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Research Papers

A QFT Framework for Antiwindup Control Systems Design

[+] Author and Article Information
J. C. Moreno

Departamento Lenguajes y Computación, University of Almeria, Carretera de la Playa, s/n La Cañada de San Urbano, Almeria 04120, Spainjcmoreno@ual.es

A. Baños

Departamento Informática y Sistemas, University of Murcia, Campus de Espinardo, Murcia 30100, Spainabanos@um.es

M. Berenguel

Departamento Lenguajes y Computación, University of Almeria, Carretera de la Playa, s/n La Cañada de San Urbano, Almeria 04120, Spainberen@ual.es

J. Dyn. Sys., Meas., Control 132(2), 021012 (Feb 09, 2010) (15 pages) doi:10.1115/1.4000812 History: Received May 23, 2008; Revised November 12, 2009; Published February 09, 2010; Online February 09, 2010

The paper is devoted to the robust stability problem of linear time invariant feedback control systems with actuator saturation, especially in those cases with potentially large parametric uncertainty. The main motivation of the work has been twofold: First, most of the existing robust antiwindup techniques use a conservative plant uncertainty description, and second, previous quantitative feedback theory (QFT) results for control systems with actuator saturation are not suitable to achieve robust stability specifications when the control system is saturated. Traditionally, in the literature, this type of problems has been solved in terms of linear matrix inequalities (LMIs), using less structured uncertainty descriptions as given by the QFT templates. The problem is formulated for single input single output systems in an input-output (I/O) stability sense, and is approached by using a generic three degrees of freedom control structure. In this work, a QFT-based design method is proposed in order to solve the robust stability problem of antiwindup design methods. The main limitation is that the plant has poles in the closed left half plane, and at most, has one integrator. The work investigates robust adaptations of the Zames–Falb stability multipliers result, and it may be generalized to any compensation scheme that admits a decomposition as a feedback interconnection of linear and nonlinear blocks (Lur’e type system), being antiwindup systems as a particular case. In addition, an example will be shown, making explicit the advantages of the proposed method in relation to previous approaches.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

3DoF System with actuator saturation compensation

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Figure 2

Equivalent system as a feedback interconnection between a linear block K and a nonlinear block N

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Figure 3

The boundary B(pl(ω),pr(ω)) given by stability multipliers

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Figure 4

A loop transformation

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Figure 5

An equivalent system

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Figure 6

An equivalent system with an adequate nonlinear block

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Figure 7

An infinite nl-template

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Figure 8

Anti-reset windup structure

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Figure 9

Feedback structure for the Hanus conditioning technique

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Figure 10

CAW feedback structure

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Figure 11

The Horowitz 3DoF control structure

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Figure 12

Root locus of 1+kP0⋅G, k∊(0,∞)

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Figure 13

Nominal system output for a step reference

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Figure 14

Control signal (saturated) for a step reference

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Figure 15

Nichols plots of 1/XD, for (a,b)=(0.5,0.1) and (a,b)=(0.7,0.04) (solid for D(s)=1 and dotted for D(s)=s(s+0.05)/(s2+100.2s+20)

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Figure 16

℘nl(ω) and X0, for ω in W

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Figure 17

Bode plot of (1−Z(s))−1

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Figure 18

Nichols plot of 1/XD with (a,b)=(0.5,0.1) and (a,b)=(0.7,0.04), for D(s)=s(s+0.05)/(s2+100.2s+20)

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Figure 19

Boundaries B(ω) given by stability multiplier based on Eq. 55, and Nichols plot of 1/XD0(jω), for D(s)=(s2+100.2s+20)/s(s+0.05)

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Figure 20

Step response for some values of parameters (a,b), for H(s)=(100.25s+20)/s(s+0.05)

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Figure 21

Control signal for different parameters combinations, for H(s)=(100.25s+20)/s(s+0.05)

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Figure 22

Nichols plot of 1/XD, for (a,b)=(0.5,0.1) and (a,b)=(0.7,0.04) (solid for Tr→+∞, dashed for Tr=10, and dotted for Tr=0.1)

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Figure 23

Boundaries B(ω) corresponding to (1−Z(s))−1=(s/0.01+1)/(s/0.5+1), and Nichols plot of 1/XD0(jω), for D(s)=(s+10)/s

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Figure 24

System output for some values of parameters (a,b)

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Figure 25

Control signal for some values of parameters (a,b)

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