Self-tuning deadbeat controllers

Matko, Drago; Schumann, R.

doi:10.1080/00207178408933282

Cited by 24 publications

(5 citation statements)

References 3 publications

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“…Such a noise model is often encountered, a particular field in which it is commonly taken as 'the' way of modelling noise being in Predictive Control (Clarke, 1994). Another class of controllers exists, widely termed Deadbeat controllers (Matko and Schumann, 1984;Warwick, 1986), which concentrate on the servo properties of the closed-loop system. A look is taken here at the directly straightforward implementation of such controllers.…”

Section: F'1~ Controllersmentioning

confidence: 99%

Relationship between deadbeat and pole-placement discrete-time PID controllers

Warwick

Yong

1996

Transactions of the Institute of Measurement and Control

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This paper considers PID control in terms of its implementation by means of an ARMA plant model. Two controller actions are considered, namely pole placement and deadbeat, both being applied via a PID structure for the adaptive real-time control of an industrial level system. As well as looking at two controller types separately, a comparison is made between the forms and it is shown how, under certain circumstances, the two forms can be seen to be identical. It is shown how the pole-placement PID form does not in fact realise an action which is equivalent to the deadbeat controller, when all closed-loop poles are chosen to be at the origin of the z-plane.

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Section: F'1~ Controllersmentioning

confidence: 99%

Relationship between deadbeat and pole-placement discrete-time PID controllers

Warwick

Yong

1996

Transactions of the Institute of Measurement and Control

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“…One Downloaded by [UZH Hauptbibliothek / Zentralbibliothek Zürich] at 04:42 22 December 2014 (27) possibility is to include an estimate of d, called J, in the parameter estimate vector; the implementation of such a scheme is considered later in this section. A deterministic self-tuning controller, e(t) = 0, employing a controller of the type (9) was described in Matko and Schumann (1984), the stability of this controller being dependent on (a) B(I) #°and (b) all the roots of A lying within the unit circle, i.e., an open-loop stable system. Both of these properties must be apparent in all of the algorithms described in this paper, each algorithm contains A as a common factor of the closed-loop disturbance equation and each algorithm employs a division by the summed coefficients of the estimated B polynomial.…”

Section: Self-tuning Implementationmentioning

confidence: 99%

“…For systems where both reference inputs and disturbances occur, a trade-off can be made in the form of a detuned controller such that as well as limiting the effects of any disturbances an attempt is made to obtain a desired step response performance, As the disturbances become less important, so more emphasis can be placed on servo-following capabilities, For adaptive digital controller types the differences can be found on the one hand in terms of purely optimal regulatory control action (Astrom and Wittenmark 1973), and on the other, purely deterministic servo control (Matko andSchumann 1984, Isermann 1981). Other controllers, such as pole placement (Wellstead et al 1979) or pole-zero placement (Astrom and Wittenmark 1980), lie between these extremes.…”

Section: Introductionmentioning

confidence: 98%

Adaptive deadbeat control of stochastic systems

Warwick

1986

International Journal of Control

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This paper considers the use of a discrete-time deadbeat control action on systems affected by noise, Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a selftuning control framework is shown to satisfy, under certain conditions, the selftuning property, generally though only when an extended form of least-squares estimation is incorporated.

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“…Die Betrachtungen zum Mehrgrößenfall ergeben, daß die Konvergenzaussagen auf den parameteradaptiven entkoppelnden Mehrgrö-ßenkompensationsregler bei Ansatz einer /»-kanonischen Modellstruktur direkt übertragen werden können. In [7] wird darüberhinaus gezeigt, daß für einen Mehrgrößen-Deadbeatregler analoge Konvergenzaussagen auch für ein allgemeines Matrizenpolynommodell zu erreichen sind. …”

Section: A M (Q-')b(q ') U(k) = B M (Q-1 [A(q' 1 ) W(k) +unclassified

Konvergenzeigenschaften digitaler parameteradaptiver Kompensationsregeler / Convergence properties of digital parameter-adaptive compensation controllers

