Advertisement

H ∞ Controller

  • Wodek Gawronski
Part of the Mechanical Engineering Series book series (MES)

This chapter presents the tuning process of the H controller. It describes the H controller modified for tracking purposes, gives the closed loop equations, and presents the 34-m antenna example, with the limits of the performance.

Definition and Gains

Application of the H controllers to antennas and telescopes is discussed in [ 1, 2, 3, 4, 5, 6, 7, 8]. The structure of an H controller is similar to that of the LQG controller, although its parameters are obtained from a different algorithm. The algorithm minimizes the system H norm, which is, in the case of a SISO system, the maximal magnitude of its transfer function. Also, in the algorithm the control ( u) and the disturbance ( w) inputs of a system are separated (see Fig. 9.1). The control ( y) and performance ( z) outputs are also parted. In our case the plant-controlled input ( u) is the velocity input to the drives, the disturbance input ( w) is the wind pressure at the antenna structure, the controlled output ( y) is the encoder...

Keywords

Wind Gust Algebraic Riccati Equation Wind Disturbance Close Loop Transfer Function Acceleration Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Erm T, Bauvir B, Hurak Z. (2004). Time to Go H-infinity? Proc. SPIE, Advanced Software, Control, and Communication Systems for Astronomy, Glasgow, UK, vol. 5496.Google Scholar
  2. 2.
    Gawronski W. (1996). H Controller for the DSS13 Antenna with Wind Disturbance Rejection Properties. TDA Progress Report, vol. 42–127, 1996. Available at http://ipnpr.jpl.nasa.gov/progress_report/42-127/127G.pdf
  3. 3.
    Gawronski W. (2001). Antenna Control Systems: From PI to H . IEEE Antennas and Propagation Magazine, 43(1).Google Scholar
  4. 4.
    Gawronski W. (2004). Advanced Structural Dynamics and Active Control of Structures, Springer, New York.CrossRefGoogle Scholar
  5. 5.
    Li K, Kosmatopoulos EB, Ioannou PA et al. (2000). Large Segmented Telescopes: Centralized, Decentralized and Overlapping Control Designs. IEEE Control Systems Magazine, 20(5): 59–72.CrossRefGoogle Scholar
  6. 6.
    Li K, Kosmatopoulos EB, Ioannou PA et al. (1998). Control Techniques for a Large Segmented Reflector. Proc. 37th IEEE Conf. on Decision and Control, Tampa, FL.Google Scholar
  7. 7.
    Schoenhoff U, Klein A, Nordmann R. (2000). Attitude Control of the Airborne Telescope SOFIA: μ-Synthesis for a Large-Scaled Flexible Structure. Proc. 39 th IEEE Conf. Decision and Control, Sydney, Australia.Google Scholar
  8. 8.
    Whorton M, Angeli G. (2003). Modern Control for the Secondary Mirror of a Giant Segmented Mirror Telescope. Proc. SPIE, Future Giant Telescopes, vol. 4840.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Wodek Gawronski
    • 1
  1. 1.Jet Populsion LaboratoryCalifornia Institute of TechnologyPasedenaUSA

Personalised recommendations