Linear conditioning for systems containing saturating actuators

Weston, Paul; Postlethwaite, Ian

doi:10.1016/s0005-1098(00)00044-3

Cited by 179 publications

(163 citation statements)

References 8 publications

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“…From (60) -(62), it can be shown that λ Tṡ = 0 anḋ λ Tṡ = 0 also hold (see [20,24] for details). Then premultiplying (59) and its derivative by λ T respectively leads to (7) and (8); premultiplying the derivative of (59) byλ T leads to (9).…”

Section: Appendix -Proofs Of Resultsmentioning

confidence: 99%

“…λ T Lu + λ T Mẏ = 0 whereu exists (8) λ T Lu +λ T Mẏ = 0 whereu andλ exist (9) where λ ∈ R l is the Lagrangian multiplier corresponding to the inequality constraints in the KKT conditions.…”

Section: Stability Establishmentmentioning

confidence: 99%

“…[1][2][3][4][5] for general analysis; [6][7][8] for saturation analysis and [9][10][11] for anti-windup design). Primbs [12] and Primbs and Giannelli [13] observed that an important subclass of such nonlinearities can be represented as the solution of a convex QP -see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program

Heath²,

Lennox³

2008

IET Control Theory &Amp; Applications

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We consider the stability of the feedback connection of a strictly proper linear time invariant (LTI) stable system with a static nonlinearity expressed by a convex quadratic program (QP). From the Karush-Kuhn-Tucker (KKT) conditions for the QP, we establish quadratic constraints that may be used with a quadratic Lyapunov function to construct a stability criterion via the S-procedure. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion and is much easier to implement. Our approach can be extended to model predictive control (MPC), and gives equivalent results to those in the literature but with a much lower dimension LMI criterion.

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Section: Appendix -Proofs Of Resultsmentioning

confidence: 99%

Section: Stability Establishmentmentioning

confidence: 99%

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Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program

Heath²,

Lennox³

2008

IET Control Theory &Amp; Applications

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“…The advantage to the traditional anti-windup approach is the well-defined, two-part structure: the main (baseline) controller is solely responsible for stabilisation and performance when saturation does not occur; in the event of saturation an additional element (the anti-windup compensator) then becomes active to deliver improved performance and enhanced stability properties. The anti-windup compensator remains inactive unless saturation occurs and, once saturation is over, allows a "graceful recovery" of the un-saturated behaviour [18,26,30]. The design of the anti-windup compensator is completely separate from that of the baseline controller.…”

Section: Introductionmentioning

confidence: 99%

Positiveμmodification as an anti-windup mechanism

Turner

2017

Systems & Control Letters

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This paper proposes a simple anti-windup mechanism for a model reference adaptive control scheme subject to saturation constraints. The anti-windup compensator has, in essence, the same structure as positive µ modification for the same class of systems. It is shown how this structure can, under certain circumstances, display characteristics similar to anti-windup schemes proposed for linear control systems. In particular, it is shown that if the (unknown) ideal control signal eventually lies within the control constraints, then the response of the adaptive control system will converge to that of the reference system -provided certain conditions are satisfied. The paper illustrates the challenge of designing anti-windup compensators for model-reference adaptive control systems.

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“…The compensator design generally boils down to a construction of a state feedback controller, which drives the plant's copy so that the real system tends towards the intended behavior. If there is no uncertainty in the system the MRAW compensator is totally independent of the actual controller, so it can work with any control method [4], [11]. Though all advantages of MRAW algorithms can be enjoyed only if the plant is precisely known, there are results for uncertain systems as well [10], [9].…”

Section: Introductionmentioning

confidence: 99%

Model recovery anti-windup control for linear discrete time systems with magnitude and rate saturation

Péni

Kulcsár

Bokor

2012

2012 American Control Conference (ACC)

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Abstract-The paper proposes a model recovery anti-windup (MRAW) scheme for linear time-invariant and discrete-time systems under magnitude and rate saturation. The method is a modified, discrete-time counterpart of the algorithm presented in [4]. As it is usual in the MRAW framework the AW compensator contains the exact copy of the plant in order that the ideal (unsaturated) behavior can be preserved in the states. The compensator is a controller that aims to push the plant towards this intended behavior. The design of this control action can be reduced to a construction of a stabilizing state feedback acting on the saturated plant. In [4] this feedback is a linear one, which is designed by convex optimization by enlarging the ellipsoidal approximation of the invariant domain. This paper presents a different, set-theoretic approach, which is based on the precise construction of the maximal control invariant set. The proposed control is a nonlinear one generated by point wise convex optimization.

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Linear conditioning for systems containing saturating actuators

Cited by 179 publications

References 8 publications

Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program

Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program

Positiveμmodification as an anti-windup mechanism

Model recovery anti-windup control for linear discrete time systems with magnitude and rate saturation

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