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Technical Briefs

Quasi-Linear Control Approach to Designing Step Tracking Controllers for Systems With Saturating Actuators

[+] Author and Article Information
Pierre T. Kabamba

Professor
Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: kabamba@umich.edu

Semyon M. Meerkov

Professor
Department of Electrical Engineering and Computer Science,
University of Michigan,
Ann Arbor, MI 48109
e-mail: smm@umich.edu

Hamid R. Ossareh

Department of Electrical Engineering and Computer Science,
University of Michigan,
Ann Arbor, MI 48109
e-mail: hamido@umich.edu

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement and Control. Manuscript received March 31, 2012; final manuscript received March 22, 2013; published online July 18, 2013. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 135(5), 054504 (Jul 18, 2013) (8 pages) Paper No: DS-12-1098; doi: 10.1115/1.4024562 History: Received March 31, 2012; Revised March 22, 2013

This paper provides a novel method for designing step tracking controllers for systems with saturating actuators. The approach is based on the theory of Quasi-linear Control (QLC), which offers methods for designing random reference tracking controllers for systems with nonlinear actuators and sensors. In the current paper, a QLC approach to designing step tracking controllers is presented. The development is based on two ideas: introducing a precompensator, which observes given step tracking specifications, and recasting the output of the precompensator into a random reference bandwidth requirement, with subsequent utilization of QLC. Unlike other techniques, the method developed here takes the saturation into account directly at the initial stage of the design and does not require subsequent augmentations (e.g., anti-windup). Nevertheless, for the sake of completeness, a comparison with the anti-windup approach is provided.

Copyright © 2013 by ASME
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References

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Figures

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Fig. 2

Step tracking in the motivating example

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Fig. 3

Reference tracking systems

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Fig. 4

Stochastically linearized system

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Fig. 5

s-root loci of the motivating example

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Fig. 6

Trajectories of the systems of Fig. 3(a) and 3(b) for the motivating example of Sec. 1 with α = 25 and K = 1

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Fig. 7

Trajectories of the systems of Fig. 3(a) and 3(b) for the motivating example of Sec. 1 with α = 10 and K = 1

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Fig. 8

s-root locus for the example of subsection 5.1

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Fig. 9

Trajectories of the system in subsection 5.1

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Fig. 10

s-root locus of the example of subsection 5.2

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Fig. 11

Trajectories of the system in subsection 5.2

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Fig. 12

Output of saturation for the example of subsection 5.2

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Fig. 13

Trajectories of the system of Sec. 6.1

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Fig. 14

Output of saturation in the example of Sec. 6.1

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Fig. 15

Trajectories of the tracking systems in Sec. 6.2

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Fig. 16

Trajectories of the tracking systems in Sec. 6.3

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Fig. 17

The anti-windup mechanism.

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Fig. 18

Tracking performance for the system with saturating actuator and anti-windup

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