Transactions on Control, Automation and Systems Engineering

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

A Study on Singularly Perturbed Open-Loop Systems by Delta Operator Approach

  • Shim, Kyu-Hong (Sejong-Lockheed Martin Aerospace Research Center Sejong University) ;
  • M. Edwin Sawan (Dept. of Electrical and Computer Engineering, Wichita State University, Kansas)
  • Published : 2001.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the open-loop state response of the two-time-scale systems by unified approach using the $\delta$-operator is presented with an example of the aircraft longitudinal dynamics. First, the $\delta$-operator system unifies both the continuous system and the discrete system simultaneously, and the $\delta$-operator approach improves the finite word-length characteristics. This saves more computing time than that of the discrete system. Second, the singular perturbation method by block diagonalization reduces the sizes and orders of the systems. This also reduces the floating-point operations (flops). The advantage of those two approaches is shown by comparing our results with the earlier ones in the illustrative example of the longitudinal motion of F-8 aircraft.

Keywords

References

  1. Proceedings of the 32nd Conference on Decision and Control Stabilizing receding horizon control: a unified continuous/discrete time formulation Bouslimani, M.;M'Saad M.;Dugard, L.
  2. Journal of mathematical analysis and application v.48 Diagonalization method for a vector boundary problem of singular perturbation type Chang, K. W.
  3. IFAC Symposium on Large Scale Systems Eigenvalue placement in two-time-scale systems Chow, J.;Kokotovic, P. V.
  4. IEEE Trans. on Automatic Control v.20 A Riccati equation for Block diagonalization of ill-conditioned systems Kokotovic, Peter V.
  5. Singular perturbation methods in control analysis and design Kokotovic, P. V.;Khalil, H.;O'Reilly, J.
  6. IEEE Trans. on Automatic Control v.38 Comparative study of finite wordlength effects in shift and delta operator parametrizations Li, G.;Gevers, M.
  7. IEEE Trans. on Signal Processing v.41 Roundoff noise minimization using delta-operator realizations Li, G.;Gevers, M.
  8. IEE PROC. v.129 no.4 Order reduction and control of discrete systems Mahmoud, M. S.
  9. Appl. Math. Modelling v.7 Design of feedback controllers by two-time-stage methods Mahmoud, M.S.;Chen,Y.
  10. Automatica v.21 no.4 On the use of reduced-order models in output feedback design of discrete systems Mahmoud, M. S.;Singh, M. G.
  11. International Journal of Systems Science v.17 Discrete two-time-scale systems Mahmoud, M. S.;Chen, Y.;Singh, M. G.
  12. IEEE Trans. on Automatic Control v.31 no.11 Improved finite word length characteristics in digital control using delta operators Middleton, R. H.;Goodwin, G. C.
  13. Digital control and estimation: A unified approach Middleton, R. H.;Goodwin, G. C.
  14. Optimal Control Application & Methods v.5 Singular perturbation analysis of the closed-loop discrete optimal control system Naidu,D.S.;Rao, A.K.
  15. Journal of Guidance v.10 no.5 Time-scale synthesis of a closed-loop discrete optimal control system Naidu, D. S.;Price, D. B.
  16. Singular perturbation methodology in control systems Naidu, D. S.
  17. NASA Technical Paper 2844 Singular perturbations and time scales in the design of digital flight control systems Naidu,D.S.;Price D.B.
  18. Proceedings of the American Control Conference Unified Approach to H-2 and H-inf optimal control of a hypersonic vehicle Naidu, D. S.;Banda, S. S.;Buffington, J. L.
  19. International Journals of Systems Science v.32 no.9 Linear quadratic regulator design for singularly perturbed systems by unified approach using delta operators Shim, K. H.;Sawan, M. E.