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Journal of Dynamic Systems, Measurement, and Control | Volume 135 | Issue 5 | Technical Brief
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
Article
References
Figures
Citing Articles

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

1
Ching, S., Eun, Y., Gokcek, C., Kabamba, P. T., and Meerkov, S. M., 2011, Quasilinear Control, Cambridge University Press, Cambridge, UK.
2
Goodwin, G. C., Graebe, S. F., and Salgado, M. E., 2000, Control System Design, Prentice-Hall, Englewood Cliffs, NJ.
3
Doyle, J., Smith, R. S., and Enns, D. F., 1987, “Control of Plants With Input Saturation Nonlinearities,” American Control Conference, pp. 1034–1039.
4
Kothare, M. V., Campo, P. J., Morari, M., and Nett, C. N., 1994. “A Unified Framework for the Study of Anti-Windup Designs,” Automatica, 30(12), pp. 1869–1883. [CrossRef]
5
Zheng, A., Kothare, M. V., and Morari, M., 1994, “Anti-Windup Design for Internal Model Control,” Int. J. Control, 60, pp. 1015–1024. [CrossRef]
6
Kapoor, N., Teel, A., and Daoutidis, P., 1998, “An Anti-Windup Design for Linear Systems With Input Saturation,” Automatica, 34(5), pp. 559–574. [CrossRef]
7
Zhou, B., Duan, G.-R., and Lin, Z., 2010, “A Parametric Periodic Lyapunov Equation With Application in Semi-Global Stabilization of Discrete-Time Periodic Systems Subject to Actuator Saturation,” American Control Conference (ACC), pp. 4265–4270.
8
Zaccarian, L., and Teel, A., 2011, Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation, Princeton, NJ.
9
Gilbert, E. G., and Kolmanovsky, I., 1995, “Discrete-Time Reference Governors and the Nonlinear Control of Systems With State and Control Constraints,” Int. J. Robust Nonlinear Control, 5, pp. 487–504. [CrossRef]
10
Bemporad, A., 1998, “Reference Governor for Constrained Nonlinear Systems,” IEEE Trans. Autom. Control, 43(3), pp. 415–419. [CrossRef]
11
Bemporad, A., and Morari, M., 1999, “Control of Systems Integrating Logic, Dynamics, and Constraints,” Automatica, 35, pp. 407–427. [CrossRef]
12
Gilbert, E. G., and Kolmanovsky, I., 1999. “Fast Reference Governors for Systems With State and Control Constraints and Disturbance Inputs,” Int. J. Robust Nonlinear Control, 9, pp. 1117–1141. [CrossRef]
13
Camacho, E. F., and Alba, C. B., 2000, Model Predictive Control, Prentice-Hall, Englewood Cliffs, NJ.
14
Doni, J. A. D., Goodwin, G. C., and Seron, M. M., 2000, “Anti-Windup and Model Predictive Control: Reflections and Connections,” Eur. J. Control, 6(5), pp. 467–477. [CrossRef]
15
Maciejowski, J., 2002, Predictive Control With Constraint, Prentice-Hall, Englewood Cliffs, NJ.
16
Rossiter, J., 2003, Model-Based Predictive Control: A Practical Approach, CRC Press, Boca Raton, FL.
17
Roberts, J. B., and Spanos, P. D., 2003, Random Vibration and Statistical Linearization, Dover, New York.
18
Astrom, K., and Hagglund, T., 1995, PID Controllers: Theory, Design and Tuning, ISA Press, Research Triangle Park, NC.
19
Zhang, H., Shi, Y., and Mehr, A., 2011, “Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems,” IEEE Trans. Ind. Electron., 58(12), pp. 5396–5405. [CrossRef]
20
Zhang, H., Shi, Y., and Mehr, A. S., 2012. “Robust h∞ PID Control for Multivariable Networked Control Systems With Disturbance/Noise Attenuation,” Int. J. Robust Nonlinear Control, 22(2), pp. 183–204. [CrossRef]

Figures

Grahic Jump Location
Fig.1

Motivating example

+Motivating example
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Motivating example
Grahic Jump Location
Fig. 2

Step tracking in the motivating example

+Step tracking in the motivating example
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Step tracking in the motivating example
Grahic Jump Location
Fig. 3

Reference tracking systems

+Reference tracking systems
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Reference tracking systems
Grahic Jump Location
Fig. 4

Stochastically linearized system

+Stochastically linearized system
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Stochastically linearized system
Grahic Jump Location
Fig. 5

s-root loci of the motivating example

+s-root loci of the motivating example
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s-root loci of the motivating example
Grahic Jump Location
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

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

+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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Trajectories of the systems of Fig. 3(a) and 3(b) for the motivating example of Sec. 1 with α = 10 and K = 1
Grahic Jump Location
Fig. 8

s-root locus for the example of subsection 5.1

+s-root locus for the example of subsection 5.1
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s-root locus for the example of subsection 5.1
Grahic Jump Location
Fig. 9

Trajectories of the system in subsection 5.1

+Trajectories of the system in subsection 5.1
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Trajectories of the system in subsection 5.1
Grahic Jump Location
Fig. 10

s-root locus of the example of subsection 5.2

+s-root locus of the example of subsection 5.2
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s-root locus of the example of subsection 5.2
Grahic Jump Location
Fig. 11

Trajectories of the system in subsection 5.2

+Trajectories of the system in subsection 5.2
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Trajectories of the system in subsection 5.2
Grahic Jump Location
Fig. 12

Output of saturation for the example of subsection 5.2

+Output of saturation for the example of subsection 5.2
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Output of saturation for the example of subsection 5.2
Grahic Jump Location
Fig. 13

Trajectories of the system of Sec. 6.1

+Trajectories of the system of Sec. 6.1
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Trajectories of the system of Sec. 6.1
Grahic Jump Location
Fig. 14

Output of saturation in the example of Sec. 6.1

+Output of saturation in the example of Sec. 6.1
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Output of saturation in the example of Sec. 6.1
Grahic Jump Location
Fig. 15

Trajectories of the tracking systems in Sec. 6.2

+Trajectories of the tracking systems in Sec. 6.2
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Trajectories of the tracking systems in Sec. 6.2
Grahic Jump Location
Fig. 16

Trajectories of the tracking systems in Sec. 6.3

+Trajectories of the tracking systems in Sec. 6.3
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Trajectories of the tracking systems in Sec. 6.3
Grahic Jump Location
Fig. 17

The anti-windup mechanism.

+The anti-windup mechanism.
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The anti-windup mechanism.
Grahic Jump Location
Fig. 18

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

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

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