

Zaccarian

2010

Proceedings of the 2010 American Control Conference

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Abstract-We address the anti-windup augmentation problem for plants with saturations on the magnitude, rate and curvature of the control input. To this aim, given an unconstrained closed-loop, we generate a slightly modified strictly proper controller for which the derivatives of the control signal are available and we solve the anti-windup problem for this modified control scheme (namely, an almost anti-windup for the original closed-loop). Based on this "almost" approach, we revisit an existing Model Recovery anti-windup solution for rate and magnitude saturated plants and then we extend the results to the case of rate, magnitude and curvature saturation, by providing a Model Recovery solution to this additional problem. Several examples are used to illustrate the peculiarities and the effectiveness of the proposed solutions.

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“…The presence of saturation nonlinearities in otherwise linear closed loop systems can cause dramatic performance losses known as "windup" effects; in order to avoid such losses, several anti-windup compensation techniques have been developed, starting with the pioneering, heuristic solutions proposed in the 1950's (e.g. [20]; see also the surveys [19], [1]) until general results with formal proofs of stability started appearing during the last decade (see e.g. [28], [21], [10], [11] and references therein).…”

mentioning

confidence: 99%

Model based, gain-scheduled anti-windup control for LPV systems

Forni¹,

Galeani²

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-In this paper we show that a recently proposed technique for anti-windup control of exponentially unstable plants can be easily extended to solve the corresponding robust anti-windup problem for linear parameter varying systems, for which the time varying parameters are measured online. For this class of plants, it is shown that the proposed technique is minimally conservative with respect to the size of the resulting operating region: in particular, such a region is (up to an arbitrarily small quantity) exactly the largest set on which asymptotic stability can be guaranteed for the considered plant, for the given saturation level and uncertainty characteristics.

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A steady state approach to the theory of saturable servo systems

Cited by 53 publications

References 1 publication

Antiwindup for stable linear systems with input saturation: An LMI-based synthesis

Antiwindup for stable linear systems with input saturation: An LMI-based synthesis

An almost Anti-Windup scheme for plants with magnitude, rate and curvature saturation

Model based, gain-scheduled anti-windup control for LPV systems

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