Schumann¹

1990

at - Automatisierungstechnik

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Stabilität und Konvergenz digitaler parameteradaptiver Kompensationsregler werden zunächst ausführlich für den Eingrößenfall untersucht. Auf der Grundlage der Konvergenzeigenschaften des eingesetzten Parameterschätzver-fahrens, der rekursiven Methode der kleinsten Quadrate, werden für den verwendeten Kompensationsregelalgorithmus spezifische Bedingungen angegeben, unter denen der parameteradaptive Regelkreis zu einem stabilen Gesamtsystem mit verschwindender Regelabweichung konvergiert. Die Konvergenzuntersuchungen werden dann ausgedehnt auf den Spezialfall des parameteradaptiven Deadbeatreglers sowie den entkoppelnden Kompensationsregler im Mehrgrößenfall. Convergence and stability properties of the parameteradaptive compensation controller are analyzed in detail for the singlevariable case. Based on the convergence properties of the recursive least squares method which is used for parameter estimation, specific conditions are derivedfor the compensation control algorithm, under which the resulting parameter-adaptive control loop converges to a stable system without steady-state control error. The convergence results are extended for the special case of the parameteradaptive deadbeat controller and for the decoupling controller in the multivariable case. 1. Einführung Parameteradaptive Regler entstehen aus der Kombination eines Parameterschätzverfahrens für die laufende Prozeßidentifikation mit einem Synthesealgorithmus für Bild 1. Parameteradaptiver Regler. die Bestimmung der Reglerparameter (siehe Bild 1). Das Konvergenzverhalten parameteradaptiver Regler ist in verschiedenen Publikationen schon praktisch und theoretisch untersucht worden (siehe ζ. B. Kurz [1], Lachmann und Goedecke [2] und Schumann [3]). Die theoretische Untersuchung in [3] zeigte dabei unter allgemeinen Voraussetzungen für den deterministischen wie auch den stochastischen Fall, daß der parameteradaptive Regelkreis für k -* oo zu einem asymptotisch stabilen Gesamtsystem konvergiert, sofern das eingesetzte Parameterschätzver-fahren bestimmte Konvergenzeigenschaften aufweist und der verwendete Regelalgorithmus das geschätzte Prozeß-modell prinzipiell stabilisieren kann. In diesem Beitrag soll nun die Konvergenzuntersuchung für parameteradaptive Kompensationsregler durchgeführt werden, da in diesem Fall die in [3] allgemein formulierten Voraussetzungen anschaulich dargestellt und über den allgemeinen Fall hinausreichende Aussagen gemacht werden kön-nen. ProzeßmodellDas dynamische Verhalten des Prozesses soll sich durch die folgende lineare Differenzengleichung beschreiben lassen(1)Hierbei stellen und U{k) die (absoluten) Ausgangsund Eingangssignalwerte des Prozesses zu den diskreten Zeitpunkten k dar, a t und b { sind die Prozeßmodellpara-meter, wobei b x φ 0 und eine nicht verschwindende Verstärkung vorausgesetzt wird, m ist die Ordnung und d die diskrete Totzeit des Prozesses, die die Totzeit T d als Vielfaches der Abtastzeit T 0 mit T d = dT 0 beschreibt. Die Gleichwertkonstante C bestimmt den Zusammenhang zwischen den Beharrungswerten U 0 un...

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Self-tuning deadbeat controllers

Abstract: A deterministic self-tuning deadbeat control scheme is presented which is extremely simple to implement in the aingle-var-iuhlc and multivariable cases. Its convergence properties are analysed by straightforward application of de Lerminec'a convergence results.

Cited by 24 publications

References 3 publications

Relationship between deadbeat and pole-placement discrete-time PID controllers

Relationship between deadbeat and pole-placement discrete-time PID controllers

Adaptive deadbeat control of stochastic systems

Konvergenzeigenschaften digitaler parameteradaptiver Kompensationsregeler / Convergence properties of digital parameter-adaptive compensation controllers

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